Gérald Dujardin and Elizabeth Boer-Duchemin have contributed much in helping me shape this dissertation. I am much obliged to them for their continuous support and for the great working environment that they have offered me during the last ten years. The major part of the work presented in this dissertation has been carried out in close partnership with them.

I would like to acknowledge all my collaborators for their trust and enthousiam. In particular, I am grateful for the great inspiration that Andrei Borisov, Sylvie Marguet, Stéphane Berciaud and Guillaume Schull have given me.

Many thanks to all the colleagues who have participated in my projects and shared their expertise with me (Andrew Mayne, Hamid Oughaddou, Georges Raseev, Damien Riedel, Aimeric Ouvrard, Hocine Khemliche).

Moreover, I wish to express my warm appreciation to all the tireless and passionate PhD students of our group (Tao Wang, Benoît Rogez, Shuiyan Cao, Ala Husseen, Moustafa Achlan, Delphine Pommier and Rémi Bretel) and of Stéphane and Guillaume's groups (Luis E. Parra Lópes and Benjamin Doppagne), who have carried out a large part of the work presented here.

I warmly thank all the staff at the Institute of Molecular Sciences of Orsay.

Last but not least, none of this would have been possible without the unwavering support of Séverine, to whom I am most indebted.

i Chapter 1

Introduction: nano-optics and the STM

Nano-optics generally designates the study of light-matter interactions on the nanometer scale [START_REF] Novotny | Principles of Nano-Optics[END_REF]. This very active field of research has originally emerged from near-field optics [START_REF] Novotny | Chapter 5 The history of near-field optics[END_REF], i.e., the study of evanescent waves of light and their use to break the diffraction limit in optical microscopy [START_REF] Pohl | Optical stethoscopy: Image recording with resolution λ 20[END_REF][START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF][START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF][START_REF] Dürig | Near-field optical scanning microscopy[END_REF][START_REF] Harootunian | Super-resolution fluorescence near-field scanning optical microscopy[END_REF]. Thus the initial motivation for this area of research was to "see" details or objects smaller than the smallest ones that a conventional light microscope is capable of resolving, and ultimately to enter the realm of single-molecule imaging and spectroscopy with light [START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF][START_REF] Anger | Enhancement and Quenching of Single-Molecule Fluorescence[END_REF]. In line with this long tradition, a key part of nano-optics is the development of novel instruments and methods to probe the optical properties of materials on the nanometer scale [START_REF] Betzig | Combined shear force and near-field scanning optical microscopy[END_REF][START_REF] Novotny | Scanning near-field optical probe with ultrasmall spot size[END_REF][START_REF] Bachelot | Near-field optical microscope based on local perturbation of a diffraction spot[END_REF][START_REF] Lahrech | Infrared-reflection-mode near-field microscopy using an apertureless probe with a resolution of λ/600[END_REF][START_REF] Hecht | Scanning near-field optical microscopy with aperture probes: Fundamentals and applications[END_REF][START_REF] Anderson | Locally enhanced raman spectroscopy with an atomic force microscope[END_REF][START_REF] Stöckle | Nanoscale chemical analysis by tip-enhanced Raman spectroscopy[END_REF][START_REF] Hayazawa | Metallized tip amplification of nearfield raman scattering[END_REF][START_REF] Michaelis | Optical microscopy using a single-molecule light source[END_REF][START_REF] Kalkbrenner | A single gold particle as a probe for apertureless scanning near-field optical microscopy[END_REF][START_REF] Hettich | Nanometer resolution and coherent optical dipole coupling of two individual molecules[END_REF][START_REF] Hubert | Near-field photochemical imaging of noble metal nanostructures[END_REF]. Recently, this approach has attained achievements still unimaginable a decade ago, with the luminescence and Raman spectroscopy of large organic molecules with spatial resolution in real space on the submolecular scale, i.e., virtually on the level of the atom size [START_REF] Zhang | Chemical mapping of a single molecule by plasmon-enhanced raman scattering[END_REF][START_REF] Neuman | Coupling of molecular emitters and plasmonic cavities beyond the point-dipole approximation[END_REF][START_REF] Lee | Visualizing vibrational normal modes of a single molecule with atomically confined light[END_REF][START_REF] Zhang | Visually constructing the chemical structure of a single molecule by scanning Raman picoscopy[END_REF][START_REF] Yang | Sub-nanometre resolution in single-molecule photoluminescence imaging[END_REF][START_REF] Rafael | Single-molecule resonance Raman effect in a plasmonic nanocavity[END_REF].

Since its infancy, the scientific scope of nano-optics and the community of researchers involved in nano-optics have continuously broadened, now including the fields of condensed matter physics, surface science, molecular spectroscopy, heterogenous catalysis, biological imaging and sensing and quantum-mechanical physics, just to name a few. In particular, nano-optics has made a vital contribution to the birth and growth of nanophotonics [START_REF] Ch | Near-field optics theories[END_REF][START_REF] Greffet | Image formation in near-field optics[END_REF][START_REF] Gersen | Influencing the angular emission of a single molecule[END_REF][START_REF] Shen | Nanophotonics: Interactions, materials, and applications[END_REF][START_REF] Colas Des Francs | Theory of near-field optical imaging with a single molecule as light source[END_REF][START_REF] Joulain | Definition and measurement of the local density of electromagnetic states close to an interface[END_REF][START_REF] Paras | Nanophotonics[END_REF][START_REF] Mühlschlegel | Resonant optical antennas[END_REF][START_REF] Greffet | Nanoantennas for light emission[END_REF][START_REF] Carminati | Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle[END_REF][START_REF] Genet | Light in tiny holes[END_REF][START_REF] Lal | Nano-optics from sensing to waveguiding[END_REF][START_REF] Hartschuh | Tip-enhanced near-field optical microscopy[END_REF][START_REF] Curto | Unidirectional Emission of a Quantum Dot Coupled to a Nanoantenna[END_REF][START_REF] Belacel | Controlling Spontaneous Emission with Plasmonic Optical Patch Antennas[END_REF][START_REF] Gorodetski | Generating far-field orbital angular momenta from near-field optical chirality[END_REF][START_REF] Koenderink | Nanophotonics: Shrinking light-based technology[END_REF], plasmonics [START_REF] Hollander | Near field plasmon and force microscopy[END_REF][START_REF] Barnes | Photonic gaps in the dispersion of surface plasmons on gratings[END_REF][START_REF] Hecht | Local excitation, scattering, and interference of surface plasmons[END_REF][START_REF] Bouhelier | Plasmon optics of structured silver films[END_REF][START_REF] Maier | Plasmonicsa route to nanoscale optical devices[END_REF][START_REF] Bouhelier | Near-field second-harmonic generation induced by local field enhancement[END_REF][START_REF] Maier | Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures[END_REF][START_REF] Ozbay | Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions[END_REF][START_REF] Maier | Plasmonics: Fundamentals and Applications[END_REF][START_REF] Ebbesen | Surface-plasmon circuitry[END_REF][START_REF] Laux | Plasmonic photon sorters for spectral and polarimetric imaging[END_REF][START_REF] Teperik | Huygens-Fresnel principle for surface plasmons[END_REF][START_REF] Stein | Surface plasmon mode steering and negative refraction[END_REF][START_REF] Liu | Three-dimensional plasmon rulers[END_REF] and excitonics [START_REF] Bellessa | Strong coupling between surface plasmons and excitons in an organic semiconductor[END_REF][START_REF] Sugawara | Strong coupling between localized plasmons and organic excitons in metal nanovoids[END_REF][START_REF] Zhang | Semiconductor-metal nanoparticle molecules: Hybrid excitons and the nonlinear Fano effect[END_REF][START_REF] Scholes | Excitons in nanoscale systems[END_REF][START_REF] Nche | Plexcitonic nanoparticles: Plasmon-exciton coupling in nanoshell-J-aggregate complexes[END_REF][START_REF] Georgi | Probing exciton localization in single-walled carbon nanotubes using high-resolution near-field microscopy[END_REF][START_REF] Semion | Photonics meets excitonics: natural and artificial molecular aggregates[END_REF][START_REF] Ballarini | All-optical polariton transistor[END_REF][START_REF] Schneider | An electrically pumped polariton laser[END_REF][START_REF] Guzelturk | Excitonics of semiconductor quantum dots and wires 123 for lighting and displays[END_REF][START_REF] Sanvitto | The road towards polaritonic devices[END_REF][START_REF] Gary Rozenman | Long-range transport of organic exciton-polaritons revealed by ultrafast microscopy[END_REF][START_REF] Melissa Konzelmann | Interaction of orbital angular momentum light with Rydberg excitons: Modifying dipole selection rules[END_REF][START_REF] Epstein | Highly confined in-plane propagating exciton-polaritons on monolayer semiconductors[END_REF][START_REF] Lingstädt | Interaction of edge exciton polaritons with engineered defects in the hyperbolic material Bi2Se3[END_REF], which are the sciences and technologies based on nanoscaleminiature devices using photons, surface plasmons and excitons as information vectors, respectively. In a near future, the technological spillovers of nano-optics may have a significant impact in key societal and industrial sectors, e.g., renewable energy, healthcare, water sanitization, quantum computing, and information and communication technologies.

One of the most significant evolutions of nano-optics during the last two decades is the increasing contribution of techniques using a combination of light and electrons [START_REF] Douillard | High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies[END_REF][START_REF] Kociak | Mapping plasmons at the nanometer scale in an electron microscope[END_REF][START_REF] Losquin | Electron microscopy methods for space-, energy-, and timeresolved plasmonicsfront[END_REF][START_REF] Kuhnke | Atomic-Scale Imaging and Spectroscopy of Electroluminescence at Molecular Interfaces[END_REF]. Paradoxically enough, electrons have been used to probe the optical properties of materials for a relatively long time, starting from well before the emergence of nano-optics. Indeed, the first experimental evidence for surface plasmon polaritons was obtained in 1957 by R. H. Ritchie [START_REF] Ritchie | Plasma losses by fast electrons in thin films[END_REF] using electron energy loss spectroscopy (EELS) [START_REF] Egerton | Electron Energy-Loss Spectroscopy in the Electron Microscope[END_REF]. Photoemission electron microscopy (PEEM) [START_REF] Bauer | Surface studies by low-energy electron microscopy (LEEM) and conventional UV photoemission electron microscopy (PEEM)[END_REF] has been used to map the electric near field of optically excited nanostructures with subwavelength spatial resolution [START_REF] Cinchetti | Photoemission Electron Microscopy as a Tool for the Investigation of Optical Near Fields[END_REF][START_REF] Kubo | Femtosecond Imaging of Surface Plasmon Dynamics in a Nanostructured Silver Film[END_REF][START_REF] Meyer Zu Heringdorf | Femtosecond photoemission microscopy[END_REF][START_REF] Douillard | Short range plasmon resonators probed by photoemission electron microscopy[END_REF][START_REF] Aeschlimann | Coherent Two-Dimensional Nanoscopy[END_REF][START_REF] Hrelescu | Selective Excitation of Individual Plasmonic Hotspots at the Tips of Single Gold Nanostars[END_REF][START_REF] Awada | Selective Excitation of Plasmon Resonances of Single Au Triangles by Polarization-Dependent Light Excitation[END_REF][START_REF] Lethiec | Plasmonics of opal surface: A combined near-and far-field approach[END_REF][START_REF] Davis | Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution[END_REF]. Light emitted due to the inelastic tunneling of electrons between the tip of a scanning tunneling microscope (STM) and a metallic sample was first reported in 1988 [START_REF] Coombs | Photon emission experiments with the scanning tunnelling microscope[END_REF][START_REF] Gimzewski | Enhanced Photon Emission in Scanning Tunnelling Microscopy[END_REF][START_REF] Peter Johansson | Theory for light emission from a scanning tunneling microscope[END_REF][START_REF] Berndt | Inelastic tunneling excitation of tip-induced plasmon modes on noble-metal surfaces[END_REF] and soon after envisioned as a nanoscale optical probe [START_REF] Abraham | Nanometer resolution in luminescence microscopy of III-V heterostructures[END_REF][START_REF] Sivel | Photon emission stimulated by scanning tunneling microscopy in air[END_REF][START_REF] Berndt | The role of proximity plasmon modes on noble metal surfaces in scanning tunneling microscopy[END_REF][START_REF] Berndt | Enhanced photon emission from the STM: a general property of metal surfaces[END_REF][START_REF] Berndt | Electromagnetic interactions of metallic objects in nanometer proximity[END_REF][START_REF] Ph | STM-induced light emission of supported silver nanocrystallites[END_REF]. Nevertheless, the combination of a local excitation with electrons and the detection of the resulting light in the far field has been increasingly used since the beginning of the 21st century and has become during the last years an essential pillar of the research in nano-optics. For a larger part, such an evolution stems from the instrumental progress in the electron microscopes and STMs and their coupling to optics.

Moreover, a few seminal, experimental and theoretical papers have given a strong momentum toward this development [START_REF] Zhang | Chemical mapping of a single molecule by plasmon-enhanced raman scattering[END_REF][START_REF] Cohen | Near-Field Electron Energy Loss Spectroscopy of Nanoparticles[END_REF][START_REF] Kociak | Plasmons in layered nanospheres and nanotubes investigated by spatially resolved electron energy-loss spectroscopy[END_REF][START_REF] Qiu | Vibrationally Resolved Fluorescence Excited with Submolecular Precision[END_REF][START_REF] Van Wijngaarden | Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy[END_REF][START_REF] Jan | Direct observation of plasmonic modes in au nanowires using high-resolution cathodoluminescence spectroscopy[END_REF][START_REF] Nelayah | Mapping surface plasmons on a single metallic nanoparticle[END_REF][START_REF] García De Abajo | Probing the photonic local density of states with electron energy loss spectroscopy[END_REF][START_REF] García De Abajo | Optical excitations in electron microscopy[END_REF][START_REF] Bourrellier | Nanometric resolved luminescence in h-BN flakes: Excitons and stacking order[END_REF][START_REF] Talebi | Merging transformation optics with electron-driven photon sources[END_REF]. For instance, the inclusion of parabolic collection optics in commercially available scanning electron microscopes (SEM) have considerably expanded the use of cathodoluminescence (CL) spectroscopy and imaging in plasmonics and semiconductor physics [START_REF] Coenen | Angle-resolved cathodoluminescence spectroscopy[END_REF]. The combination of an STM head with an optical microscope, which our group has contributed to pioneer [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF], has extended the nano-optics toolbox with a novel probe of the optical modes and elementary excitations in nanomaterials [START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Zhang | Edge scattering of surface plasmons excited by scanning tunneling microscopy[END_REF][START_REF] Divitt | The role of gap plasmons in light emission from tunnel junctions[END_REF][START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Rogez | Optical and Electrical Excitation of Hybrid Guided Modes in an Organic Nanofiber-Gold Film System[END_REF][START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF].

STM is at the core of the work presented in this dissertation. STM is based on the tunneling of low-energy (< 4 eV) electrons, which constitutes a crucial advantage over the high-energy (10 -100 keV) electron beam spectroscopies mentionned above (CL, EELS). STM yields comparatively less electron-induced damages and is compatible with the excitation of single molecules. A greater control of the excited modes or transitions is possible in STM, where the bias voltage fixes an upper bound on the highest energy an electron may transfer to the sample. In STM, the quantum efficiency of the electron interaction with the material is not dependent on the material thickness, which makes it ideal for nanoscale optical investigations on two-dimensional (2D) materials, e.g., graphene [START_REF] Beams | Electroluminescence from graphene excited by electron tunneling[END_REF] or other atomically thin semiconductors [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF][START_REF] Javier | Tunneling-current-induced local excitonic luminescence in p-doped WSe 2 monolayers[END_REF][START_REF] Schuler | Electrically driven photon emission from individual atomic defects in monolayer WS 2[END_REF]. Unlike the techniques based on high-energy electron beams, STM does not require the use of high voltages and the high vacuum environment of an electron microscope. STM is compatible with experiments under ambiant conditions. This constitutes a strong advantage for STM in the context of device-oriented research, since STM experiments may be carried out under conditions similar to those of the operation of electronic devices, i.e., in air at a few volts and a few nanoamperes. Many prototypes of integrated plasmonic microdevices have been described in the literature [START_REF] Jord | Electrically Connected Resonant Optical Antennas[END_REF][START_REF] Rai | Electrical Excitation of Surface Plasmons by an Individual Carbon Nanotube Transistor[END_REF][START_REF] Kevin | Electrically driven subwavelength optical nanocircuits[END_REF][START_REF] Wu | On-Chip Single-Plasmon Nanocircuit Driven by a Self-Assembled Quantum Dot[END_REF], some of which use a tunnel nanojunction as an electrical source of optical signal or as a receiver [START_REF] Kern | Electrically driven optical antennas[END_REF][START_REF] Cazier | Electrical excitation of waveguided surface plasmons by a light-emitting tunneling optical gap antenna[END_REF][START_REF] Du | Highly efficient on-chip direct electronicplasmonic transducers[END_REF][START_REF] Dasgupta | Optical wireless link between a nanoscale antenna and a transducing rectenna[END_REF][START_REF] Parzefall | Light from van der Waals quantum tunneling devices[END_REF][START_REF] Kullock | Electrically-driven Yagi-Uda antennas for light[END_REF]. In this context, STM-induced light emission allows one to test and validate the design and performance of such electrical nanosources of surface plasmons and/or photons and of the plasmonic circuits in which they are integrated. In addition, operations in air makes possible the coupling of STM to an optical microscope equipped with high numerical aperture collection optics [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF].

In this dissertation, I focus on the use of the tunnel current as an electrical nanosource of light and, more generally, as a nanoprobe producing extremely local optical excitation, a source of surface plasmons, excitons, and photons. In particular, I show the new possibilities offered by the combination of the STM with spatially, spectrally and angularly resolved optical microscopy for the study of plasmonic materials and nanostructures and new electroluminescent materials such as two-dimensional semiconductors.

The dissertation is organized as follows. In Chap. 2, I introduce the methods and experimental setups that are used in the present work. In Chaps. 3 -5, inelastic electron tunneling from an STM tip is used to selectively excite the plasmonic modes of individual gold nanoparticles (see Chap. 3), to drive the emission of light beams from plasmonic lenses (Chap. 4), and to reveal the energy-momentum dispersion of propagating waves in plasmonic crystals and metal-insulator-metal stacks (Chap. 5). In Chap. 6, the first observation of STM-induced excitonic luminescence from a 2D semiconductor is reported. Finally, in Chap. 7, an on-going research project on singlemolecule luminescence spectroscopy in an ultrahigh vacuum low-temperature STM is presented.

Chapter 2

Methods: combining STM with optics

The introduction of this chapter is adapted with permission from Refs. [START_REF] Le | La nano-optique sous la pointe d´un microscope à effet tunnel[END_REF][START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]. Copyright (2020) American Chemical Society.

Electron tunneling through the junction between electrodes made of plasmonic materials is known to produce light. This was first reported by Lambe and McCarthy [START_REF] Lambe | Light emission from inelastic electron tunneling[END_REF] in 1976 and this was ascribed to the radiative decay of surface plasmon polaritons electrically excited by inelastic effects of the tunnel current [START_REF] Mccarthy | Enhancement of light emission from metal-insulator-metal tunnel junctions[END_REF][START_REF] Davis | Theory of surface-plasmon excitation in metal-insulator-metal tunnel junctions[END_REF][START_REF] Rendell | Role of local plasmon modes in light emission from smallparticle tunnel junctions[END_REF][START_REF] Daniel Hone | Theory of light emission from small particle tunnel junctions[END_REF][START_REF] Mccarthy | LEIT effect in metal-insulator-semiconductor tunnel junctions[END_REF][START_REF] Jain | Stable room-temperature light emission from metal-insulatormetal junctions[END_REF][START_REF] Siu | Stimulated emission of surface plasmons by electron tunneling in metal-barriermetal structures[END_REF][START_REF] Laks | Photon emission from slightly roughened tunnel junctions[END_REF][START_REF] Laks | Light emission from tunnel junctions: The role of the fast surface polariton[END_REF][START_REF] Rendell | Surface plasmons confined by microstructures on tunnel junctions[END_REF][START_REF] Kirtley | Light emission from tunnel junctions on gratings[END_REF]. (Surface plasmon polaritons, SPPs, are electromagnetic waves bound to collective oscillations of electrons at the surface of a metal [START_REF] Maier | Plasmonics: Fundamentals and Applications[END_REF][START_REF] Raether | Surface Plasmons on Smooth and Rough Surfaces and on Gratings[END_REF].) Since the invention of STM by Binnig and Rohrer in 1981 [START_REF] Binnig | Surface Studies by Scanning Tunneling Microscopy[END_REF][START_REF] Binnig | Scanning tunneling microscopy -from birth to adolescence[END_REF], light from below the STM tip has been widely studied, either in the tunnel regime [START_REF] Coombs | Photon emission experiments with the scanning tunnelling microscope[END_REF][START_REF] Berndt | Inelastic tunneling excitation of tip-induced plasmon modes on noble-metal surfaces[END_REF] or in tip-sample atomic contact [START_REF] Schull | Electron-Plasmon and Electron-Electron Interactions at a Single Atom Contact[END_REF][START_REF] Schneider | Optical Probe of Quantum Shot-Noise Reduction at a Single-Atom Contact[END_REF], and used as a spectroscopic nano-tool [START_REF] Uehara | Optical observation of single-electron charging effect in metallic particles[END_REF][START_REF] Schull | Imaging confined electrons with plasmonic light[END_REF][START_REF] Chen | Visualization of fermi's golden rule through imaging of light emission from atomic silver chains[END_REF]. Since 2011, our group has contributed to reviving the interest in STM-induced light from plasmonic structures, with the development of setups combining optical microscopy and an STM operating in air [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF][START_REF] Wang | Scattering of electrically excited surface plasmon polaritons by gold nanoparticles studied by optical interferometry with a scanning tunneling microscope[END_REF]. We have reported on a number of experiments using inelastic electron tunneling as a nanosource of light or surface plasmons [START_REF] Zhang | Edge scattering of surface plasmons excited by scanning tunneling microscopy[END_REF][START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Rogez | Optical and Electrical Excitation of Hybrid Guided Modes in an Organic Nanofiber-Gold Film System[END_REF][START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF][START_REF] Wang | Scattering of electrically excited surface plasmon polaritons by gold nanoparticles studied by optical interferometry with a scanning tunneling microscope[END_REF][START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF][START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF][START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF][START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF][START_REF] Cao | Using a plasmonic lens to control the emission of electrically excited light[END_REF][START_REF] Cao | Directional light beams by design from electrically driven elliptical slit antennas[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF][START_REF] Wang | Plasmon scattering from holes: from single hole scattering to Young's experiment[END_REF][START_REF] Wang | Temporal coherence of propagating surface plasmons[END_REF].

Different experimental configurations may be used to detect the light emitted from below the tip of an STM. When the instrument is operated in ultra-high vacuum, light collection can be performed in situ using optical fibers [START_REF] Kemerink | Lowtemperature scanning-tunneling microscope for luminescence measurements in high magnetic fields[END_REF],

a prism [START_REF] Iida | Mechanism of Prism-Coupled Scanning Tunneling Microscope Light Emission[END_REF], one or more lenses [START_REF] Keizer | Simple and efficient scanning tunneling luminescence detection at low-temperature[END_REF][START_REF] Wu | A low-temperature scanning probe microscopy system with molecular beam epitaxy and optical access[END_REF], a parabolic mirror [START_REF] Wang | Enhancement of radiative plasmon decay by hot electron tunneling[END_REF], or specially engineered STM tips [START_REF] Guo | Scanning tunneling microscopy luminescence from nanoscale surface of GaAs(110)[END_REF][START_REF] Edelmann | Light collection from a low-temperature scanning tunneling microscope using integrated mirror tips fabricated by direct laser writing[END_REF]. These configurations offer highly variable collection efficiencies, typically 0.1 -1% with a fiber, 1% -10% with a lens, and > 10% with a parabolic mirror. The most advantageous configuration in terms of collection is the use of an oil immersion microscope objective [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF]. This solution is not yet compatible with ultra-high vacuum and/or a low temperature environment and requires the use of transparent samples. However, when it can be implemented, this approach allows the collection of more than 50% of the emitted light, up to 80% in some cases, because the light is mostly emitted in the medium with the highest refractive index, in this case the substrate.

The combination of optical microscopy and STM opens up new possibilities in the analysis of inelastic tunnelling (c) Energy diagram showing the tip-to-surface junction polarized at a voltage V and the passage of an electron by elastic (ET) and inelastic (IET) tunnelling accompanied by the emission of a photon of energy hν ≤ eV . Adapted from [START_REF] Rossel | Luminescence experiments on supported molecules with the scanning tunneling microscope[END_REF] with permission from Elsevier. Reprinted from [START_REF] Le | La nano-optique sous la pointe d´un microscope à effet tunnel[END_REF], published under the conditions of the Creative Commons Attribution License CC-BY. induced light emission. Indeed, while the tunneling current may excite the sample modes very locally, the STM does not make it possible to visualize from where in the sample light is emitted, nor in which direction light is emitted.

However, this information is crucial to determine the nature of the excited modes, especially if propagating modes are excited [START_REF] Rogez | Optical and Electrical Excitation of Hybrid Guided Modes in an Organic Nanofiber-Gold Film System[END_REF][START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]. The use of a microscope objective to collect light in transmission through the sample allows one to obtain an image of the object plane, which reveals the spatial distribution of the emitted light (i.e., a real-space image), and an image of the back focal plane of the objective, which reveals the angular distribution of the emission (i.e., a Fourier-space image). The Fourier image contains information about the spatial frequencies of the emitted field, from which the dispersion relationship between energy and momentum of the excited propagating modes may be retrieved. This dispersion relationship may be recorded, for example, by optically projecting the Fourier image (e.g., using lenses) onto the input slit of an imaging optical spectrometer [START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF][START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF].

Other STM-based optical experiments may greatly benefit from the high collection efficiency obtained using a microscope objective. Among these, hyperspectral imaging and intensity interferometry measurements are particularly "expensive" in terms of photons. STM-induced emission generally generates very low photon fluxes, due to the very low quantum efficiency of inelastic tunneling effects, on the order of 10 -7 to 10 -5 photons emitted per tunneling electron, and the low currents used (i.e., a few nanoamperes). Hyperspectral imaging consists of recording an optical spectrum at each position of the STM tip on the sample. Intensity interferometry (Hanbury Brown -Twiss) is a technique for measuring temporal correlations between photons emitted by a single source. Such a technique makes it possible to identify anti-bunching when the light source is a quantum emitter, i.e. a single photon source [START_REF] Rosławska | Atomic-scale dynamics probed by photon correlations[END_REF].

The emission of light is associated with the radiative decay of the electromagnetic modes of the system. In order to identify the energies of these modes, we measure the spectra of the emitted light upon excitation with the STM-nanosource [START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]. The STM-nanosource is inherently broadband and depends on the applied voltage (leading to a high energy cutoff) [START_REF] Berndt | Inelastic tunneling excitation of tip-induced plasmon modes on noble-metal surfaces[END_REF][START_REF] Lambe | Light emission from inelastic electron tunneling[END_REF]. In order to ensure that we excite the inherent resonances of the sample [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF] and not the nanocavity resonances of the tip-sample system [START_REF] Aizpurua | Role of tip shape in light emission from the scanning tunneling microscope[END_REF], we use a tungsten STM tip. Since tungsten is a non-plasmonic metal in the energy range under consideration (i.e., the real part of the permittivity is positive and the spectral response is broad and damped [START_REF] Aleksandar | Optical properties of metallic films for vertical-cavity optoelectronic devices[END_REF]) nanocavity resonances are thus avoided. A drawback of using a non-plasmonic tip is that it yields comparatively low numbers of emitted photons per tunneling electron, as compared to the use of a gold tip, for instance. Thus, the detection of the emitted light through the substrate by using a microscope objective of high collection efficiency is key.

Experimental setup no. 1

This section is adapted with permission from Refs. [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. Copyright (2013) American Chemical Society. Copyright (2016) by the American Physical Society. The setup consists of a commercial STM/AFM head operating in air in ambient conditions, mounted on top of an inverted optical microscope [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF]. A nanopositioning stage holds the sample between the STM tip and the objective lens. The sample is biased (e.g., to 2.8 V) while the tip is grounded. We use tungsten tips made by electrochemical etching in sodium hydroxide, which typically have curvature radius of 30 nm at the apex. The light emission in the substrate is collected using a high numerical aperture objective lens (oil immersion, NA = 1.45). The angular distribution of the STM-induced light emission is retrieved by optical imaging in the Fourier plane using a water-cooled CCD camera, with the tip located at a fixed position on the sample.

A different setup is used to measure light scattering spectra of plasmonic nanoparticles (NP), which is described in Fig. 2.3b. The sample is illuminated from above with a collimated beam of polarized white light in almost grazing incidence (≈ 80 ○ off the z-axis). The light scattered in the substrate is collected using an air objective lens of sufficiently low NA to reject the incident light (NA = 0.7, angle of acceptance ≈ 44 ○ ). The polarization of the incident light is controlled using a polarizer in front of the light source. The collected light is focused on the end of a bundle of optical fibers that is coupled to an optical spectrometer. A pinhole is placed just before the fiber end in order to select the light originating from a circular area (2 µm in diameter) of the sample plane. Thus the scattering spectrum of single gold NPs can be measured. When s-polarized light is sent onto the sample, only the in-plane modes

[along the x-axis, see Fig. 2.3(b)] of the NPs are excited, whereas a combination of vertical (z-axis) and in-plane (y-axis) modes is excited with p-polarized light, since the incidence angle is not 90 ○ . In the latter case, a second polarizer is thus added between the objective and tube lenses, with its transmission axis along the x-axis, to reject In both setups, light is collected through the substrate. Inscriptions on the housing of the objective lenses indicate immersion medium and numerical aperture. Reprinted with permission from Ref. [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. Copyright (2016) by the American Physical Society.

the contribution of in-plane modes. In this way, we disentangle the contributions of the two types of modes.

Experimental setup no. 2

This section is adapted with permission from Refs. [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF][START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF][START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF][START_REF] Bryche | k-space optical microscopy of nanoparticle arrays: Opportunities and artifacts[END_REF]. Copyright (2017)(2019) by the American Physical Society. Adapted with permission from AIP Publishing. Copyright (2018) Optical Society of America. Reprinted with permission from Ref. [START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]. Copyright (2019) Optical Society of America.

Thus, an image with angular (or wavevector) coordinates along one axis and wavelength (or energy) coordinates along another is measured. From such a measurement, the energy-momentum dispersion of the excited modes may be retrieved.

The configuration shown in Fig. 2.4(b) is used for the electrical excitation of the sample with tunnel electrons. A commercial STM head (JPK Nanowizard III) is mounted on the inverted optical microscope, so that the sample is between the objective lens and the STM tip [START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. The inelastic electron tunnel current from the tip to the surface excites both the plasmonic and photonic modes in the sample [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF]. On a planar metallic surface, this excitation may be considered equivalent to an oscillating electric dipole located in the tip-surface gap and oriented orthogonally to the metallic surface [START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]. The electrically excited waves that propagate along the surface may be detected when they leak in the substrate at angles within the acceptance cone of the microscope objective [START_REF] Hecht | Local excitation, scattering, and interference of surface plasmons[END_REF][START_REF] Drezet | Leakage radiation microscopy of surface plasmon polaritons[END_REF].

The configuration shown in Fig. 2.4(a) is designed for the optical excitation of the sample, i.e., with a laser. The microscope objective is used both to focus the beam of a continuous-wave He-Ne laser (λ 0 = 632.8 nm) onto the substrate-sample interface and also to collect the reflected light. The laser beam is expanded using a telescope configuration to completely fill the rear pupil of the microscope objective. Thus, the reflectivity of the substratesample interface is measured at all incident angles within the acceptance cone of the objective in a single Fourierspace image. Moreover, since the initial beam is linearly polarized, the focused incident light is s-polarized in one plane and p-polarized in a perpendicular plane. In this way, the reflectivity for both s-and p-polarized incidence are measured simultaneously [START_REF] Bryche | k-space optical microscopy of nanoparticle arrays: Opportunities and artifacts[END_REF].

A "one-shot" technique for measuring the dispersion relation is presented in Figure 2.4 (configuration 2). A removable mirror is used to switch between two configurations of the setup, where light is either (1) directly imaged on a water-cooled CCD camera or [START_REF] Novotny | Chapter 5 The history of near-field optics[END_REF] spectrally dispersed by a Czerny-Turner imaging spectrometer equipped with a water-cooled CCD camera. The angular distribution of the emitted light is determined from the Fourier plane image obtained using configuration 1 of the setup. We use bandpass filters to select narrow energy ranges within the visible and near-infrared spectrum (from emission wavelengths of 550 to 900 nm). Thus we record a series of "spectrally filtered" Fourier-space images [START_REF] Rogez | Optical and Electrical Excitation of Hybrid Guided Modes in an Organic Nanofiber-Gold Film System[END_REF][START_REF] Wang | Temporal coherence of propagating surface plasmons[END_REF]. To further resolve the spectral dependence of the angular emission pattern, we use configuration 2 of the setup, where the Fourier-space image is formed on the entrance slit of the spectrometer. Thus, we record an image whose axes are the emission wavelength and the angular coordinate n sin θ, respectively, where θ is the emission angle in the substrate and n is the substrate's refractive index. Such an image contains the energy-momentum dispersion relation of the excited modes, since the in-plane wavevector component is k ∥ = k 0 n sin θ, where k 0 is the free-space photon wavevector. This approach is similar to other angle-resolved spectroscopy techniques that have been developed for cathodoluminescence in a scanning electron microscope (SEM) [START_REF] Coenen | Angle-resolved cathodoluminescence spectroscopy[END_REF][START_REF] Coenen | Directional Emission from Plasmonic Yagi-Uda Antennas Probed by Angle-Resolved Cathodoluminescence Spectroscopy[END_REF]. Alternatively, the CCD image may be vertically integrated before the readout (i.e. intensity is integrated over the angular coordinate) in order to obtain the spectral distribution of the light emitted in the substrate. In either case, the collection angle for the emitted light is limited to the angle defined by the finite aperture of the objective lens, i.e., to θ max ≈ 79 ○ when NA = 1.49. The spectra (not the images) shown in this dissertation are corrected for the spectral response of the instrument.

We define the detection efficiency (or "spectral response of the instrument") as the product of the transmission coefficient of the microscope objective, the quantum efficiency of the detector and the diffraction efficiency of the grating in the spectrometer. For instance, at photon wavelength λ 0 = 784 nm, this yields detection efficiencies of 46% and 31% for photon mapping and optical spectrum measurements, respectively. In addition, there must be light emitted from the front side of the sample as well, which is not collected by the microscope objective. This is not taken into account in the detection efficiency. For instance, a photon emission quantum efficiency up to 10 -7

photons per electron actually means that up to 10 -7 photons per electron are emitted in the collection cone of the microscope objective. Neglecting the light emitted on the front side yields an underestimation of the total photon emission quantum efficiency by about 20 to 40%, when considering a sample deposited on an ITO-coated glass substrate [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF]. This estimation may be significantly different when considering a sample on a gold-coated glass substrate, with in that case a strong dependence on both the thickness of the gold film and the emission frequency. In the field of nano-optics, tunneling nanojunctions have often been considered the simplest design of an electron-plasmon or electron-photon transducer. However, the drawback of its simplicity is the lack of control of the emission properties (i.e., directivity, spectrum, polarization). In 2012, we began to investigate the possibility of attaining such control through the local excitation of localized surface plasmons (LSP) on individual crystalline gold nanoparticles (NP) of well-defined geometry, using the tip of an STM. In Sec. 3.1, we show that the angular distribution of the emitted light can be controlled through the lateral position of the tip with respect to the symmetry center of the NP. Thus, an electrically driven nanoscale light source with controllable emission direction may be obtained.

We demonstrate that this behavior is linked to the selective excitation of the out-of-plane and in-plane dipolar LSP modes of the NP. In Sec. 3.2, we introduce a new theoretical framework within which the emission properties of the tip-NP system may be predicted. We propose that the intensity and angular distribution of the emitted light as a function of the lateral position of the tip on the NP is mainly determined by the electric nearfield distributions at resonance of its dipolar LSP modes, which may be simply calculated without considering the presence of the tip.

We demonstrate that this is true on a transparent substrate and with a non-plasmonic tip. A consequence of this is that the STM-induced light is a probe of the local density of these dipolar LSP modes. In Sec. 3.3, we extend this reasoning to include all the plasmonic modes (not only the dipolar ones). To that purpose, we consider compara-tively large gold nanoplatelets, which have higher order multipolar LSP resonances in the visible, including breathing and edge plasmonic modes. Based on EELS measurements on similar structures and finite-element calculations, we demonstrate that the STM-induced light is a probe of the local density of photonic modes. [115]

An electrical light nanosource

Context and motivation. Nanoscale light sources with controllable angular emission are highly desirable for future technological developments in nanophotonics. Many different concepts for directional photon nanosources have been proposed; most of them exploit the plasmonic modes of metallic nanostructures that are commonly called optical antennas [START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Koenderink | Plasmon nanoparticle array waveguides for single photon and single plasmon sources[END_REF][START_REF] Esteban | Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances[END_REF][START_REF] Giannini | Plasmonic Nanoantennas: Fundamentals and Their Use in Controlling the Radiative Properties of Nanoemitters[END_REF][START_REF] Li | Directional light emission from propagating surface plasmons of silver nanowires[END_REF][START_REF] Shegai | Unidirectional Broadband Light Emission from Supported Plasmonic Nanowires[END_REF]. In general, the principle of optical antennas for emission is the conversion of spatially confined, evanescent electromagnetic fields into free propagating radiation [START_REF] Greffet | Nanoantennas for light emission[END_REF][START_REF] Novotny | Antennas for light[END_REF]. One way to drive these optical antennas is to couple the near-field emission of a single fluorescent molecule [START_REF] Ahmed | Directivity enhanced raman spectroscopy using nanoantennas[END_REF][START_REF] Aouani | Plasmonic Antennas for Directional Sorting of Fluorescence Emission[END_REF][START_REF] Aouani | Ultrasensitive Broadband Probing of Molecular Vibrational Modes with Multifrequency Optical Antennas[END_REF][START_REF] Zhu | Direct observation of beamed raman scattering[END_REF][START_REF] Lu | Plasmonicenhanced molecular fluorescence within isolated bowtie nano-apertures[END_REF] or nanocrystal [START_REF] Curto | Unidirectional Emission of a Quantum Dot Coupled to a Nanoantenna[END_REF][START_REF] Belacel | Controlling Spontaneous Emission with Plasmonic Optical Patch Antennas[END_REF][START_REF] Taminiau | Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna[END_REF] to the plasmonic modes of metallic nanostructures. This requires that the emitter be excited with photons from the far field, which gives rise to a strong excitation light background, thus limiting the possible integration with miniaturized devices. Moreover, except for a few cases where the emission directivity can be tailored through the polarization of the excitation light [START_REF] Dregely | 3D optical YagiUda nanoantenna array[END_REF][START_REF] Lal | Noble Metal Nanowires: From Plasmon Waveguides to Passive and Active Devices[END_REF] or its incidence angle [START_REF] Munárriz | Optical nanoantennas with tunable radiation patterns[END_REF], these optically driven photon nanosources only allow passive control of the radiation pattern; namely, their design must be modified in order to obtain a different result.

Results and discussion.

Here, we electrically excite localized surface plasmons with low-energy electrons (< 3 eV) tunneling from a sharp tungsten tip to a single gold NP of well-adapted shape to produce a nanoscale light source with active angular control of the emitted light. This concept uses the low energy electrons of a tunnel junction, works in an ambient environment, and may be adapted to a planar geometry. Using tunneling electrons guarantees the very high spatial selectivity of the electrical excitation. In our case, the tunnel junction is formed between the tip of an STM and the sample. The STM is also used to image the gold NP and locate the appropriate excitation sites. In Figure 3.1, a single NP is electrically excited with the STM tip above the center of the particle and the resulting light is imaged in the Fourier plane (see image in Fig. 3.1(e)) and in the real plane (see image in Fig. 3.1(f)) using the optical microscope. Both the Fourier-space and real-space images are rotationally symmetric with respect to the optical axis. The Fourier image shows that the emitted light is equally distributed with respect to the azimuthal angle φ and that it is mainly emitted above the polar angle θ c , the air/glass critical angle. The doughnut-shaped spot in the real-space image, with its intensity drop at the center, is the signature of p-polarized emission typical of a vertical radiating dipole. that the experimental Fourier images fit best with the emission pattern of a dipole that is not vertical but tilted (in the plane that is defined by the vertical axis and the median of the NP) when the tip is not above the center of the NP. Moreover, this tilt gradually varies as the tip moves from the vertex to the edge. This observation, together with polarization and spectral measurements (not shown in this dissertation, see in [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]), leads to the conclusion that the STM tip efficiently excites both the in-plane (horizontally polarized) and out-of-plane (vertically polarized) dipolar LSP of the NP when it stands above the vertex, leading to the equivalent of a tilted dipole, whereas the out-of-plane (vertically polarized) dipolar LSP dominates when the tip is centered (only this mode is compatible with p-polarized emission). In the following, thanks to time-dependent numerical calculations, we propose an explanation of the mechanisms behind this selective excitation of the NP modes.

We conduct FDTD calculations using a freely available software package (Meep) [START_REF] Ardavan | Meep: A flexible free-software package for electromagnetic simulations by the fdtd method[END_REF]. Briefly, we define a three-dimensional computational domain including the tungsten tip, the gold NP, the surrounding air, and the glass substrate. We consider a point dipole source located in the STM junction, equidistant between the closest points of the tip and the NP. In order to get an idea of the system behavior at resonance, we choose a monochromatic source and wait for the steady-state electromagnetic field to fully evolve before analyzing the results. The oscillation frequency of the source corresponds to the average of the two dipolar LSP resonances of the NP (photon energy 1.81 eV). We simplify the truncated bitetrahedral shape of the NP with that of a triangular nanoprism with upper and lower triangular faces of the same size and vertical rectangular side faces (see sketch in the inset of Figure 3.3).

We obtain the vector components of the electric field along the horizontal x (E x ) and vertical z (E z ) axes. As shown in Figure 3.3, we consider two tip locations: one above the NP center (a,b) and the other above the vertex (d,e). In each case, a snapshot of the electric field at a given time is displayed. The red and blue of the color scale denote field amplitudes of opposite sign. We see in Fig. 3.3(a) that the horizontal components of the electric field are out of phase on opposite sides of the NP, while in Fig. 3 Adapted with permission from [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. Copyright(2013) American Chemical Society.

---

+ + + + + + + ---- (a) (b) (d) (e) E x E z E x E z z x (c) (f) +1 -1
(arb. units) Reprinted with permission from [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. Copyright(2013) American Chemical Society.

z x
system assures that the horizontal components of the electric field cancel out on average. This outcome with the zero averaged horizontal field and in-phase vertical electric field, shows that the near-field of the vertical electric dipole (tip-induced gap plasmon) can vertically polarize the NP when the tip is centered, as illustrated in Fig. 3.3(c).

The result when the tip is at its most off-centered position is very different; the horizontal components of the electric field are in phase on opposite sides of the NP (see Fig. 3.3(d)), while its vertical components are out of phase on the upper and lower faces (see Fig. 3.3(e)). Thus, the vertical electric dipole nearfield mainly polarizes the NP along its horizontal axis (see Fig. 3.3(f)). Hence we conclude that the tip-induced gap plasmon between the tip and NP can selectively excite either the out-of-plane or in-plane dipolar LSP modes of the NP depending on where on the NP the STM excitation takes place. Control of this selective excitation is possible via the accurate positioning of the STM tip above the NP. Thus, we elucidate the mechanism through which the emission direction of our electrical light nanosource is controlled. Now, a more general theoretical framework is necessary to further develop our approach and explain or predict the properties of the STM-induced light emitted for any plasmonic NP geometry.

Engineering the light emitted from a tunneling junction

Collaborators: Andrey G. Copyright (2016) by the American Physical Society. [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF] Context and motivation. Tunnel junctions may become key elements for the design of electrically driven nanosources of light with controllable emission [START_REF] Kern | Electrically driven optical antennas[END_REF][START_REF] Pohl | Stacked optical antennas[END_REF][START_REF] Parzefall | Antenna-coupled photon emission from hexagonal boron nitride tunnel junctions[END_REF]. However, the control of the emission properties is often an issue when the tunnel junction is formed by the gap between two plasmonic nanostructures; an issue that has been known for a long time in the STM community. Indeed, in most of the reported STM-induced light studies, the emission is completely dominated by the resonance of the gap plasmon mode induced by the strong tip-sample interaction when both the tip and the sample are made of plasmonic materials such as gold or silver [START_REF] Nilius | Tip influence on plasmon excitations in single gold particles in an STM[END_REF][START_REF] Myrach | Photon mapping of individual ag particles on MgO/mo(001)[END_REF][START_REF] Aizpurua | Electromagnetic Coupling on an Atomic Scale[END_REF]. The extreme spatial confinement of the gap plasmon inside the junction makes it exceedingly sensitive to very slight yet unavoidable and unpredictable changes in the morphology of the tip apex [START_REF] Aizpurua | Role of tip shape in light emission from the scanning tunneling microscope[END_REF][START_REF] Hoffmann | Influence of tip geometry in light emission from the scanning tunnelling microscope[END_REF]. Consequently, the common wisdom in the field is that STM-induced light emission suffers from this "arbitrary" character [START_REF] Hoffmann | Influence of tip geometry in light emission from the scanning tunnelling microscope[END_REF]. Similar issues have also been reported for plasmonic nanostructures on a plasmonic (or highly-reflective) substrate, where a gap plasmon occurs at the nanostructure-substrate interface [START_REF] André | Resonant electromagnetic field cavity between scanning tunneling microscope tips and substrate[END_REF][START_REF] Cvitkovic | Infrared Imaging of Single Nanoparticles via Strong Field Enhancement in a Scanning Nanogap[END_REF]. Nonetheless, the experiment reported in Sec. 3.1 using a tip made of a non-plasmonic material (i.e., tungsten) and a transparent substrate (i.e., glass)

suggests that the STM-induced light emitted from a gold NP may be controlled in a reproducible way by changing the excitation position of the tip on the NP [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. Understanding and mastering this effect opens up new possibilities for engineering the light emitted from an STM tunnel junction by using the resonant modes of a plasmonic nanostructure. Here, we demonstrate that the properties of the light emitted from an STM tip-plasmonic NP junction may be predicted and controlled in a simple way. For a sufficiently small radius of curvature as compared to the NP size, the non-plasmonic tip need not to be treated explicitly. Essentially, the effect of the tip results in the renormalisation of the fluctuating (point) dipole associated in classical descriptions with inelastic tunneling current [START_REF] Peter Johansson | Theory for light emission from a scanning tunneling microscope[END_REF][START_REF] Persson | Theory of photon emission in electron tunneling to metallic particles[END_REF]. The dependence of the angular profile and intensity of the emitted light as a function of the tip position may be obtained from the Green's tensor G NP of the plasmonic NP only [START_REF] García De Abajo | Optical excitations in electron microscopy[END_REF][START_REF] Taminiau | Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna[END_REF][START_REF] Coenen | Directional emission from a single plasmonic scatterer[END_REF]. In particular, simple and intuitive insights may be gained by considering the development of G NP in terms of the localized surface plasmon (LSP) eigenmodes [START_REF] Colas Des Francs | Theory of near-field optical imaging with a single molecule as light source[END_REF][START_REF] Sauvan | Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators[END_REF][START_REF] Carminati | Electromagnetic density of states in complex plasmonic systems[END_REF]. We validate our approach by comparing experimental data with the results of electromagnetic calculations performed using complete and simplified representations of the tip-NP system.

Results and discussion. To begin with, we characterize the plasmon response of the same individual gold NPs as studied in Sec. 3.1, which are deposited on an ITO-coated glass substrate (the STM tip is not present at this stage). Figure 3.4 shows experimentally and using a complete electromagnetic calculation, that two distinct dipolar The electric nearfield distributions in a plane just above the NP, calculated at the two resonance frequencies, are shown in Fig. 3.4(e). One can unambiguously assign the observed resonances to the vertical (p z , 2.1 eV) and in-plane (p x , 1.9 eV) dipolar LSP modes. It is these electric nearfield distributions that will be used in one of the approaches proposed below to predict the intensity and angular distribution of the emitted light as a function of the tip excitation position on the NP.

In the following, we use the parameter Θ to compare the experimental and calculated results. In the experiment, Θ represents the orientation of the "effective" tilted dipole which best fits the Fourier plane angular emission results, as introduced in Sec. 3.1. In the calculations, Θ is equivalent to the orientation of the induced dipole in the NP (or in the NP-tip system).

Below, we use a classical picture where the inelastic tunneling current is represented as a point electric dipole p placed in the junction and radiating at the transition frequency ω. The total radiated electric field is given by

E tot = E d + E + NP + E + T , (3.1)
where E d is the field of the point dipole p and

E + NP T = R NP T E d + E + T NP , (3.2)
is the field scattered by the NP or tip (T). Here, R NP T is the operator that connects the incident and scattered fields for the NP/T. Obviously, R NP T is directly linked with the NP or tip Green's dyadic G NP T [START_REF] Ch | Near-field optics theories[END_REF][START_REF] Greffet | Image formation in near-field optics[END_REF] as follows from analysis of the fields created by the point dipole excitation of the individual NP or tip

e NP T = R NP T E d + E d = R NP T + 1 -4π ω 2 c 2 G 0 p = -4π ω 2 c 2 G NP T p, (3.3)
where G 0 is the free space dyadic, and the field of the point dipole is given by

E d = -4π ω 2 c 2 G 0 p. From Eq. (3.
3), the Green's dyadic of the NP or tip can be expressed as:

G NP T = 1 + R NP T G 0 . (3.4)
From Eq. (3.2) one obtains the field scattered by NP and STM tip

E + NP = R NP R T 1 -R NP R T [1 + R NP ] + R NP E d . (3.5)
This and a similar expression for E + T can be substituted into Eq. (3.1) to obtain the sought-after electric field. Note that R NP E d is the field created by the NP in response to the point dipole excitation.

The description may be greatly simplified using the assumption that for the present system the light emission is dominated by the NP contribution due to the antenna effect [START_REF] Novotny | Antennas for light[END_REF]. Indeed, only the gold NP responds resonantly to the excitation. The real part of the dielectric permittivity of tungsten is positive for the investigated ω range, i.e., the tip is not plasmonic [START_REF] Neacsu | Plasmonic light scattering from nanoscopic metal tips[END_REF][START_REF] Behr | Optical antenna properties of scanning probe tips: Plasmonic light scattering, tip-sample coupling, and near-field enhancement[END_REF]. Thus, the emitted radiation is approximately given by E tot = E + NP + E d . The validity of this approximation is demonstrated below by the direct calculation of the NP and tip contribution to the total polarization of the system. Thus we can write

E tot = S [1 + R NP ] -4π ω 2 c 2 G 0 p (3.6) = S -4π ω 2 c 2 G NP p,
where S is given by

S = R NP R T 1 -R NP R T + 1 (3.7)
In the non-retarded limit, S expresses the effect of the multiple electrostatic images of the point dipole p created by the coupled NP-tip system.

Considering the nanometer-scale junction between the NP surface and the tip, as well as the tip curvature radius (≈ 30 nm) which is small compared to the NP size (≈ 130 nm in edge length), the enhanced near fields are confined to a localized spot. Therefore, as a reasonable approximation, the operator S can be replaced by the scalar value S so that

E tot = -4π ω 2 c 2 G NP p, (3.8)
where p = Sp. Thus, the field emitted from the STM junction may be interpreted as the field resulting from the excitation of the NP by the effective point dipole p given by the simple rescaling of the inelastic tunneling dipole p.

Eq. (3.8) describes the field created by a point dipole located at r d above the NP surface and oriented along the tip-axis p = êz p. Thus, the effect of the tip location on the intensity and angular profile of the emitted light may be predicted from the Green's function of the NP only since E tot ∝ G NP êz . The Green's function G NP expansion in terms of the plasmonic eigenmodes of the NP [START_REF] Colas Des Francs | Theory of near-field optical imaging with a single molecule as light source[END_REF][START_REF] Sauvan | Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators[END_REF][START_REF] Carminati | Electromagnetic density of states in complex plasmonic systems[END_REF] leads to:

E tot ≈ n 4πω 2 ω 2 + iωη n -ω 2 n (ê z f * n (r d ))f n (r), (3.9)
where f n (r), ω n , and η n represent respectively the field, frequency and attenuation of the n th plasmonic eigenmode of the NP.

If only the dipolar-like modes are retained because of the small NP size, the fields f n are those created by the n-th plasmon eigendipole p n . p n can be obtained by integrating over the NP volume the polarization density vector corresponding to the n th plasmonic eigenmode. For the broad overlapping resonances here, the ω-dependence of the expansion coefficients may be neglected. Then, direct comparison between E tot given by Eq. (3.9) and the field radiated by the ensemble of the point dipoles allows to conclude that Eq. (3.9) describes the electric field radiated by the induced dipole at the NP:

P = C n (ê z f * n (r d )) p n , (3.10)
where C is a constant, and êz f * n is essentially the E z map of plasmonic eigenfields, as shown in Fig. 3.4(e). The nanotriangle supports four basic dipolar excitations: a vertical dipole perpendicular to the substrate, and three degenerate in-plane dipolar modes [START_REF] Awada | Selective Excitation of Plasmon Resonances of Single Au Triangles by Polarization-Dependent Light Excitation[END_REF][START_REF] Losquin | Unveiling Nanometer Scale Extinction and Scattering Phenomena through Combined Electron Energy Loss Spectroscopy and Cathodoluminescence Measurements[END_REF] which can be expressed as p x = êx p , and p ± = -1 2 êx ± √ 3 2 êy p . In order to test the validity of the models of Eq. (3.8) and Eq. (3.10), we compare the experimental data with theoretical results of decreasing level of complexity:

(i) Rigorous calculations including the complete NP-tip coupled system [START_REF] Borisov | Lanczos pseudospectral method for initial-value problems in electrodynamics and its applications to ionic crystal gratings[END_REF];

(ii) Model calculations based on Eq. (3.8) where the NP has been excited with a point dipole. Here, scattering by the tip and the ω dependence of p are neglected, but the Green's function of the NP G NP is calculated exactly using the Comsol Multiphysics package (version 4.2a);

(iii) Model calculations based on E z maps of the plasmonic eigenfields, as given by Eq. (3.10) where the f n fields of the NP plasmon eigenmodes are calculated at the resonance frequency, i.e., only the resonant dipolar contributions are taken into account. This makes the calculations in (iii) much less memory and time-consuming than those of (i) and (ii). While being less exact, approach (iii) has the advantage of retrieving all the data from a single calculation of the plasmonic eigenfields, while (i) and (ii) require calculations to be performed for each tip position. In (i) and (ii) the polarization density integrated over the NP or/and the NP and the tip volume defines the tip excitation position-dependent induced dipole P, its tilt angle Θ with respect to the tip axis, and intensity of emitted radiation I(ω) ∼ ω 4 P 2 . Since in our calculations the E z maps of plasmonic fields are not normalized, applying approach (iii) implies that the P ∥ P z ratio be normalized for one tip position using, e.g., one point in (ii), and all the other points are then retrieved, for both Θ and I, from this single normalization step. Figure 3.5 compares the results of the three theoretical approaches and experimental data taken from Ref [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF].

The effective dipole orientation Θ and the intensity of emitted radiation I are shown as a function of the tip position along the median of the upper NP triangular face (0 corresponds to the center of the triangle). In our experiments statistics does not allow to perform the radiation frequency resolved measurements. Therefore the intensity and the dipole orientation represent the values averaged over the radiated spectrum. To compare with experiment, the frequency resolved theoretical results have been integrated over the experimental energy window using a weighting function given by the ω-dependent detection efficiency and the IET power spectrum (∝ eU b -̵ hω, for ̵ hω ≤ eU b ; 0 otherwise [START_REF] Daniel Hone | Theory of light emission from small particle tunnel junctions[END_REF]).

We observe in Fig. 3.5(a) that the theoretical results obtained for the complete NP-tip system (approach (i))

closely reproduce the experimentally determined dependence of Θ, the effective dipole orientation, on the tip excitation position. Integration of the calculated polarization density of the NP-tip system over the gold NP and the W tip separately shows that the polarization of the W tip contributes about 30 % to the vertical P z dipole of the total system, but has little effect on the horizontal polarization P ∥ (less than 10 %). This result holds for all studied tip positions on the upper NP face. Thus, the light emission from the STM junction between non-plasmonic (here W) tip and plasmonic (here Au) NP is dominated by the polarization induced in the NP, which fully justifies the simplifying As follows from Fig. 3.5(b), the models (ii) and (iii), neglecting the presence of the STM tip reproduce the experimentally measured effective dipole angle Θ on a semi-quantitative level correctly capturing all the main trends.

Slightly larger tilt angle of the "effective dipole" is obtained in these simplified treatments because the tip polarization is neglected effectively reducing the P z component of the effective dipole. Remarkably, the calculation of the effective dipole angle Θ using (ii) the NP Green's function, and (iii) the simple model based on the E z maps of the plasmonic NP fields agree very well. This confirms the validity of the E z normalization and the utility of this simple approach. The striped areas in Fig. 3.5(a,b) indicate the position ranges where the tip is outside the upper NP face (light grey) and outside the NP (dark grey) so that experimental and calculated data cannot be compared because of the boundary effects. First, theory assumes right-angled side faces so that the field structure at the NP boundaries is not reproduced. Second, within these areas the tunneling current and associated transition dipole is not aligned along the z-axis. The difference between the complete and approximated theoretical treatments as appears in Fig. 3.5(d) close to the edges of the NP face can be also related to the boundary effects. Indeed, even provided small curvature of the tip, in these regions the axial symmetry of the near field distribution below the tip apex should be strongly perturbed. The assumption of axial orientation of the effective dipole does not hold in this case (an approximation S → S is not valid).

Conclusions and outlooks.

We have shown that the intricate NP-tip system may be substituted by a much simpler model system where the plasmonic NP is excited by a point dipole and the tip is not explicitly included in the calculations. Our results greatly simplify both the understanding and prediction of the light emission properties of the system, since they are solely determined by the plasmonic modes of the NP. Since the local density of photonic states (photonic LDOS) is related to the Green's function [START_REF] Carminati | Electromagnetic density of states in complex plasmonic systems[END_REF], the inelastic electron tunneling in the STM tunnel junction between a non-plasmonic tip and a plasmonic NP may be considered a probe of the local density of photonic modes, similarly to cathodoluminiscence and scanning near field optical microscopy [START_REF] Joulain | Definition and measurement of the local density of electromagnetic states close to an interface[END_REF][START_REF] García De Abajo | Probing the photonic local density of states with electron energy loss spectroscopy[END_REF][START_REF] Coenen | Directional emission from a single plasmonic scatterer[END_REF][START_REF] Carminati | Electromagnetic density of states in complex plasmonic systems[END_REF][START_REF] García-Etxarri | Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes[END_REF]. Above, our approach is discussed for a small particle and thus restricted to the dipolar modes. In the next section, it is applied to the general case of high-order multipolar excitations existing in larger particles. Spectral, spatial and angular distributions, polarization and radiative rates are thus expected to be controllable using all the wellestablished strategies in nanophotonics to engineer the local density of photonic modes. Our approach provides a simple means to optimize the design of electrically driven nanosources of light in view of their integration with microelectronics.

A new probe of the local density of photonic states

Collaborators: Javier Context and motivation. Controlling the rate of elementary quantum processes, e.g., light absorption and spontaneous emission, in quantum emitters is at the core of nanophotonics. Such control is possible through the modification of the electromagnetic surrounding of the quantum emitters, i.e., by engineering the local density of radiative and non-radiative electromagnetic states (R-and NR-EMLDOS). For instance, the lifetime of an excited molecule before it spontaneously decays to the ground state through the emission of a photon is directly related to the R-EMLDOS at the position of the molecule and at the frequency ω (the emitted photon has energy ̵ hω).

Thus, the dynamics of the optical processes that are fundamental in light sources may be controlled through the R-EMLDOS, which is crucial in particular for nanophotonics applied to information and communication technologies.

Indeed, accelerating the emission rate of a light source allows to modulate faster its emission, i.e., to increase the information capacity of the device driven by this source. Moreover, speeding up the radiative decay processes results in favoring them over coexisting non-radiative decay processes (i.e., the quantum yield is enhanced). Thus, less energy may be wasted into heat, resulting in a lower energy consumption of the device.

On a macroscopic scale (i.e., larger than the emission wavelength), the R-EMLDOS may be tailored using an optical cavity. At specific oscillation frequencies that may be tuned through the length of the cavity, the propagating waves reflected at the cavity ends form a standing wave pattern. The nodes and antinodes of this pattern correspond to density minima and maxima of the cavity eigenmodes, respectively. When placed at these nodes and antinodes, an electric dipole oscillating at the eigenmode frequency experiences the strongest inhibition or enhancement of its radiative emission, respectively. Importantly enough, the cavity effect on the emission rate may not only depend on the position of the dipole but also its orientation, i.e., the EMLDOS is a tensor (not a scalar ). Thus, it is the projected EMLDOS along the dipole direction that is relevant. On the nanometer scale, a different approach may be employed, based on the near-field coupling of the emitter to plasmonic nanostructures. At resonant excitation of the LSP eigenmodes in the nanostructures, the emitter may benefit from extremely strong and spatially localized increases of the R-EMLDOS, in so-called hot spots, by up to several orders of magnitude compared to free space.

As a consequence, measuring the EMLDOS in such cases requires the use of a nanoscale probe. Using electron energy loss spectroscopy (EELS) [START_REF] Kociak | Mapping plasmons at the nanometer scale in an electron microscope[END_REF][START_REF] Nelayah | Direct imaging of surface plasmon resonances on single triangular silver nanoprisms at optical wavelength 139 using low-loss eftem imaging[END_REF][START_REF] Talebi | Breaking the mode degeneracy of surface plasmon resonances in a triangular system[END_REF][START_REF] Hörl | Tomographic imaging of the photonic environment of plasmonic nanoparticles[END_REF] in a scanning transmission electron microscope (STEM), it has been shown that in most cases a high energy (≥ 10 keV) electron beam passing through a thin sample loses its energy in proportion to the EMLDOS (thus reflecting both the radiative and nonradiative contributions) projected along the direction of the electron beam [START_REF] García De Abajo | Probing the photonic local density of states with electron energy loss spectroscopy[END_REF][START_REF] Hohenester | Electron-energy-loss spectra of plasmonic nanoparticles[END_REF]. The lateral component may be determined from the lateral deflection of the inelastically scattered electrons [START_REF] Krehl | Spectral field mapping in plasmonic nanostructures with nanometer resolution[END_REF]. In a related technique, cathodoluminescence, where again a high-energy electron beam is used for excitation, the resulting emitted light is detected and it is the projected R-EMLDOS that is probed [START_REF] Losquin | Unveiling Nanometer Scale Extinction and Scattering Phenomena through Combined Electron Energy Loss Spectroscopy and Cathodoluminescence Measurements[END_REF][START_REF] Kuttge | Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence[END_REF][START_REF] Sapienza | Deep-subwavelength imaging of the modal dispersion of light[END_REF][START_REF] Losquin | Link between cathodoluminescence and electron energy loss spectroscopy and the radiative and full electromagnetic local density of states[END_REF], though dark modes may also be detected through a combination of methods [START_REF] Myroshnychenko | Unveiling and imaging degenerate states in plasmonic nanoparticles with nanometer resolution[END_REF]. Other techniques for mapping the EM-LDOS are based on the use of fluorescent probes [START_REF] Hoogenboom | The single molecule probe: Nanoscale vectorial mapping of photonic mode density in a metal nanocavity[END_REF][START_REF] Beams | Nanoscale fluorescence lifetime imaging of an optical antenna with a single diamond nv center[END_REF][START_REF] Ropp | Nanoscale imaging and spontaneous emission control with a single nano-positioned quantum dot[END_REF][START_REF] Krachmalnicoff | Towards a full characterization of a plasmonic nanostructure with a fluorescent near-field probe[END_REF][START_REF] Schell | Scanning single quantum emitter fluorescence lifetime imaging: Quantitative analysis of the local density of photonic states[END_REF][START_REF] Da Cao | Mapping the radiative and the apparent nonradiative local density of states in the near field of a metallic nanoantenna[END_REF][START_REF] Aigouy | Mapping and quantifying electric and magnetic dipole luminescence at the nanoscale[END_REF][START_REF] Cuche | Nearfield hyperspectral quantum probing of multimodal plasmonic resonators[END_REF],

two-photon luminescence [START_REF] Viarbitskaya | Tailoring and imaging the plasmonic local density of states in crystalline nanoprisms[END_REF][START_REF] Imaeda | Static and dynamic near-field measurements of high-order plasmon 141 modes induced in a gold triangular nanoplate[END_REF], and scanning near-field optical microscopy (SNOM) [START_REF] Chicanne | Imaging the local density of states of optical corrals[END_REF][START_REF] Rang | Optical near-field mapping of plasmonic nanoprisms[END_REF][START_REF] Imaeda | Imaging of plasmonic eigen modes in gold triangular mesoplates by near-field optical microscopy[END_REF]. Photoelectron emission microscopy (PEEM) is also a remarkable technique for imaging optical near-fields [START_REF] Awada | Selective Excitation of Plasmon Resonances of Single Au Triangles by Polarization-Dependent Light Excitation[END_REF][START_REF] Frank | Short-range surface plasmonics: Localized electron emission dynamics from a 60-nm spot on an atomically flat single-crystalline gold surface[END_REF].

The scanning tunneling microscope (STM) is a well-known tool for mapping the electronic local density of states [START_REF] Tersoff | Theory of the scanning tunneling microscope[END_REF], that is, the number of electronic levels per unit volume in an infinitesimal energy range, which may even be investigated optically in certain cases [START_REF] Schull | Imaging confined electrons with plasmonic light[END_REF]. While light was first seen from the STM tunnel junction as early as the late 1980s [START_REF] Gimzewski | Enhanced Photon Emission in Scanning Tunnelling Microscopy[END_REF], it is not until recently that an "STM-nanosource" has been used systematically to study the properties of surface plasmon polaritons (SPPs) in plasmonic gaps and nanostructures [START_REF] Kuhnke | Atomic-Scale Imaging and Spectroscopy of Electroluminescence at Molecular Interfaces[END_REF][START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Wang | Plasmon scattering from holes: from single hole scattering to Young's experiment[END_REF][START_REF] Myrach | Photon mapping of individual ag particles on MgO/mo(001)[END_REF][START_REF] Yu | Tunneling-electron-induced light emission from single gold nanoclusters[END_REF][START_REF] Leon | Photon superbunching from a generic tunnel junction[END_REF][START_REF] Martín-Jiménez | Unveiling the radiative local density of optical states of a plasmonic nanocavity by stm[END_REF] and to locally and electrically activate directional sources of light [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Cao | Directional light beams by design from electrically driven elliptical slit antennas[END_REF]. Strikingly, aperture SNOM, i.e., a version of SNOM based on the detection of the electric nearfield of the sample through an uncoated tapered optical fiber, has long been considered the natural counterpart of STM for the measure of EMLDOS and sometimes refered to as the "photon STM". This illustrates quite well that the potential of STM-induced light as a probe of the EMLDOS has long been unconsidered.

The electrical excitation of photons and plasmons in the STM is generally attributed to the inelastic tunneling current between the tip and the sample [START_REF] Gimzewski | Enhanced Photon Emission in Scanning Tunnelling Microscopy[END_REF][START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF][START_REF] Parzefall | Optical antennas driven by quantum tunneling: a key issues review[END_REF]. Similar to the classical description of quantum emitters, the inelastic tunneling current may be represented as an oscillating electric point dipole. This dipole is located in the nanocavity formed between the STM tip and the sample and oriented in the direction of the tunneling current [START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Aizpurua | Role of tip shape in light emission from the scanning tunneling microscope[END_REF][START_REF] Parzefall | Optical antennas driven by quantum tunneling: a key issues review[END_REF][START_REF] Uehara | Theory of visible light emission from scanning tunneling microscope[END_REF]. Given this description of the inelastic tunneling current and the above definition of the EMLDOS, the question naturally arises whether the STM-nanosource may be used to probe the electromagnetic local density of states. More specifically, does the radiative yield of this nanosource provide a useful tool for determining the radiative component of the EMLDOS?

Results and discussion.

In order to answer the question posed above, we carry out a series of spectrally and spatially resolved measurements using our STM-nanosource on individual triangular gold platelets. We also use spatially resolved EELS to obtain maps of the total EMLDOS. Along with this experimental study, we perform electromagnetic calculations of the EMLDOS and R-EMLDOS, leading to maps of these quantities as a function of position on the triangular gold platelet. Similarly, calculations of the emitted light when an STM tip and vertical oscillating dipole are scanned over a triangular gold platelet are performed. This theoretical analysis is further used to unambiguously identify the nature of the plasmonic modes and their contributions to the near and far fields.

All the experiments are performed on monotwinned gold crystals of triangular shape, either deposited on ITOcoated substrate glass coverslips (for STM measurements), or 15 nm thick silicon nitride membranes (for EELS measurements). The connection between these experimental spectra and the R-EMLDOS is made in Fig. 3.6(f). Here we calculate the spectrum of the light emitted into the substrate when the STM-nanosource excites the platelet. These results include the STM tip and take into account the STM excitation spectrum [START_REF] Lambe | Light emission from inelastic electron tunneling[END_REF] and the collection geometry in transmission (i.e., only the emission in the half space below the platelet is considered). The theoretical results in Fig. 3.6(f) are obtained for triangles of different side lengths and for the two relevant tip positions addressed experimentally. While the peaks in the simulated spectra are narrower than in the experiment, probably due to the idealization of the system used for the calculations, the same general trend emerges from the calculated and measured data. Figures 3.6(g) and 3.6(h) display the calculated surface charge densities for the center and edge tip excitation positions at two specific photon wavelengths, i.e., λ 0 = 620 and 860 nm, respectively. As in Fig. 3.6(f), the calculations include the STM tip. At the short wavelength (λ 0 = 620 nm), the excitation in the center of the triangle (see Fig. 3.6(g)) yields a concentric surface charge distribution that is typical of a breathing mode, or film-like modes [START_REF] Schmidt | Dark plasmonic breathing modes in silver nanodisks[END_REF][START_REF] Schmidt | Universal dispersion of surface plasmons in flat nanostructures[END_REF][START_REF] Krug | Probing plasmonic breathing modes optically[END_REF][START_REF] Keast | Higher order plasmonic modes excited in ag triangular nanoplates by an electron beam[END_REF][START_REF] Campos | Plasmonic breathing and edge modes in aluminum nanotriangles[END_REF][START_REF] Schmidt | How dark are radial breathing modes in plasmonic nanodisks[END_REF] launched on a gold film by a vertical oscillating dipole and discretized by the reflections at the platelet boundaries. Breathing modes contribute preferentially to the EMLDOS above the center of the platelet. At the longer wavelength (λ 0 = 860 nm), the excitation on the edge of the triangle (see Fig. 3.6(h)) induces a symmetric surface charge distribution that resembles that of an edge mode. Such modes contribute preferentially to the EMLDOS above the vertices and edges of the triangle, and the number of nodes in (g,h) Surface charge density induced at a wavelength of (g) 620 and (h) 860 nm for the tip location indicated in the insets. The calculations are performed with a tip (curvature radius 40 nm, length 400 nm) placed 2 nm above the platelet surface (substrate index of refraction is 2). Adapted with permission from [START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]. Copyright (2020) American Chemical Society. (e) Calculated energy-resolved maps of the EM-LDOS, R-EM-LDOS, and of the intensity of the light emitted by the tunneling STM-nanosource when scanned over a triangular platelet with side length L = 650 nm. The EM-LDOS is calculated 1 nm above the upper face of the platelet. The STM tip scans the upper face of the platelet at a constant tipsurface distance of 2 nm. Different columns correspond to the maps obtained for different radiation wavelengths as indicated. Adapted with permission from [START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]. Copyright(2020) American Chemical Society.

the induced charge density distribution of these modes increases with decreasing wavelength [START_REF] Schmidt | Universal dispersion of surface plasmons in flat nanostructures[END_REF][START_REF] Keast | Higher order plasmonic modes excited in ag triangular nanoplates by an electron beam[END_REF][START_REF] Campos | Plasmonic breathing and edge modes in aluminum nanotriangles[END_REF]. The low-order modes of this type appear at long wavelengths and include the dipolar plasmon resonance (located above λ 0 = 2500 nm) and the quadrupolar plasmon resonance at about λ 0 = 1300 nm. By symmetry, the breathing modes have no net induced dipole moment and are, in general, much less radiative as compared to the edge modes. A typical red shift with increasing size (due to the reduction of the restoring force on the induced surface charge with distance) is seen in both cases; however, this shift is less pronounced for the excitation in the center of the top face, consistent with excited breathing modes [START_REF] Dousse | Ultrabright source of entangled photon pairs[END_REF][START_REF] Hoang | Ultrafast spontaneous emission source using plasmonic nanoantennas[END_REF]. Now, we examine the capacity of our STM-nanosource to reveal the spatial distribution of the R-EMLDOS. We perform an experiment where the STM tip is raster-scanned across a triangular gold platelet and, at each point in the scan, the emitted radiation is collected in the far field. Thus, a map of the STM-excitation efficiency on the sample (or "radiation map") is measured. Since EELS is a loss spectroscopy, it reflects the total EMLDOS projected along the axis of the incoming electron beam [START_REF] García De Abajo | Probing the photonic local density of states with electron energy loss spectroscopy[END_REF]; that is, it is equally sensitive to both the dark (i.e., nonradiative) and bright (or radiative) modes of the system. In the STM excitation experiment, however, the emitted light is detected in the far field. This would suggest that the STM-nanosource experiments are only sensitive to the radiative R-EMLDOS, whose leading contribution is from the bright modes of the sample. The dark modes of the triangular platelet should only contribute to the observed light emission maps if the STM tip or retardation effects allow these modes to couple to the far field. In order to fully interpret the STM-nanosource results and to conclude on the link between the experimental data and the R-EMLDOS, we perform calculations of the total EMLDOS, of the R-EMLDOS, and of the photon emission as a function of position for selected wavelengths. Each selected wavelength in Fig. 3.7(e) corresponds to the excitation of a different plasmonic mode of the platelet.

From the calculated total EMLDOS, R-EMLDOS, and intensity maps in Fig. 3.7(e) it follows that, for longer wavelengths (820 -1300 nm), the edge plasmon modes are predominantly excited, as seen from the intense bright spots along the edges and vertices of the platelet. The strong radiative nature of the excited edge modes explains the close similarity between the EM-LDOS, R-EMLDOS, and intensity maps at these wavelengths. As the wavelength decreases from 750 to 600 nm, the signal in the center of the maps increases, reflecting the increasing role of the breathing modes (see the left-hand side of Fig. 3.7(e)). This is in full agreement with the STM and EELS measurements of Figs. 3.7(a) and 3.7(c). The third row of Fig. 3.7(e) shows the calculated photon emission maps (i.e., the emission into the substrate taking into account the presence of the tip and the STM-excitation spectrum).

These results match the radiative R-EMLDOS: the number of nodes along the triangle edges as well as the structure in the center of the platelet are well reproduced in both types of images. Our joint experimental and theoretical study shows that the radiation maps obtained with an STM-nanosource are directly related to the R-EMLDOS. Thus, the STM offers an extremely attractive method to locally, and eventually simultaneously, probe the atomic, electronic, and photonic structure of a nano-object.

Note, however, that the relative intensities of the different contributions are not always the same in the calculated R-EMLDOS and photon emission maps (i.e., second and third rows in Fig. 3.7(e)). This is attributed to the presence of the STM tip. While it has been shown that a nonplasmonic tip does not perturb the energy spectrum of the inherent modes of the particle (see in Ref. [START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]), it appears that the tip alters the mode coupling to the far field, as seen from the increased intensity from the center of the photon emission maps. In particular, the tip enhances the far-field coupling of the numerous breathing modes at short wavelengths.

Conclusions and outlooks.

In summary, we have used the inelastic tunneling current from an STM working in air to locally and electrically excite the plasmonic modes of a triangular gold platelet. The light resulting from the radiative decay of these plasmonic modes is collected through the transparent substrate. Both tip positiondependent light emission spectra as well as emission maps have been acquired, revealing that breathing modes of higher energy are more efficiently excited when the STM tip is positioned in the center of the upper face of the platelet, while edge modes at lower energies are preferably excited when the STM tip is positioned on an edge.

Acquiring EELS maps on similar triangular platelets yields qualitatively similar results. The theoretical study of STM-induced light emission reproduces the main experimental trends and confirms the excitation of breathing and edge modes of the nanoparticle, associated with particular tip positions and emission energies. More importantly, a detailed comparison of the calculated total EMLDOS and the radiative R-EMLDOS reveals subtle differences in the corresponding mapping of each mode, depending on its radiative nature. Thus, the STM may be considered not only a tool for mapping the electronic LDOS in its usual operation mode, but also for investigating the R-EMLDOS when the emitted light is collected. This work introduces a new technique for probing the radiative R-EMLDOS and may be applied to obtain relevant information on nanoantennas [START_REF] Giannini | Plasmonic Nanoantennas: Fundamentals and Their Use in Controlling the Radiative Properties of Nanoemitters[END_REF][START_REF] Novotny | Antennas for light[END_REF][START_REF] Biagioni | Nanoantennas for visible and infrared radiation[END_REF][START_REF] Koenderink | Single-photon nanoantennas[END_REF], improved nanoplatforms for surface-enhanced Raman scattering (SERS) [START_REF] Kleinman | Creating, characterizing, and controlling chemistry with sers hot spots[END_REF], single photon emission [START_REF] Koenderink | Single-photon nanoantennas[END_REF] and strong coupling in hybrid plasmonic-emitter systems [START_REF] Törma | Strong coupling between surface plasmon polaritons and emitters: a review[END_REF].

What is next? Recently, we have focused our investigations on the tip effects on the STM-induced emission spectrum, which may not be negligible in the case of comparatively small plasmonic NPs, i.e., when the NP radius is comparable to the curvature radius of the tip. Investigating these effects is crucial to definitely establish STMinduced light as a nanoprobe of the EMLDOS, or to determine under what conditions it may be considered as such.

Thus, we experimentally and theoretically analyze the relationship between the STM-induced emission spectra of gold NPs and the "natural" resonance of their plasmonic modes. Strong energy shifts and broadening have been reported in STL of plasmonic NPs in comparison with their "natural" dipolar LSP resonances [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Nilius | Tip influence on plasmon excitations in single gold particles in an STM[END_REF], as measured using dark-field optical microscopy (DFM) or calculated using analytical models. These discrepancies have been ascribed to the contribution of tip-induced gap plasmons. Such tip effects have also been discussed in the context of scattering-type scanning near-field optical microscopy (s-SNOM) [START_REF] García-Etxarri | Influence of the tip in near-field imaging of nanoparticle plasmonic modes: Weak and strong coupling regimes[END_REF]. However, the discrepancies described above were also observed in the absence of tip-surface gap plasmon, e.g., using a non-plasmonic tungsten tip [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. As STL is increasingly used as a nanoscale optical imaging and spectroscopic probe of plasmonic NPs [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF][START_REF] Myrach | Photon mapping of individual ag particles on MgO/mo(001)[END_REF][START_REF] Yu | Tunneling-electron-induced light emission from single gold nanoclusters[END_REF][START_REF] Downes | Two-sphere model of photon emission from the scanning tunneling microscope[END_REF][START_REF] Olkhovets | Scanning tunneling microscope induced luminescence of lithographically prepared Au dots[END_REF][START_REF] Nilius | Photon emission spectroscopy of individual oxide-supported silver clusters in a scanning tunneling microscope[END_REF][START_REF] Silly | Coupled plasmon modes in an ordered hexagonal monolayer of metal nanoparticles: A direct observation[END_REF][START_REF] Silly | Single nanoparticle manipulation with simultaneously recorded STM-induced light emission[END_REF][START_REF] Kusová | Plasmon modes in light emission from silver nanoparticles induced by a scanning tunneling microscope[END_REF], it is crucial that the origins of these energy shifts and broadening be clarified. The people involved in this project are Andrey G. Borisov (ISMO), Sylvie Marguet (NIMBE), Mario Zapata-Herrera (postdoc, DIPC, San Sebastían, Spain), Benoît Rogez (formerly a PhD student at ISMO, now a postdoc at Institut Fresnel, Marseille).

Chapter 4

Applications in plasmonics (II): driving the emission of a plasmonic lens

In the previous chapter (Chap. 3), we have considered the inelastic tunneling of electrons between the sharp tip of an STM and a metallic sample as a local, low-energy, electrical excitation of optical modes, which may be used to map the local density of photonic states at the sample surface or to drive the emission of light from a plasmonic nanostructure. Thus, we have merely focused on the light nanosource character of the tunneling junction. However, on a flat metallic surface, the tip-sample junction may also behave as an ideal, isotropic, nanosource of circular plasmonic waves, i.e., propagating surface plasmon polaritons (SPPs). Actually, this property is already underlying in the STM-excitation of breathing modes on the flat facet of a gold platelet shown in Sec. 3.3, since such modes result from the discretization of SPPs due to the reflections at the facet boundaries. Our group has demonstrated the possibility of exciting such circular plasmonic waves using an STM [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF]. In addition, we have experimentally measured the temporal [START_REF] Wang | Temporal coherence of propagating surface plasmons[END_REF] and spatial [START_REF] Wang | Plasmon scattering from holes: from single hole scattering to Young's experiment[END_REF] coherence of such an SPP nanosource, as well as the mutual coherence of the emitted light and SPP waves [START_REF] Wang | Scattering of electrically excited surface plasmon polaritons by gold nanoparticles studied by optical interferometry with a scanning tunneling microscope[END_REF], which is key for the use of local excitations with electrons in optical interferometry and holography experiments [START_REF] Schilder | Phase-resolved surface plasmon scattering probed by cathodoluminescence holography[END_REF][START_REF] Sannomiya | Cathodoluminescence phase extraction of the coupling between nanoparticles and surface plasmon polaritons[END_REF]. Below, we use our STM nanosource of SPPs to drive comparatively large (micrometer-sized) lithographied structures that may be considered basic components in future electrically driven plasmonic microdevices. In particular, such microstructures may be plasmonic lenses.

In Sec. 4.1, we demonstrate the generation of cylindrical vector (CV) beams, a class of light beams that is highly valued in various fields of optics. Here, such beams are produced from a low-energy, electric, microscale light source, by combining a plasmonic lens with the ability to locally excite propagating SPPs on gold films using the STM. In particular, radially polarized beams (a prototype of CV beam) are emitted with a high directivity that overpasses the performance of the existing integrated microsources of CV beams. In Sec. 4.2, we use the unique combination of STM and angle-resolved optical spectroscopy to probe the spectral response of various plasmonic lenses. Based on these results, we propose simple design rules for optimized light beaming devices with the smallest possible footprint.

An electrical microsource of radially polarized light beams

Collaborators: Aurélien Drezet and Serge Huant (Institut Néel, Grenoble). Student involved: Shuiyan Cao (PhD, ISMO). Aurélien Drezet performed the numerical simulations. Shuiyan and I carried out the STM-based experiments.

The plasmonic structures were fabricated by Jean-François Motte at the NanoFab facility in Grenoble.

This section is adapted from Shuiyan Cao, Eric Le Moal, Elizabeth Boer-Duchemin, Gérald Dujardin, Aurélien

Drezet, and Serge Huant, "Cylindrical vector beams of light from an electrically excited plasmonic lens." Appl. Phys.

Lett., 105 [START_REF] Bachelot | Near-field optical microscope based on local perturbation of a diffraction spot[END_REF]:111103, September 2014, with permission from AIP Publishing. [START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF] Context and motivation. Cylindrical vector (CV) beams are light beams that have spatially varying polarization properties of cylindrical symmetry and zero intensity along the propagation axis [START_REF] Zhan | Cylindrical vector beams: from mathematical concepts to applications[END_REF]. The unique propagation, diffraction and focusing properties of CV beams are attracting increasing interest, in particular for their use in the control of light-matter interactions on a submicrometer scale [START_REF] Oscar | Optical nanoprobing via spin-orbit interaction of light[END_REF][START_REF] Neugebauer | Polarization tailored light driven directional optical nanobeacon[END_REF]. Applications have been reported in various fields including quantum optics [START_REF] Gabriel | Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes[END_REF], high-resolution imaging [START_REF] Colin | Annular pupils, radial polarization, and superresolution[END_REF], and in the trapping and manipulation of nano-objects [START_REF] Zhan | Trapping metallic rayleigh particles with radial polarization[END_REF]. Numerous optical methods have been reported either for the generation of CV beams using a macroscopic light source [START_REF] Zhan | Cylindrical vector beams: from mathematical concepts to applications[END_REF] or for the conversion of light beams with homogeneous polarization into CV beams using birefringent materials, phase plates, spatial light modulators [START_REF] Maurer | Tailoring of arbitrary optical vector beams[END_REF], subwavelength gratings [START_REF] Lombard | Polarization control of non-diffractive helical optical beams through subwavelength metallic apertures[END_REF] or metallic apertures [START_REF] Lezec | Beaming light from a subwavelength aperture[END_REF]. Comparatively much less has been reported for electrically driven microscale light sources generating CV beams [START_REF] Ding | An electrical injection metallic cavity nanolaser with azimuthal polarization[END_REF][START_REF] Xu | The generation of a compact azimuthally polarized vertical-cavity surface emitting laser beam with radial slits[END_REF][START_REF] Cai | Generation of compact radially polarized beam at 850 nm in vertical-cavity surface-emitting laser via plasmonic modulation[END_REF], though such sources are highly desirable for integrated applications, e.g., in data communications or optical sensors. An electrically driven metallic cavity nanolaser generating an azimuthally polarized light beam has been demonstrated recently [START_REF] Ding | An electrical injection metallic cavity nanolaser with azimuthal polarization[END_REF], as well as microscale vertical cavity surface emitting lasers (VCSEL) incorporating surface gratings so as to yield either azimuthally [START_REF] Xu | The generation of a compact azimuthally polarized vertical-cavity surface emitting laser beam with radial slits[END_REF] or radially polarized beams [START_REF] Cai | Generation of compact radially polarized beam at 850 nm in vertical-cavity surface-emitting laser via plasmonic modulation[END_REF].

The applications of these sources are limited, however, by the relatively high angular spread of their emission (±11.5 ○ [270] and ±37 ○ [START_REF] Ding | An electrical injection metallic cavity nanolaser with azimuthal polarization[END_REF]).

Results and discussion.

In this Section, we report on an original method for the electrical generation of radially polarized beams of very low angular spread (±4 ○ ) from a microscale plasmonic structure. As shown in Fig. 4.1(a), the plasmonic structure is a plasmonic lens [START_REF] Chen | Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination[END_REF] consisting of concentric circular slits etched in a thick gold film.

Local, low-energy, electrical excitation of SPPs is achieved with tunnel electrons from the tip of an STM on the central disk region of the structure. SPPs propagate from the excitation site to the slits which then scatter the SPPs into light. The resulting emitted radiation is radially polarized and forms a cylindrical beam with a diameter that is approximately that of the central disk of the plasmonic lens. In this work, we experimentally and theoretically study how the central disk diameter, the number of slits and the excitation site affect the angular spread. We show that by changing the excitation position of the tip we can vary the emission direction up to about 10 ○ from the normal while preserving a beam of low angular spread (±6 ○ ). However, the polarization state is gradually modified as the tip is moved off-center, thus destroying the pure CV nature of the light, while maintaining a highly collimated beam.

We use the experimental setup described in Sec. 2.1, which consists of an STM head mounted on an inverted optical microscope [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. A nanopositioning stage controls the sample position between the tip of the STM and a high numerical aperture oil-immersion objective lens (NA = 1.45). The plasmonic structure is prepared by focused ion beam (FIB) etching of a gold film, 200 nm in thickness, thermally evaporated on a glass coverslip coated with a 100 nm-thick layer of indium tin oxide (ITO). The design of the structure is either a five-slit circular grating or a single circular slit, with the following parameters: slit width 300 nm, etch depth 200 nm, grating period 700 nm. Structures with central disks of inner diameters D in = 1, 2, 3, 4, 5 and 6 µm are examined. STM tips are electrochemically etched tungsten wires. The sample is biased to 2.8 V while the tip is grounded (setpoint tunnel current in the range of 1 -6 nA). Inelastic tunneling of the electrons from the tip to the sample leads to the excitation of two-dimensional circular SPP waves that propagate isotropically away from the tip location [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF]. The gold film is thick enough so as to prevent SPP leakage radiation in the glass; thus, only the light from SPPs scattered at the slits of the structure is detected below the substrate. The collected light is imaged on a cooled CCD camera, either in the real plane or in the Fourier plane, thus providing the spatial and the angular emission distributions, respectively. emission is distributed with cylindrical symmetry over the five slits; the emission intensity rapidly decreases in an exponential manner in the outer slits. This is expected since SPP scattering at the slits greatly reduces the SPP propagation length. We then measure the real-plane image under similar conditions but with a linear polarizer in front of the CCD camera (the polarization axis is oriented as shown in Fig. 4.1(c)). Total extinction along the orthogonal axis indicates that the polarization of the collected light is purely radial.

-30°30°0 °30°0 °-30°30°0 °-60°- 30°6 0°3 0°0 °-60°- 30°± 4°±4°± 6°± 17°θ = 2°θ = 0°θ = -10°( a) (b) (c) (d) (e) (f) (g) (h)
When the tip is centered on the plasmonic lens, a small and intense doughnut-shaped spot is seen in the center of the Fourier plane (see Fig. . This is at least three times lower than previously reported values for other electrically driven microscale sources of CV beams (e.g., ±11.5 ○ for a VCSEL source [START_REF] Xu | The generation of a compact azimuthally polarized vertical-cavity surface emitting laser beam with radial slits[END_REF] or ±37 ○ for a metallic cavity nanolaser [START_REF] Ding | An electrical injection metallic cavity nanolaser with azimuthal polarization[END_REF]). Remarkably, the angular spread of our microscale light source is also much lower than that which has been reported so far for vertically emitting plasmonic antennas such as patch [START_REF] Belacel | Controlling Spontaneous Emission with Plasmonic Optical Patch Antennas[END_REF], aperture [START_REF] Yaacobi | Vertical emitting aperture nanoantennas[END_REF], and bull's eye optical antennas [START_REF] Aouani | Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations[END_REF] which are driven by emitter or waveguide near-field coupling. This effect is both due to the design of our plasmonic lens and to the extreme spatial selectivity of the electrical excitation with tunnel electrons [START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF].

The Fourier-plane images in Fig , a tilt of 10 ○ is obtained, with basically the same azimuthal angular spread (±4 ○ ) but a slightly higher radial angular spread (±6 ○ ). When beam collimation is the desired result, this technique provides a method to electrically generate a narrow beam from a microscale light source, and the ability to control the emission direction within a 0-10 ○ polar range and-thanks to cylindrical symmetry-a 0-360 ○ azimuthal range. Figure 4.2(g) reveals, however, that the polarization state is no longer purely radial when the tip is moved substantially from the center. This is even more obvious with the tip at 1.8 µm (i.e., only 0.7 µm from the inner edge of the first slit). In Fig. 4.2(d), the emission is highly divergent, with a strong contribution above the critical angle. As well, the polarization-filtered image of When compared to each other, these images reveal that the number of slits has an important effect on the beam collimation. The emission from a single circular slit yields a second order Bessel function intensity profile in the Fourier plane, with non-negligible secondary maxima, and an intense donut-shaped central pattern. The existence of the secondary lobes in the emission pattern means that the collimation is degraded when only one circular slit is present. Conversely, the intensity profile in the Fourier plane for a multiple slit grating is a coherent superposition of Bessel functions with secondary maxima at different radii; therefore, only the central doughnut-shaped patterns interfere constructively and the secondary maxima cancel each other out.

We use a simple analytical model [START_REF] Mollet | Plasmonic interferometry: Probing launching dipoles in scanning-probe plasmonics[END_REF] to simulate the Fourier-plane images of Fig. 4.3 and determine the theoretical angular spread of the emitted light. The SPP scattering into photons at the slits is modeled as the radiation of multiple electric dipoles located along circles of the same diameter as the circular slits. We then calculate the complex electric field vector of these dipoles in the far field. Due to the subwavelength width of the slit, we assume that only the in-plane radial field component is scattered toward the substrate; hence the dipoles in the model are horizontally oriented along the radial direction. When the tip is centered, all the dipoles along each circle emit in phase and with the same amplitude. In the model, we set a relative weight on the contribution of the five circles that exponentially decreases with their diameter. from a five-slit circular grating and a single circular slit. We note, however, that the model overestimates the angular spread for single circular slits with the smaller central disk diameters, probably because the width of the slit (not taken into account in the model) becomes non-negligible as compared to the diameter of the structure. In summary, a plasmonic lens consisting of a single circular slit may be preferable when the smallest total size of the structure is desired; however, a structure with multiple concentric slits yields better beam collimation with lower angular spread and improved damping of secondary lobes. Moreover, it is expected that the efficiency of the SPP scattering into light is significantly higher for a five-slit circular grating than for a single circular slit, a crucial point for the optimization of the emission flux of a light source.

Conclusions and outlooks.

In this section, we have demonstrated an electrically driven, microscale light source emitting radially polarized beams with very low angular spread (±4 ○ ). The basis of this light source is a plasmonic lens, whose SPPs are locally excited through the inelastic tunneling of low-energy electrons from the tip of an STM. This excitation method may be described by the radiation of a vertical electric dipole inside the tip-sample gap [START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]. This makes it ideal for plasmonic structures with cylindrical symmetry. Furthermore, this excitation method may be integrated with current microelectronic technology, since it requires only low voltage (< 3 V), low current (nA) and may be adapted on a chip as a planar tunnel junction. (This is an important advantage over other local SPP excitation methods which use high-energy electron beams or near-field optical probes). We expect that our technique may be extended to the generation of many other kinds of CV beams, simply by changing the design of the pattern etched in the gold film. In particular, two-dimensional chiral structures such as spirals may be used to generate light beams that carry optical orbital angular momentum. Such light beams have promising applications in the manipulation of nano-objects [START_REF] Gorodetski | Generating far-field orbital angular momenta from near-field optical chirality[END_REF]. It should also be noted that the emission of a radially polarized beam through the local SPP excitation in the center of a plasmonic lens constitutes the perfect time-reversed process of the SPP focusing of a radially polarized beam from the far-field [START_REF] Chen | Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination[END_REF][START_REF] Liu | Focusing surface plasmons with a plasmonic lens[END_REF][START_REF] Lee | The use of plasmonics in light beaming and focusing[END_REF]. Thus, in order to produce a "designer light beam", the suitable pattern to be etched in the gold film may be found for virtually any desired emission pattern through a numerical time-reversal procedure [START_REF] Leuchs | Time-reversal symmetry in optics[END_REF].

So far, in the work presented above, we have ignored the broad power spectrum of the excitation source and the frequency-dependent behavior of the plasmonic lenses; however, even of simple design, such microstructures may have intricate spectral response. This issue is addressed in the next section (Sec. 4.2), where we combine STM and angle-resolved optical spectroscopy to reveal the spectral response of a plasmonic lens. Context and motivation. Just as light may be manipulated using glass elements, the propagation of SPPs may be controlled using a plasmonic lens [START_REF] Fu | Plasmonic Lenses: A Review[END_REF]. Such a lens may be constructed from a series of concentric circular slits etched in a gold film. In particular, such a structure is used to transform a propagating light beam into a focused plasmon spot [START_REF] Chen | Visualization of fermi's golden rule through imaging of light emission from atomic silver chains[END_REF][START_REF] Steele | Resonant and non-resonant generation and focusing of surface plasmons with circular gratings[END_REF][START_REF] Yanai | Plasmonic focusing with a coaxial structure illuminated by radially polarized light[END_REF][START_REF] Wróbel | Focusing Radially Polarized Light by a Concentrically Corrugated Silver Film without a Hole[END_REF][START_REF] Yue | Ultrasmall and ultrafast all-optical modulation based on a plasmonic lens[END_REF][START_REF] Ji | Optimization of structure parameters of concentric plasmonic lens for 355 nm radially polarized illumination[END_REF]. Reciprocally, a nanoscale emitter at the lens focus (e.g., a quantum dot) may transfer energy via near-field coupling to SPPs which propagate and scatter at the circular slits into an outgoing light beam [START_REF] Chul Jun | Plasmonic beaming and active control over fluorescent emission[END_REF][START_REF] Harats | Full Spectral and Angular Characterization of Highly Directional Emission from Nanocrystal Quantum Dots Positioned on Circular Plasmonic Lenses[END_REF]. Thus a plasmonic lens is both a light/SPP converter and a focusing/collimating optical component which, like an optical antenna, links the optical near and far-fields. Above in Sec. 4.1, we have been shown that the combination of such a plasmonic structure with a local, electrical source of SPPs leads to the emission of a cylindrical vector beam of light [START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF], a class of light beams that has various applications ranging from optical communications to manipulation of single nanoparticles [START_REF] Zhan | Cylindrical vector beams: from mathematical concepts to applications[END_REF]. The local, electrical excitation of propagating SPPs may be achieved with low-energy electrons in an STM [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Zhang | Edge scattering of surface plasmons excited by scanning tunneling microscopy[END_REF][START_REF] Uehara | Theory of visible light emission from scanning tunneling microscope[END_REF], or high-energy electrons in a scanning electron microscope (SEM) [START_REF] Van Wijngaarden | Direct imaging of propagation and damping of near-resonance surface plasmon polaritons using cathodoluminescence spectroscopy[END_REF][START_REF] García De Abajo | Optical excitations in electron microscopy[END_REF][START_REF] Schoen | The Planar Parabolic Optical Antenna[END_REF]. Low-energy electrical excitation of a plasmonic lens opens up new possibilities for the integration of plasmonics with electronics.

Revealing the emission response of a micro-optical component

However, a particularity of the excitation of SPPs with electrons is that the result is broadband in frequency [START_REF] Zhang | Edge scattering of surface plasmons excited by scanning tunneling microscopy[END_REF].

Notably, low-energy electrons in a tunnel junction may excite SPPs of any energy lower than the electron energy fixed by the applied voltage [START_REF] Daniel Hone | Theory of light emission from small particle tunnel junctions[END_REF]. Thus, the resulting SPP power spectrum may spread over the visible and infrared frequencies. This poses the question of how a plasmonic lens responds to such a broadband source, given that such structures are usually designed for one specific photon energy or wavelength [START_REF] Yu | Quantum cascade lasers with integrated plasmonic antenna-array collimators[END_REF].

A clear understanding of the spectral response of a plasmonic lens in the visible and near infrared frequency domains is pivotal for future applications. The frequency-dependent response of a plasmonic lens to a local excitation source has been addressed in a few specific cases [START_REF] Aouani | Plasmonic Antennas for Directional Sorting of Fluorescence Emission[END_REF][START_REF] Harats | Full Spectral and Angular Characterization of Highly Directional Emission from Nanocrystal Quantum Dots Positioned on Circular Plasmonic Lenses[END_REF][START_REF] Hofmann | Plasmonic modes of annular nanoresonators imaged by spectrally resolved cathodoluminescence[END_REF][START_REF] Ginzburg | Plasmonic Resonance Effects for Tandem Receiving-Transmitting Nanoantennas[END_REF][START_REF] Livneh | Efficient Collection of Light from Colloidal Quantum Dots with a Hybrid Metal-Dielectric Nanoantenna[END_REF], yet comprehensive studies have been sorely missing up until now. This need is even more urgent with the recent development of novel integrated electrically-driven light and SPP nanosources [START_REF] Rai | Electrical Excitation of Surface Plasmons by an Individual Carbon Nanotube Transistor[END_REF][START_REF] Kern | Electrically driven optical antennas[END_REF][START_REF] Cazier | Electrical excitation of waveguided surface plasmons by a light-emitting tunneling optical gap antenna[END_REF][START_REF] Parzefall | Antenna-coupled photon emission from hexagonal boron nitride tunnel junctions[END_REF] which have an inherently broad power spectrum, and the rapid emergence of new fields in plasmonics that use ultrashort (and thus spectrally broad) light pulses [START_REF] Aeschlimann | Optimal open-loop near-field control of plasmonic nanostructures[END_REF][START_REF] Lemke | The Interplay between Localized and Propagating Plasmonic Excitations Tracked in Space and Time[END_REF].

Results and discussion. Below, we investigate the spectral response of the plasmonic lenses considered in Sec. 4.1, which consist of a circular-slit grating etched in a gold film. Low-energy electrons tunneling from the tip of an STM are used to electrically excite the plasmonic lens and the resulting light is analyzed using far-field optical microscopy and spectroscopy, using the experimental setup introduced in Sec. 2.2. From Fourier-space optical images and angle-resolved optical spectra, we obtain the spectral dependence of the emission pattern. We show that the spectral response of such a plasmonic lens may be tuned by varying its inner diameter, slit period and number. In particular, the spectral response may be tailored in such a way that the plasmonic lens yields angularly narrow light beams for a large portion of the broad energy range of SPPs excited with electrons. We demonstrate that the emission pattern of the plasmonic lens essentially results from far-field interference, whereas the spectral response is strongly affected by the dispersion relation of the slit grating and the cavity modes supported by the inner disk of the plasmonic structure, as well as the dissipative losses in the metal. Notably, the results of this study provide design rules for electrically driven, low-energy, light beam microsources based on plasmonic microstructures and tunnel nanojunctions in view of integrated device applications.

In all the experiments discussed below, the STM tip is located in the center of the plasmonic lens. Inelastic electron tunneling from the tip to the sample leads to the excitation of a circular SPP wave that propagates isotropically away from the tip location. This results from the fact that the inelastic electron tunneling-induced excitation may be The plasmonic lens is a five-slit circular grating of period 700 nm and inner diameter 5 µm. For this image, light is collected using an objective lens of NA = 1.49, the full emission spectrum is used (no spectral filtering) and the image resolution is 0.0098 k 0 per pixel (i.e. the NA = 1.5 circle has a diameter of 306 pixels). The STM bias is U b = 2.8 V, the current setpoint is I t = 6 nA and the acquisition time is 600 s. (b) Intensity profiles taken from the Fourier image in panel a, along the direction of the Fourier-space vectors k x and k y . The profile along k y is vertically offset for clarity. The Fourier-space coordinates (k ∥ stands for k x or k y ) are normalized by the wavevector corresponding to the spectral peak wavelength in free space k 0 . The angular spread of the emitted beam is defined as the difference in angle corresponding to the two peaks observed in the intensity cross-sections in Fourier space. (c-j) Spectrally filtered Fourier-space optical images, in false color, of the light emitted in the substrate. The collected light is filtered using bandpass filters that have the following central wavelengths / bandwidths: (c) 550 88 nm, (d) 600 14 nm, (e) 650 13 nm, (f) 700 13 nm, (g) 750 40 nm, (h) 800 40 nm, (i) 850 40 nm and (j) 900 40 nm. Intensity profiles taken from the Fourier images are shown below each image in a polar plot. For these images, light is collected using an objective lens of NA = 1.45 and the image resolution is 0.027 k 0 per pixel (i.e., the NA = 1.5 circle has a diameter of ≈ 108 pixels) and the acquisition time is 300 s. Reprinted with permission from [START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society. considered as a point-like, out-of-plane, electric dipole located inside the tip-sample gap [START_REF] Peter Johansson | Theory for light emission from a scanning tunneling microscope[END_REF][START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF][START_REF] Uehara | Theory of visible light emission from scanning tunneling microscope[END_REF]. Here again, the gold film is thick enough to prevent SPP leakage radiation in the glass; thus, only the light from SPPs scattered at the slits of the structure is detected below the substrate.

(c) (d) (e) (f) (g) (h) (i) (j)
As already demonstrated in Sec. 4.1, when the STM tip excitation is in the center of the plasmonic lens, the scattering of the excited SPPs at the slits gives rise to the emission of a cylindrical vector beam of light with radial polarization [START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF]. Figure 4.4(a) shows the resulting Fourier-space optical image for a five-slit circular grating of period 700 nm and inner diameter 5 µm. The k-vector (angular) resolution of this image is more than three times as high as the image shown in Fig. 4.2(b) for a plasmonic lens of same geometrical parameters, because a different setup is used here as compared to Sec. 4.1 (see details in Sec. 2.2). The image in Fig. 4.4(a) shows a small, doughnut-shaped spot in the center which is characteristic of a highly collimated, radially polarized, light beam emitting orthogonally to the plane of the plasmonic lens. From the intensity profiles shown in Fig. 4.4(b), we evaluate the angular spread of the emitted beam at ±4.1 ○ with respect to the optical axis [see how angular spread is defined in Fig. 4.4(b)]. This very low angular spread as well as beaming of light along the optical axis is obtained because the scattered light is emitted in phase from the five slits of the plasmonic lens [START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF]. This occurs when the period of the circular grating (i.e., the radial distance between two nearest slits) equals an integral number of SPP wavelengths.

The observation of such beam collimation might seem surprising since electrical SPP excitation by inelastic electron tunneling is known to inherently be broadband [START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]; thus, the phase condition mentioned above is only met for a narrow part of the emission spectrum while a large portion of spectrum of the collected light is used to obtain the Fourier image shown in Fig. 4.4(a). (Indeed, the collected light is not spectrally filtered and is detected up to photon wavelengths of at least 1 µm.) The system formed by a tungsten tip and a gold film with a junction bias of U b = 2.8 V is known to produce an emission maximum with a photon wavelength around λ 0 = 720 nm (≈ 1.7 eV in energy) and a full-width-at-half-maximum of ∆λ 0 ≈ 200 nm (≈ 0.5 eV) [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF]. Nevertheless, we demonstrate below that the spectral response of such a plasmonic lens upon local, central excitation is advantageously broad, thus preserving this "beaming effect" for a large portion of the power spectrum of the electrical SPP source. This study, which investigates the spectral response of a plasmonic lens for an energy range greater than 1 eV (i.e., from λ 0 ≈ 550 to 1000 nm), is possible thanks to the combination of a spatially localized, spectrally broad, accurately positionable source of SPPs (i.e., the tunnel junction under the STM tip) with the necessary optical tools to angularly and spectrally resolve the emitted light.

In Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].4(c) to 4.4(j), Fourier-space images obtained with different interferometric bandpass filters in front of the CCD camera are shown. The plasmonic lens is the same as the one used in Fig. 4.4(a) (i.e., P = 700 nm, D = 5 µm, 5 slits) and the STM tip is again located in the center of the structure. The filters used have central wavelengths ranging from 550 to 900 nm as indicated in the bottom left corner of the images. All the images of this series exhibit a doughnut-shaped spot centered on the Fourier space origin; yet the size of this spot varies as a function of the detection wavelength. The spot is smallest for a detection wavelength of 700 nm. As well, the polar plots below the images show that the angular spread of the beam is the largest at the extrema of the investigated spectral range. To confirm these observations and using the definition given in Fig. 4.4(b), we determine the angular spread of the light beam from the Fourier-space optical images, and plot it versus the emission wavelength as shown in Fig. 4.5(b) to 4.5(d). The angular spread minimum is found to be 3.2 ○ at λ 0 = 700 nm. For the energy corresponding to a photon wavelength of λ 0 = 700 nm in vacuum, the SPP wavelength on an ideal smooth gold/air interface is λ SP P ≈ 678 nm, which is indeed close to the period of the circular slit grating. Interestingly, the angular spread remains lower than 4.0 ○ within a 100 nm-wide wavelength range around 700 nm, and lower than 7.0 ○ until λ 0 = 850 nm. In order to explain this effect, we use a simple two-slit interference model (see details below) to determine the spectral dependence of the angular spread. The light emitted in the substrate from the two slits interferes constructively in the direction denoted by the angle θ. δ is the optical path difference for the light emitted at θ at the two slits. If the period P of the slit grating is longer than the SPP wavelength λ SP P , then the SPPs scattered into light interfere constructively in the forward direction. For P < λ SP P , constructive interference is in the backward direction. Only first-order diffraction is considered here. [(b) to (d)] The experimental values of the angular spread [see Fig. 4.4(b) for definitions] measured for three different five-slit circular gratings are compared with the angle of constructive interference θ (red line) calculated using the model shown in a. The grating period is P = 700 nm in b, P = 600 nm in c and P = 800 nm in d. The inner diameter of the plasmonic lens is D = 5 µm in b and D = 6 µm in c and d. The theoretical lower bound for the angular spread due to the finite size of the slit grating is shown by the black line. L is the outer diameter of the plasmonic lens. The experimental data are obtained from the analysis of spectrally filtered Fourier-space images following the method described in Fig. 4.4. Reprinted with permission from [START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society. sources, separated by the slit grating period P . The emission from these two point sources is assumed isotropic in the glass. Thus, the light in the far field is expected to be the most intense at an angle where constructive interference occurs between the waves emitted from the two slits. Consequently, a maximum in the emission of light in the direction orthogonal to the interface only occurs if the two sources are in phase, i.e., P = λ SP P . Otherwise, SPPs will preferentially scatter in the direction where the optical path difference in glass δ compensates the phase shift between the two sources. Within this simple representation, we assume that the energy-dependent SPP wavelength is that of SPPs propagating on the interface between infinite gold and vacuum half-spaces. This reads

n ′ SP P P -n g δ = λ 0 (4.1)
where n g = 1.51 is the refractive index of glass, λ 0 is the photon wavelength in vacuum and n ′ SP P is the effective index of the SPPs propagating at the gold-air interface. n ′ SP P is defined as the real part of the wavenumber ratio between SPPs and photons in vacuum, as follows:

n ′ SP P = Re k SP P k 0 ≅ ′ m ′ m + 1 1 2 (4.2)
for ′′ m ≪ ′ m where ′ m and ′′ m are the real and imaginary parts of the frequency-dependent relative permittivity of the metal respectively. Equivalently, n ′ SP P = λ 0 λ SP P . From Eq. 4.1, we see that constructive interference occurs for

θ = arcsin n ′ SP P -λ 0 P n g . (4.3)
Only first order diffraction is considered here. Consequently, SPPs interfere constructively in the forward direction if P > λ SP P , and in the backward direction if P < λ SP P . We come back now to a three-dimensional problem where SPPs scatter on circular slits and, as a first step, we ignore the effects of the finite size of the slit grating. Thus, we find that the emitted beam has the shape of a cylinder in the far field only if P = λ SP P . If P ≠ λ SP P , the emitted beam has the shape of a cone in the far field, with an angular spread θ given by Eq. 4.3.

θ ≳ arcsin λ 0 n g L . (4.4)
The simple model based on Eqs. 4.3 and 4.4 reproduces the main trends of the experimentally determined spectral dependence of the angular spread sufficiently. Thus the desired optimum operating frequency range and size of the plasmonic lens as well as the required angular spread may be simply obtained by choosing specific geometric design parameters (inner diameter, grating period, number of slits). Such simple control over the plasmonic lens characteristics is crucial for its future integration with a broadband excitation nanosource. Neither the model nor the spectrally filtered Fourier-space images (which are not intensity-normalized with respect to each other) provide the power spectrum of the emitted light versus its angular distribution, however. To obtain this key information, angleresolved optical spectroscopy is necessary where the angular and spectral dependence are revealed in one single image. of the projected image is adjusted so that the light entering the entrance slit of the spectrometer is from a line along k y and crosses the Fourier space origin. Thus, we record an image (on the CCD camera of the spectrometer) with spectral and angular coordinates along the horizontal and vertical axes, respectively. When the system exhibits axial symmetry with respect to the optical axis, the angular dependence of the emission pattern is only radial (not azimuthal); therefore, all information about the energy-momentum dispersion (within the investigated energy range) The general aspect of the energy-momentum dispersion diagram for all four structures may be easily understood by drawing an analogy to Young's double-slit experiment. In the case of a single circular slit, we may assume that the light detected in one direction k ∥ k 0 in Fourier space results from the interference of the light emitted from two opposite point sources on the slit. Thus, a periodic fringe pattern is expected in Fourier space, with a period varying as the emission wavelength over the slit diameter [START_REF] Wang | Plasmon scattering from holes: from single hole scattering to Young's experiment[END_REF]. This is indeed what is observed in Fig. 4.6(e). In a five-slit circular grating, five fringe patterns of different periods superimpose in Fourier space and coherently interfere with each other. Constructive interference in the emission direction orthogonal to the grating only occurs if the slit period is a multiple of the emission wavelength. This explains why the shape of the energy-momentum dispersion diagrams seen in Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].6(b) to 4.6(d) varies with wavelength and why these "bow ties" shift in energy as the slit grating period is changed. The angular spread is lowest and the light emitted in the substrate is most intense at the center of the bow tie. Around this energy value, the angular spread and the radiated power remain almost constant (and at their optimal values) within a ≈ 0.3 eV-wide range.

We can now explain why the angular spread obtained from the full-spectrum Fourier-space image shown in Fig. 4.4(a) is very close to its lowest value despite the spectral broadness of the electrical SPP nanosource.

Two main effects determine the angular spread of our electrical light microsource: the spectral width of the SPP nanosource and the finite size of the structure at which SPPs scatter into light. When the latter dominates over the former, the angular spread remains almost constant over the emission spectrum. Thus the size of the plasmonic microstructure should be decreased to the smallest possible diameter where the angular width of the emitted beam is not limited by the size effect. Beyond this point, further downsizing of the plasmonic microstructure is inefficient, since it broadens the angular distribution of the emitted light without improving the matching between the spectral response of the plasmonic structure and the power spectrum of the SPP nanosource. Obtaining optimal light beaming while keeping the smallest possible spatial footprint thus requires that the spectral width and size effects contribute equally to the angular spread of the source. From Eqs. 4.3 and 4.4 for small θ ≈ 0, we evaluate the contributions of these two effects at ∆λ 0 (n g P ) and λ 0 (n g L), respectively, where ∆λ 0 and λ 0 are the spectral width and central wavelength of the source (P and L are the period and outer diameter of the slit grating and n g is the substrate's refractive index). The best trade-off between narrow light beaming and small spatial footprint is thus obtained when using a plasmonic lens with period-to-size ratio P L ≈ ∆λ 0 λ 0 .

The data shown in Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].6(b) and 4.6(e) also reveal the advantages and drawbacks of increasing the number of slits N of the structure. From Fourier-space images, we evaluate the angular spread of the light beam emitted from the five-slit circular grating (D = 4 µm and P = 700 nm) and the single circular slit (D = 5 µm) at 4.4 ○ and 5.6 ○ , respectively (data not shown). Therefore, the latter structure, which is almost half the size of the former (5.6 µm in outer diameter, as compared to 10.2 µm), has an angular spread that is only ≈ 25% higher. Moreover, using one circular slit rather than five extends the energy range for which optimal beaming and power radiation are obtained.

However, the emission pattern obtained from a single circular slit exhibits multiple secondary lobes of non-negligible intensity which persist within all the investigated energy range [see Fig. 4.6(e)]. This off-axis emission represents an important power loss for a light beam source. Furthermore, in an applied context, cross-talk issues may occur when several of these sources are used to transfer information to distinct receptors. In this regard, a multiple-slit structure is advantageous.

A feature that all panels of Fig. 4.6 have in common is the strong damping of the radiated power at an energy higher than about 2.1 eV (i.e., λ 0 ≲ 590 nm). This is due to losses in tungsten and gold, i.e., the metals of which the STM tip and the plasmonic lens are made. Generally, the power spectrum of the emission radiated from a tunnel junction is modeled as the product of a source term given by inelastic tunneling statistics [∝ (eU b -̵ hω), for ̵ hω ≤ eU b ;

0 otherwise [START_REF] Daniel Hone | Theory of light emission from small particle tunnel junctions[END_REF]] and an emission term related to the local density of electromagnetic states (EMLDOS) [START_REF] Joulain | Definition and measurement of the local density of electromagnetic states close to an interface[END_REF][START_REF] Douillard | High-resolution mapping of plasmonic modes: photoemission and scanning tunnelling luminescence microscopies[END_REF].

As a result, the radiation has a broad power spectrum that spreads over the infrared and part of the visible range and falls to zero at energy eU b (quantum cutoff ). Still, the power spectrum radiated by a W-Au tip-surface junction is known to rapidly fall beyond 2.1 eV in energy [START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF], even when the tunnel junction is biased at U b = 2.8 V. This is notably ascribed to interband transitions in gold. In the system that we study here, the dissipative losses in gold play a double role, since they decrease the power emitted by the SPP nanosource and they shorten the SPP propagation length, thus yielding higher propagation losses before SPP scattering from the slits into light in the far field.

Figure 4.7 shows optical spectra measured for different plasmonic lenses using configuration 2 of the experimental setup with integration over the CCD lines before read-out (i.e., the signal is integrated over emission angles).

Thus, we focus on the total emitted power, which is related to the EMLDOS at the SPP nanosource position. In this way, finer spectral features, whose energy position clearly depends on the plasmonic lens parameters N , D and P , are made visible (N is the number of slits, D is the inner disk diameter, and P is the grating period). The spectrum measured on an unstructured thin (50 nm) gold film under the same conditions, shown in Fig. 4.7(b), exhibits no such features; it resembles a simple Gaussian curve. This confirms that the features seen in the plasmonic lens spectra are due to the structures etched in the gold film and not to the SPP nanosource.

The spectrum obtained from a single circular slit, shown in black in Fig. 4.7(c), differs significantly from that of the unstructured thin gold film; it exhibits peaks and dips. When varying D, the inner diameter, these features shift in energy (data not shown here, see in [START_REF] Cao | Using a plasmonic lens to control the emission of electrically excited light[END_REF]) in such a way that they may be related to the cavity modes of the plasmonic structure. These modes correspond to the SPP standing waves which form on the inner gold disk due [294] and [START_REF] Paul | Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization[END_REF]. Reprinted with permission from [START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society.

to SPP reflection at the circular slit; the existence of such modes has been confirmed by cathodoluminescence measurements on similar structures [START_REF] Hofmann | Plasmonic modes of annular nanoresonators imaged by spectrally resolved cathodoluminescence[END_REF].

Adding four slits and varying the slit period P significantly changes the spectral response of the plasmonic structure, even though the inner diameter D is kept constant [see Fig. , the peak and dip positions, relative height, and width vary. Since here the detected light is integrated over all emission angles, the spectral dependence of the emitted light that is observed as a function of slit grating period and diameter cannot be due to the phenomenon seen in Fig. 4.6. Instead, it is attributed to the effect of the lens parameters on the EMLDOS. Namely, the power of the light beam emitted from the plasmonic lens must be sensitive to the EMLDOS at the position of the SPP nanosource. Below, we explain why strong variations occur in the EMLDOS when the emission wavelength is close to the slit grating period.

The role of the circular-slit grating in the spectral response of the plasmonic lens is twofold. The grating, which surrounds the central disk, reflects part of the outgoing SPP wave back to the center of the disk, and also scatters part of the SPP wave into light in the out-of-plane direction. Thus, the slit grating and the central-disk cavity are coupled through the frequency-dependent Fresnel coefficients of the grating. The intensity of the light emitted from the slits depends on both the scattering coefficient of the grating and the intensity of the incident SPPs; the latter, however, depends on the SPP-mode density in the central-disk cavity, which in turn is determined by the complex amplitude reflection coefficient r of the slit grating. Depending on frequency, this grating-cavity coupling may have a strong enhancing or quenching effect on the spectral response of the plasmonic lens and the magnitude of this effect depends on r.

We have numerically calculated the complex amplitude SPP reflection coefficient r and transmission coefficient t of a single linear slit grating using a two-dimensional model for normal SPP wave incidence [START_REF] Cao | Stable and efficient bloch-mode computational method for one-dimensional grating waveguides[END_REF][START_REF] Paul | Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization[END_REF]. The squared moduli R = r 2 and T = t 2 are the intensity Fresnel reflection and transmission coefficients and satisfy the relationship R + T + S + A = 1 with S the out-of-plane SPP-to-light scattering coefficient and A the dissipative loss (absorption) coefficient. In Figure 4.8, R and T are plotted versus λ 0 , the photon wavelength in vacuum, along with the argument of r, arg(r), which is the relative phase shift of the SPP wave upon reflection at the slit grating. The case of a five-slit grating (as in the experiment) is considered, as well as gratings with N = 10, N = 20 and N = ∞, in order to highlight the influence of the number of slits on the spectral broadness of the plasmonic lens response. In all cases, the slit period is P = 700 nm. The reflection coefficient R exhibits a sharp peak centered at λ 0 = 700 nm, which becomes narrower and more intense with increasing N . For N = 5, the peak intensity is R = 0.13 and its width is about 60 nm. The reflection peak coincides with a sharp rise in the transmission coefficient T , with a local maximum of T = 0.23 at λ 0 = 700 nm. Since R + T + S + A = 1 as discussed above, a concomitant rise in R and T must correspond to a drop in the light emitted in the far field. This has previously been reported for a single linear SPP grating (i.e., for a single, isolated grating which is not part of a cavity) [START_REF] López-Tejeira | Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description[END_REF], where a peak in R and a dip in S occur when the SPP wavelength matches the grating period.

Recent studies on circular plasmonic structures similar to our plasmonic lens have shown a similar spectral dip; yet, the authors ascribed such a dip to either a Fano resonance [START_REF] Livneh | Efficient Collection of Light from Colloidal Quantum Dots with a Hybrid Metal-Dielectric Nanoantenna[END_REF] due to SPP coupling with a waveguiding layer atop the grating (such a layer is absent in our case), or to an instrumental artifact due to the collection geometry (see the supporting information of Ref. [START_REF] Osorio | Angle-Resolved Cathodoluminescence Imaging Polarimetry[END_REF]). The latter artifact is specific to the detection scheme used in Ref. [START_REF] Osorio | Angle-Resolved Cathodoluminescence Imaging Polarimetry[END_REF] (a parabolic mirror with a small hole) and is never present in our case, thanks to the use of an immersion objective lens. Moreover, the spectra shown in Fig. 4.7 do not systematically exhibit a dip at λ 0 = P or λ SP P = P , despite the inference from the results of Fig. 4.8 that the out-of-plane SPP-to-light scattering coefficient S must be minimal for λ 0 = P ; in the experiment, a peak or plateau may be seen as well, depending on the inner diameter D of the plasmonic lens. From this, we infer that the cavity modes of the central disk determine whether a peak or a dip appears at a specific energy in the measured spectra, as these modes influence the incident SPP intensity, and are not included in the simulation. Both the modulus and the argument of r determine the magnitude of these features.

In Fig. 4.8(c), we see that the phase arg(r) varies rapidly at the wavelength values where r is maximum. This is equivalent to a rapidly changing cavity size which may explain the abrupt changes in the spectrum that are observed around λ 0 = P . At this point, we emphasize that the experimentally observed spectra are highly reproducible and that they are not subject to spectral shifts due to STM tip shape modifications [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF][START_REF] Aizpurua | Role of tip shape in light emission from the scanning tunneling microscope[END_REF], since the tip material (tungsten) is a non-plasmonic metal in this energy range.

In Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].8(d) and 4.8(e), we explain the optical behavior of the slit grating in terms of the SPP dispersion relation.

Here, we use reduced energy and wavevector variables, P λ 0 and P k 2π, respectively (P is the grating period and k is the wavevector in the plane of the interface). The grating periodicity leads to the opening of an energy gap in the dispersion curve. Here the gap exists from 0.94 to 0.99 in reduced energy units at a reduced wavevector of 0.5.

As is visible in Fig. 4.8(e), the reflection peak (occurring at energy P λ 0 = 1) is very close in energy to the upperenergy gap edge in the dispersion relation, confirming previous interpretations reported for linear SPP gratings (i.e., that a maximum in the density of states occurs at the upper edge of the energy gap) [START_REF] López-Tejeira | Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description[END_REF][START_REF] Pincemin | Propagation and localization of a surface plasmon polariton on a finite grating[END_REF][START_REF] Søndergaard | Theoretical analysis of ridge gratings for long-range surface plasmon polaritons[END_REF]. This explains why the strongest intensity variations in the spectra shown in Fig. 4.7 occur around photon wavelength λ 0 = P .

In Fig. 4.8 we also see that the larger the slit number, the higher and the spectrally narrower the peak in the SPP reflectivity of the slit grating. Increasing N is thus expected to yield stronger and sharper features (peaks and dips)

in the spectral response of the plasmonic lens, which may be considered a drawback, depending on the targeted applications. Thus, the following design rule for light beam microsources based on circular slit gratings may be enunciated: by limiting the slit number, a smaller spatial footprint and a broader spectral response of the plasmonic structure are obtained at the expense of emission directivity. A broad spectral response may indeed be crucial if, e.g., such a microsource is used for optical transmission with wavelength multiplexing.

Conclusions and outlooks.

In this section, we have introduced an experimental method combining STM, optical microscopy and optical spectroscopy for carrying out angle-resolved optical spectroscopy measurements. This technique has been used to analyze the light emitted from a plasmonic structure upon local, low-energy, electrical excitation with tunnel electrons. Thus, we have characterized the emission pattern and spectral response of a plasmonic lens consisting of concentric circular slits etched in a thick gold film. Such a design is very attractive for building an electrically-driven microsource of highly collimated light since its spectral response is broad and optimal within a wide energy range, especially in comparison to other resonant plasmonic structures such as Yagi-Uda optical antennas [START_REF] Holger F Hofmann | Design parameters for a nano-optical Yagi-Uda antenna[END_REF]. In this way, a very simple broadband electrical SPP source, such as a tunnel nanojunction, can drive such light beam microsources. We have demonstrated that such a periodic structure with a limited number of slits, i.e., N = 5, offers a fair trade-off between low angular spread, small spatial footprint and broadband spectral response.

In the next section, we show that our STM-nanosource of SPPs may be used not only to characterize the angular emission pattern of light beam-emitting plasmonic microstructures, but also to test and improve novel designs of optical antennas, which may not necessarily have cylindrical symmetry like the circular gratings investigated in Secs. 4.1 and 4.2. This is a step more toward the use of STM and optical microscopy to fully characterize the optical response of integrated micro-optics components of arbitrary geometry and to assist the design of such components 55 with tailored emission properties. [159]

A new design: the elliptical slit antenna

Context and motivation. With the ever-growing demand for higher information capacity and the diversification of applications, the integration of nanophotonics with nanoelectronics in microdevices has never been more relevant than now [START_REF] Kevin | Electrically driven subwavelength optical nanocircuits[END_REF][START_REF] Wu | On-Chip Single-Plasmon Nanocircuit Driven by a Self-Assembled Quantum Dot[END_REF][START_REF] Hryciw | Electrifying plasmonics on silicon[END_REF][START_REF] Neutens | Electrical Excitation of Confined Surface Plasmon Polaritons in Metallic Slot Waveguides[END_REF][START_REF] Walters | A silicon-based electrical source of surface plasmon polaritons[END_REF][START_REF] Volker | Toward integrated plasmonic circuits[END_REF][START_REF] Fan | An Electrically-Driven GaAs Nanowire Surface Plasmon Source[END_REF][START_REF] Wang | Molecular electronic plasmonics[END_REF][START_REF] Du | On-chip molecular electronic plasmon sources based on self-assembled monolayer tunnel junctions[END_REF]. In this context, miniaturized electrical light sources are needed for chip-to-chip communication and optical interactions with the surrounding environment (e.g., for remote control, external communication or sensing applications). A number of electrically driven emitting optical antennas have been described in the recent literature [START_REF] Rai | Electrical Excitation of Surface Plasmons by an Individual Carbon Nanotube Transistor[END_REF][START_REF] Kern | Electrically driven optical antennas[END_REF][START_REF] Du | Highly efficient on-chip direct electronicplasmonic transducers[END_REF][START_REF] Pohl | Stacked optical antennas[END_REF][START_REF] Parzefall | Antenna-coupled photon emission from hexagonal boron nitride tunnel junctions[END_REF][START_REF] Kevin | Antenna electrodes for controlling electroluminescence[END_REF][START_REF] Li | Electrical source of surface plasmon polaritons based on hybrid Au-GaAs QW structures[END_REF][START_REF] Vardi | Fano Resonance in an Electrically Driven Plasmonic Device[END_REF][START_REF] Bigourdan | Nanoantenna for Electrical Generation of Surface Plasmon Polaritons[END_REF][START_REF] Uskov | Excitation of plasmonic nanoantennas by nonresonant and resonant electron tunnelling[END_REF], where the emission of light is activated using low voltage (V) and low current (nA -µA), compatible with integrated electronics. These antennas were based on plasmonic micro-or nanostructures of various geometries (Yagi-Uda, bull's eye, nanoparticle dimer, or wire antennas), coupled in the near field (or incorporating in their design) an electrically driven nanosource of SPPs. In particular, the electrical SPP nanosource can be a nanoscale tunnel junction where the emission process relies on inelastic electron tunneling effects [START_REF] Lambe | Light emission from inelastic electron tunneling[END_REF].

A central issue for miniaturized electrical light sources is the control of their emission direction, especially given that SPP excitation with electrons results in a broad power spectrum [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Zhang | Edge scattering of surface plasmons excited by scanning tunneling microscopy[END_REF][START_REF] Daniel Hone | Theory of light emission from small particle tunnel junctions[END_REF][START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]. When based on a single plasmonic nanoparticle, these sources exhibit angularly broad emission patterns resembling that of an electric dipole, possibly with additional higher-order multipolar contributions [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF][START_REF] Coenen | Directional emission from a single plasmonic scatterer[END_REF] (see Chap. 3). Antenna designs based on the arrangement of several plasmonic nanoparticles (e.g., Yagi-Uda antennas [START_REF] Holger F Hofmann | Design parameters for a nano-optical Yagi-Uda antenna[END_REF]) yield more directional emission [START_REF] Coenen | Directional Emission from Plasmonic Yagi-Uda Antennas Probed by Angle-Resolved Cathodoluminescence Spectroscopy[END_REF]; however, the light is most often emitted at the critical angle of the substrate-superstrate interface [START_REF] Curto | Unidirectional Emission of a Quantum Dot Coupled to a Nanoantenna[END_REF] or in directions that strongly vary depending on the optical frequency [START_REF] Kosako | Directional control of light by a nano-optical Yagi-Uda antenna[END_REF]. Light beams with an angular spread of only a few degrees [START_REF] Livneh | Efficient Collection of Light from Colloidal Quantum Dots with a Hybrid Metal-Dielectric Nanoantenna[END_REF][START_REF] Livneh | Highly Directional Emission and Photon Beaming from Nanocrystal Quantum Dots Embedded in Metallic Nanoslit Arrays[END_REF] may be obtained from periodic microstructures (e.g., bull's eye antennas [START_REF] Lezec | Beaming light from a subwavelength aperture[END_REF][START_REF] Chul Jun | Plasmonic beaming and active control over fluorescent emission[END_REF]), yet again with a strong dependence on frequency. Foremost, planar antennas with cylindrical symmetry, such as bull's eye [START_REF] Osorio | Angle-Resolved Cathodoluminescence Imaging Polarimetry[END_REF] and patch antennas [START_REF] Esteban | Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances[END_REF][START_REF] Mohtashami | Nanoscale Excitation Mapping of Plasmonic Patch Antennas[END_REF], invariably emit light in a beam or cone whose axis is orthogonal to the surface plane. Thus, for all applications where light is emitted from electrically-driven optical antennas and specific directions of emission are desired, a different antenna design has to be found [START_REF] Clarke | Direction-division multiplexed holographic free-electron-driven light sources[END_REF].

In Sec. 4.2, we have demonstrated that the electrical excitation of SPPs in the center of a plasmonic lens consisting of a single circular slit etched in a gold film results in the emission of a spectrally broad cylindrical vector beam of light [START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF][START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF]. The resulting emission direction, which is invariably orthogonal to the surface plane on average, does not depend on frequency and the angular spread of the resulting beam is determined by the ratio of the lens diameter to the emission wavelength. In addition, previous experiments carried out using a scanning electron microscope in vacuum have shown that oblique light beams may be produced from elliptical corals etched in a single crystal of gold. In order to produce the oblique beam of light, the high-energy (30 keV) electron beam is focussed onto one of the two focal points of the structure [START_REF] Schoen | The Planar Parabolic Optical Antenna[END_REF]. The emission direction is determined by the eccentricity of the coral and could, in principle, be tailored by design. Inspired by this work, we investigate here the low-energy (< 3 eV) electrical excitation and the resulting light beams from single elliptical antennas consisting of an elliptical slit etched in a gold film. We theoretically and experimentally show that when the excitation takes place at one of the two focii, these elliptical slits act as highly directional antennas that convert electrically-excited SPPs into light beams which are emitted in specific directions as determined by the ellipse eccentricity and the refractive index of the surrounding medium. The angular spread of the emitted beam is inversely proportional to the length of the ellipse axes. isotropically away from the tip along the air-gold interface [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF]. The SPPs are scattered at the slit into photons in air (not shown) and in the glass. Only the light emitted in the glass is collected using a high numerical aperture (NA) microscope objective. The angular distribution of the emitted light is acquired from Fourier-space images [START_REF] Zhang | Edge scattering of surface plasmons excited by scanning tunneling microscopy[END_REF][START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF].

Results and discussion

The angular emission pattern results from the far-field interference of the light scattered from all along the slit.

When the STM tip is positioned in the center of the disc formed by a circular slit (see Fig. 4.9(a)), all points along the perimeter of the slit are equidistant from the SPP source; thus, light is emitted in phase from all along the slit.

As a result, a light beam is emitted in the direction orthogonal to the surface plane. Due to the cylindrical symmetry of the system, the emitted beam is a cylindrical vector beam with radial polarization [START_REF] Cao | Cylindrical vector beams of light from an electrically excited plasmonic lens[END_REF].

When the tip is off-center, the emission from different positions along the circular slit is out-of-phase. As previously reported in Sec. 4.2, light beams tilted by up to 10 ○ may be obtained in this way while maintaining a comparatively low angular spread; however, beyond this limit more intricate emission patterns are obtained. A lateral shift of the excitation source is not equivalent to an angular tilt of the emitted beam. Different geometries must be found in order to produce light beams in specific directions. Such a geometry is proposed below, i.e., a very simple, broadband, optical antenna design consisting of a single elliptical slit etched in a gold film.

Here, we introduce the working principle of an elliptical slit antenna. Figure 4.10 shows a planar surface illuminated by a plane wave light beam. If the incidence angle is θ = 0, the optical field at the surface is in phase for the entire illuminated area. Otherwise, if θ ≠ 0 and the incidence plane is the (xz)-plane, the phase ϕ of the optical field at the surface varies with position, i.e., ϕ(x) = kx sin θ + ϕ 0 , where k is the wavevector modulus of the incident light and ϕ 0 is a constant. In order to emit a beam of light in a specific direction, a light source at a planar surface must reproduce this spatial phase distribution. In the specific case of a slit that scatters surface waves (emitted from a point-like source) into light, the phase is the delay due to the propagation of the surface waves from the source to the slit. Thus, the distance d traveled must vary along the slit such that the phase of the scattered light is

ϕ(x) = kx sin θ + ϕ 0 . (4.5)
We assume that the propagation and scattering of these surface waves may be treated within the scalar approximation as in the case of plane waves in free space. This approximation has been shown to be correct for the case of SPPs [START_REF] Teperik | Huygens-Fresnel principle for surface plasmons[END_REF]. Within this approximation, Eq. 4.5 reads κd = kx sin θ + ϕ 0 , where κ is the wavevector modulus of the surface waves.

The only geometry that meets this condition is an ellipse with the surface wave source located at one of the focii.

An ellipse is the ensemble of points P (x, y) that satisfies the equation The eccentricity of the ellipse is e = c a . The distance from F to P (x, y) is r = ex + a. As a result, when the source is at F , wave propagation to the slit introduces a phase shift of κ(ex + a). Thus, a light beam emitted at an angle θ is expected where θ satisfies the equation κe = k sin θ.

(4.6)

In this way the emission angle may be tailored by varying the eccentricity of the ellipse. The available angular range is from θ = 0 to θ = arcsin κe k , with e chosen between 0 (i.e., a circle) and up to but not including 1 (i.e., e = 1 yields a parabola). Figure 4.11(a) shows that the intersection of a cylinder with a plane yields an ellipse whose eccentricity is precisely e = sin θ, where θ defines the tilt of the cylinder axis with respect to the normal of the plane. Based on the similarity with Eq. 4.6, one may expect that cylindrical beams can be emitted from elliptical slit antennas fed with surface wave sources at their focii; however, Eq. 4.6 shows that this is only true if light and surface waves propagate at the same speed (i.e., κ = k). Figure 4.11(b) shows that the refraction of a cylindrical beam at a planar interface between two media does not yield a cylindrical beam if the two media do not have same index of refractive, since the shape of the beam changes as a result of the change in emission angle. (In the case of reflection, since the medium and thus the emission angle remains the same, the beam remains cylindrical).

In order to have a beam of light, the phase due to the optical path difference of light in the medium (i.e., k 0 n 1 δl 1 or k 0 n 2 δl 2 ) must equal the phase due to the difference in propagation length from the source at a focus to the slit 59 (i.e., 2κc). k 0 is the wavevector modulus of photons in vacuum. In other words, 2 κ k0 c = n 1 δl 1 = n 2 δl 2 . Air and glass have refractive indexes n 1 and n 2 of about 1 and 1.5, respectively, and the SPPs at the air-gold interface have an effective index close to 1. Our elliptical slit antennas are thus expected to emit quasi cylindrical beams on the air side, since the speed of photons in air, and of SPPs on an air/Au interface are similar; in contrast, the light beam emitted in glass must have an elliptical section. This is not directly visible in the Fourier-space images since they reveal the angular, and not the spatial distribution of the emitted light. Note that the model of a cylinder intersecting a plane introduced above yields similar results as the virtual parabola model proposed in Ref. [START_REF] Schoen | The Planar Parabolic Optical Antenna[END_REF] for the beaming of an elliptical cavity and provides a simple framework to describe the shape of the emitted beams.

We can produce beams of light emitting in the angular range from 0 ○ to arcsin k SP P nik0 , with i = 1 in air and i = 2 in glass. In principle, our elliptical slit antennas can thus emit light beams at all polar angles in air (i.e., 0 ○ to about 90 ○ ) and from 0 ○ to about 43 ○ in glass (at λ 0 = 700 nm). Interestingly, light beams at virtually all polar angles in glass (i.e., up to 90 ○ ) could be obtained if the SPP nanosource were located at the glass-gold interface or if it excited a gold film sandwiched between two media of the same refractive index (e.g., a suspended gold membrane in air).

The latter geometry (i.e., a prototypical insulating-metal-insulating waveguide) has the additional advantage that it supports long-range SPPs which have lower propagation losses [START_REF] Berini | Long-range surface plasmon polaritons[END_REF]. Figure 4.12 provides the experimental demonstration that light beams may be emitted in chosen directions from electrically-driven elliptical slit antennas. The emission angle is determined by the eccentricity of the ellipse.

Three different slits are used, i.e., Structures 1, 4 and 6 in Table 4.1 (see also Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].12(a) to 4.12(c)); they have eccentricities of 0 (circular slit), 0.51 and 0.77 (elliptical slits), respectively. The Fourier-space images recorded upon excitation with the tunnel electrons from the STM tip at one of the focii are shown in Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].12(d) to 4.12(f). Good agreement is found between the experimental data and the simulated images shown in Figs. [START_REF] Lewis | Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ 16 diameter apertures[END_REF].12(g) to 4.12(i).

These simulated images are obtained using a model based on an ensemble of in-plane oscillating electric dipoles located along the slit and oriented orthogonally to the ellipse in the plane of the sample [START_REF] Mollet | Plasmonic interferometry: Probing launching dipoles in scanning-probe plasmonics[END_REF][START_REF] Berthel | Coherence and aberration effects in surface plasmon polariton imaging[END_REF]. The same model was used to calculate the emission pattern from circular slits in Sec. 4.1. Fig. 4.12(j) shows the intensity profiles from the simulated Fourier-space images and the average emission angles retrieved from the experimental data for the eight elliptical slits whose eccentricities are given in Tab. 4.1. The chosen eccentricity values are those corresponding to the intersection of a cylinder with a plane at incidence angles of 0 ○ , 10 ○ . . . 70 ○ , respectively.

On the same graph is plotted the theoretical value of the emission angle as obtained from Eq. 4.6, which reads θ = arcsin k SP P n2k0 e , where k SP P k0 = 1.037 at λ 0 = 700 nm and n 2 = 1.518. In addition, Fig. 4.12(k) shows a polar plot of the angular emission pattern retrieved from an experimental Fourier-space image of the light emitted upon electrical excitation of Structure 8 (see Tab. 4.1) at the focus F (-c, 0). c 2 , 0) and ( c 2 , 0). The corresponding experimental and theoretical Fourier-space images are shown in Fig. 4.13. Intricated interference patterns, covering broad polar and azimuthal angular ranges, are produced when the SPP source is not located at one of the ellipse focii. Only when the excitation is located at a focus does the elliptical slit antenna yield angularly narrow light beams. As expected, the emission patterns upon excitation at F and F ′ are perfect mirror symmetries of each other with respect to the (yz)-plane.

From the experimental Fourier-space images we retrieve the angular spread of the emitted light beams in the k x and k y reciprocal-space directions. Here we define the angular spread ∆k as the half width at half maximum (HWHM) of the light spot in Fourier space. The results obtained for Structures 1 to 8 (see Tab. 4.1) are plotted in Fig. 4.14(a) versus the ellipse eccentricity. We see that the lateral size of the antenna determines the angular spread. The angular spread along k x decreases as the eccentricity increases since the major axis 2a is increased while keeping the minor axis 2b = 3µm constant. For instance, an angular spread of 9 ○ and of 4.5 ○ along k x are measured for Structure 1 (2a = 3µm) and 7 (2a = 6µm) respectively. No significant change occurs along k y where the angular spread remains within a range of 9 to 10 ○ . Fig. 4.14(b) compares the angular spread ratio ∆kx ∆ky to the minor-to-major axis ratio b a of the ellipse. Close agreement is found between the two ratios; due to the properties of Fourier transforms, the aspect ratio of the slit antenna in real space ( a b ) and its emission pattern in Fourier space ( ∆kx ∆ky ) are inversely proportional to each other. When elliptical slit antennas are fed at their focus, the angular spread of the emitted light beam is determined by the ellipse semi-radii and the emission wavelength. It is worth noticing that, despite higher SPP propagation losses is some directions, increasing a does not result in a broadening of the half width at half maximum along k x . To further describe the emission from an elliptical slit antenna, we now examine the "shape" of the emission lobes as calculated at the vacuum wavelength of λ 0 = 700 nm using the method described in Refs. [START_REF] Paul | Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization[END_REF][START_REF] Yang | Near-to-Far Field Transformations for Radiative and Guided Waves[END_REF]. In . Electrical excitation at F (-c, 0) is modeled as a monochromatic (λ 0 = 700 nm) z-oriented oscillating dipole. Both the emission in the air (upward direction) and in the glass (downward direction) is shown. The air-glass interface is at z = 0 and the ellipse is centered at (x, y) = (0, 0). In general, Fig. 4.15 confirms that light beams are emitted both downward in the substrate and upward in the superstrate. The light is emitted at larger angles in the medium of lower refractive index (i.e., in air). Moreover, we see that a stronger beaming effect occurs in glass as compared to air. The light beam in glass has a lower angular spread and less intense side lobes. Even though higher directivity is obtained in glass with comparatively more light in the beaming direction than for the case in air, more intensity on average is emitted upward than downward. Indeed, the flux of the Poynting vector integrated over the lower half space represents only 10% (for Structure 1) to 25% (for Structure 8) of the total radiation (i.e., integrated over 4π sr).

Conclusions and outlooks.

In this section, we have introduced the working principle of an electrically-driven elliptical slit antenna which is a highly directive, low-energy, electrical microsource of light beams emitting in controlled directions. The emission direction is tailored by design by controlling the eccentricity of the ellipse. The model of a cylinder intersecting a plane may be used to describe the dependence of the beam direction and geometry on the structure eccentricity and the refractive index of the surrounding medium in a simple way. We have shown that the angular spread of the emitted beam depends on the length of the ellipse axes and not on its eccentricity.

Additional results available in Ref. [START_REF] Cao | Directional light beams by design from electrically driven elliptical slit antennas[END_REF] reveal that light beaming is robust to amplitude inhomogeneities of the scattered field from the slit (which becomes more inhomogeneous as the eccentricity increases) but is highly sensitive to its phase distribution (which changes when moving the SPP source from the ellipse focus); this is expected since light beaming from a slit is essentially a far-field interference effect. From calculations of the field in the slit, we infer that the polarization of the emitted beam is predominantly radial with a minor linear contribution (along the major axis) that increases with eccentricity.

Future improvements of these optical antennas include the integration of the electrical SPP nanosource in the design of the microstructure (e.g., as an integrated metal-oxide-metal tunnel junction) and the engineering of the substrate and superstrate's refractive indices for greater control of the emission pattern, of the upward/downward power distribution and of the propagation losses. The principles of electrically-driven elliptical slit antennas may be extended to similar chiral slit structures, e.g., elliptical spirals, in order to control the optical orbital angular moment of the emitted light beams [START_REF] Gorodetski | Generating far-field orbital angular momenta from near-field optical chirality[END_REF][START_REF] Pham | Chiral optical local density of states in a spiral plasmonic cavity[END_REF].

Chapter 5

Applications in plasmonics (III): probing the energy-momentum dispersion of propagating waves in plasmonic microstructures

In the previous chapter (Chap. 4), we used the tip-sample junction as a spectrally broadband, spatially isotropic, point-like source of surface plasmon polaritons (SPP), to drive the emission of light from plasmonic microstructures.

Taken together, the geometry of the plasmonic microstructure and the lateral position of the excitation source litterally determine where, when and how many SPPs convert into light, i.e., the spatial distribution of the amplitude and phase of the emitted field. Thus, the emission wavefront and the resulting far-field angular emission pattern may be controlled. Such electrical light microsources with tailored emission may be used in wireless optical communications on a micrometer-to-millimeter scale, e.g., to exchange information using light between two devices or two chips within a device. However, some other more integrated or specific applications may require the use of SPPs themselves as an information vector, e.g., in on-chip optical communications or in applications based on near-field interactions with the environment, such as plasmonic sensing. In that case, it is the propagation properties of SPPs, or more generally their energy-momentum dispersion (which includes the energy and momentum-dependence of the local density of SPP states), that must be engineered.

In this context, the combination a movable, local SPP nanosource (under the STM tip) and the Fourier space analysis of the SPP leakage radiation using an optical microscope may be highly valuable. In Sec. 5.1, we render the SPP propagation highly anisotropic through two-dimensional periodic nanostructuring of the propagation medium in the lateral (in-plane) directions. We report the observation of SPP beam steering from the STM tip in four specific directions of the nanostructured surface, with narrow in-plane angular spread. The local character of the STM excitation makes the investigation of the effect of the SPP source location in finite-size nanostructured areas possible. In Sec. 5.2, the SPP propagation medium is nanostructured in the transverse (out-of-plane) direction, through the incorporation of a waveguiding dielectric layer in-between two plasmonic films. Using our STM-based technique, we reveal that such a stack supports hybrid plasmonic-photonic modes and we measure the optical band-gap structure that results from an avoided crossing of the SPP and waveguided mode dispersion curves. This section is adapted with permission from D. Canneson, E. Le Moal, S. Cao, X. Quélin, H. Dallaporta, G.

SPP beam steering on a periodically nanostructured gold film

Dujardin, and E. Boer-Duchemin, "Surface plasmon polariton beams from an electrically excited plasmonic crystal".

Opt. Express, 24(23):26186-26200, Nov 2016. Copyright (2016) Optical Society of America. [START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF] Context and motivation. Wave propagation in a material may be dramatically modified by periodic structuring on the scale of wavelength. In such materials, Bragg reflections from lattice planes may interfere with the incident waves, thus changing the dispersion relation of the medium and making it very anisotropic. Gaps may occur in the energy-momentum dispersion relation and as a result, wave propagation at specific frequencies and in specific directions may be forbidden [START_REF] Yablonovitch | Inhibited spontaneous emission in solid-state physics and electronics[END_REF]. This is the principle of photonic crystals [START_REF] Thomas | Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths[END_REF], which are artificial dielectric materials having optical properties tailored for applications, such as the fabrication of miniaturized waveguides and lasing resonant cavities [START_REF] Noda | Full three-dimensional photonic bandgap crystals at near-infrared wavelengths[END_REF][START_REF] Akahane | High-Q photonic nanocavity in a two-dimensional photonic crystal[END_REF]. A similar approach, referred to as plasmonic crystals, has been developed to control the propagation of SPPs. Plasmonic crystals often consist of periodic arrays of nanoholes or nanodots on a continuous metallic film. For instance, it has been reported that SPP propagation on a silver film can be blocked in all directions of the plane for a given energy range when its surface is textured with an hexagonal array of nanodots [START_REF] Kitson | Full photonic band gap for surface modes in the visible[END_REF]. This effect, which is due to the existence of energy gaps, has been used to inhibit the spontaneous emission of quantum emitters close to metallic surfaces [START_REF] Kitson | Surface-plasmon energy gaps and photoluminescence[END_REF]. There is also increasing interest in plasmonic crystals for the fabrication of diffractive optical microelements for plasmonic circuitry [START_REF] Devaux | Launching and decoupling surface plasmons via micro-gratings[END_REF][START_REF] Drezet | Surface Plasmon Polariton Mach-Zehnder Interferometer and Oscillation Fringes[END_REF][START_REF] Drezet | Plasmonic crystal demultiplexer and multiports[END_REF].

Recently, there has been a rapidly growing trend in plasmonics toward the development of nano-and microdevices that are electrically driven with low-energy electrons in the view of integration with nanoelectronics [START_REF] Rai | Electrical Excitation of Surface Plasmons by an Individual Carbon Nanotube Transistor[END_REF][START_REF] Kevin | Electrically driven subwavelength optical nanocircuits[END_REF][START_REF] Kern | Electrically driven optical antennas[END_REF][START_REF] Cazier | Electrical excitation of waveguided surface plasmons by a light-emitting tunneling optical gap antenna[END_REF][START_REF] Pohl | Stacked optical antennas[END_REF][START_REF] Parzefall | Antenna-coupled photon emission from hexagonal boron nitride tunnel junctions[END_REF][START_REF] Ding | An electrical injection metallic cavity nanolaser with azimuthal polarization[END_REF][START_REF] Wang | Molecular electronic plasmonics[END_REF][START_REF] Du | On-chip molecular electronic plasmon sources based on self-assembled monolayer tunnel junctions[END_REF][START_REF] Vardi | Fano Resonance in an Electrically Driven Plasmonic Device[END_REF][START_REF] Zia | Plasmonics: the next chip-scale technology[END_REF][START_REF] Babuty | Semiconductor Surface Plasmon Sources[END_REF][START_REF] Service | Ever-Smaller Lasers Pave the Way for Data Highways Made of Light[END_REF]. This trend has yielded some very exciting achievements Reprinted with permission from [START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF]. Copyright (2016) Optical Society of America.

such as electrical nanosources of light and SPPs based on nanoscale light emitting devices (LED) [START_REF] Kevin | Electrically driven subwavelength optical nanocircuits[END_REF] or tunnel junctions [START_REF] Kern | Electrically driven optical antennas[END_REF][START_REF] Cazier | Electrical excitation of waveguided surface plasmons by a light-emitting tunneling optical gap antenna[END_REF][START_REF] Du | On-chip molecular electronic plasmon sources based on self-assembled monolayer tunnel junctions[END_REF][START_REF] Vardi | Fano Resonance in an Electrically Driven Plasmonic Device[END_REF]]. Yet, the coupling of such electrical light and SPP nanosources to a plasmonic crystal has never been envisaged so far. Most often, plasmonic crystals are excited using a laser or, more rarely, high-energy electrons in the vacuum of an electron microscope [START_REF] Takeuchi | Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence[END_REF][START_REF] Watanabe | Size dependence of band-gaps in a onedimensional plasmonic crystal[END_REF][START_REF] Saito | Confinement of surface plasmon polaritons by heterostructures of plasmonic crystals[END_REF]; however, local, low-energy, electrical excitation under ambient conditions is preferable for applications in electronics. Another crucial requirement for future applications in plasmonic circuitry is the capacity to steer SPP beams, i.e., to concentrate the energy emitted by the SPP nanosource in specific directions. SPP steering and auto-collimation have been observed in oneand two-dimensional sinusoidal metallic gratings when the SPP wavelength matches the diagonal of the lattice unit cell [START_REF] Stein | Surface plasmon mode steering and negative refraction[END_REF][START_REF] Stein | Self-collimation of surface plasmon beams[END_REF]. Until now, however, such studies have been limited to the optical excitation of SPPs with a laser beam. A crucial advantage of using a scanning probe such as an STM tip is that the effect of the location of the SPP source within a finite-sized plasmonic array may be easily investigated. When the excitation source is in the center of a square array, directional SPP emission along the diagonals of the square array is observed. The resulting SPP beams remain visible even beyond the array boundaries, i.e., on the unstructured gold film. Indeed, SPP beaming up to 25 µm away from the array corner may be seen. The full angular width of the beams at half intensity maximum (FWHM) is 8 ○ to 10 ○ (once the isotropic background is subtracted), i.e., the in-plane angular spread is ±4 ○ to ±5 ○ with respect to the mean propagation direction. The peak-to-background intensity ratio is about 2.

Results and discussion

When the excitation point is located on the side of the array [see Fig. 5.3(e)], only half of the SPP wavefront emitted from the source propagates through the array (i.e., the part corresponding to wavevectors with k x < 0), while Images in panels (d) to (f) are in false color and saturated (intensity is given in photon counts). Exposure times range from 600 to 1800 s. STM bias is 2.8 V and the tunnel current setpoint is in the 0.1 -6 nA range. The real-space axes are defined with respect to the array axes. [(g) to (i)] Polar plots obtained from the analysis of the real-space images shown in panels (d) to (f), respectively, and [(j) to (l)] schematics showing the preferential SPP propagation directions. In (g) to (i), we use a polar coordinate system where ρ is the lateral distance from the tip apex and φ is the polar angle in the surface plane. In each graph, the two plots correspond to the radially-integrated intensity over two different ranges of ρ, i.e., from 10 µm to 15 µm (black curve) and from 26 µm to 31 µm (red curve). In (g), these ranges of ρ correspond to an area within the NP array (but far enough from the source to solely detect propagating SPPs) and an area just outside the NP array, respectively. The numbers on the graph are the full angular width at half maxima (FWHM) of the intensity peaks after the isotropic background is subtracted. Dashed lines in (h) and (i) indicate the directions of the array edges. In (j) to (l), thin and thick arrows indicate that angularly narrow (FWHM = 8 ○ to 10 ○ ) and broad (FWHM ≈ 20 ○ ) SPP beams are observed in these directions, respectively. Adapted with permission from [START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF]. Copyright (2016) Optical Society of America the other half propagates on the unstructured gold film (i.e., the part with k x > 0). SPP beams with the same angular FWHM as above exist along the two diagonal directions for the part propagating through the array. Interestingly, the part of the wavefront that does not propagate through the array nevertheless also leads to SPP beams, but of much broader angular spread [the FWHM is about 20 ○ instead of 8 ○ , see Figs. Now we examine the effect of the array geometry. In Figure 5.4, we compare the real-space images recorded upon electrical excitation of the square and rectangular plasmonic crystals introduced above, when the STM tip is in the center of the array. On the rectangular array, four preferential SPP propagation directions are also clearly seen.

They are oriented at an angle of about 30 ○ with respect to the short axis of the rectangular array (FWHM ≈ 12 ○ ).

Thus, unlike on the square array, the SPP beaming directions on the rectangular array do not coincide with the diagonals of the array.

In addition, on both arrays, dark and bright fringes may be seen between the SPP beams identified in Figs. 5.4(c) and 5.4(d). The orientation of these fringes depends on their location in the image, but in each case they are parallel to one of the two array axes. Far from the excitation source, the fringe period is equal to the pitch of the perpendicular array axis, i.e., the pitch of the axis to which the fringes are orthogonal (450 nm for the square array and 330 550 nm along the x/y axis of the rectangular array). However, the fringes do not perfectly coincide with the locations of the lines and rows of nanodisks; close to the source, the fringes bend visibly, whereas the lines and rows of nanodisks are straight. This suggests that the observed fringes are the result of interferences in the near-field between the initial and in-plane scattered SPPs [START_REF] Wang | Scattering of electrically excited surface plasmon polaritons by gold nanoparticles studied by optical interferometry with a scanning tunneling microscope[END_REF]. This near-field phenomenon is visible in real-space images since SPP leakage radiation mirrors the electric near field above the air-gold interface [START_REF] Wang | Does the leakage radiation profile mirror the intensity profile of surface plasmon polaritons?[END_REF][START_REF] Drezet | Imaging surface plasmons: From leaky waves to far-field radiation[END_REF].

The experimental real-space images are compared to FDTD calculations performed using the Lumerical software, a full electromagnetic modeling of the problem, as well as simulations carried out within a very simple dipole model, where the scattered emission from the nanodisks only depends on the scatterer's distance from the source.

Remarkably, both theoretical approaches reproduce well the preferential SPP propagation directions, including the differences between the square and rectangular arrays, and the additional fringe patterns that are observed in experiments. This confirms that the beaming effect is primarily a consequence of interferences between the initial and in-plane scattered SPP waves. Below, we examine theoretically and experimentally how such interferences translate themselves in Fourier space. k ∥ = 1.49k 0 is truncated in order to simulate the NA of the objective lens. This theoretical result is compared to the experimental Fourier-space image in Figs. [START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF].5(a) and 5.5(b). Images with both saturated and unsaturated intensity scales are shown so that the agreement between theory and experiment.

The monochromatic Fourier-space images [Figs. [START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF].5(e) to 5.5(g)] reveal that, at certain energies (or photon wavelengths), SPP propagation in the nanodisk array is forbidden in some directions of the plane and enhanced in some others. An example of the STM-induced emission spectrum measured in similar conditions on a 50 nm-thin gold film may be found in Fig. 4.7; in general, the emission spectrum exhibits a maximum at about 740 nm and a full width of about 200 nm in wavelength at half maximum. According to Figs. [START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF].5(e) to 5.5(g), SPP propagation along the diagonals of the square array is inhibited in the short wavelength range of the emission spectrum (typically λ 0 < 690 nm), whereas it is favored in the long wavelength range, where most of the power is emitted; thus, SPP beaming along the diagonals of the square array is experimentally observed.

In addition, interference between the unscattered/initial and scattered/reflected SPP waves locally modifies the shape and intensity of the SPP ring at these four particular points. This phenomenon has already been reported in the case of laser-excited 2D sinusoidal gratings on gold, and was ascribed to the opening of gaps in the SPP dispersion due to the coupling of the array diffraction orders [START_REF] Stein | Surface plasmon mode steering and negative refraction[END_REF][START_REF] Stein | Self-collimation of surface plasmon beams[END_REF]. As visible in our simulations, such effects are highly sensitive to the oscillation frequency. In our case, due to spectral averaging, gap openings may not be distinguished in both the experimental and theoretical results of Figs. Finally, a simple model may be found in Ref. [START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF] (not shown here) which elucidates why SPP beaming occurs along the diagonals of the square array and not along other directions. In brief, at wavelengths close to the emission maximum (i.e., around λ 0 = 700 nm), SPPs propagating on the air side of the gold film may be scattered in-plane (i.e., into SPPs) by the square nanodisk array only along its diagonals, whereas along the other directions they may only be scattered out-of-plane (i.e., into light).

Conclusions and outlooks.

We have investigated the optical response of gold nanodisk arrays on gold (i.e., plasmonic crystals) to a local, electrical excitation based on the low-energy tunnel electrons from the tip of an STM.

SPPs propagate away from the excitation source and are scattered in-plane (into SPPs) and out-of-plane (into light) by the nanodisk array. Interference in the near field between the emitted and in-plane scattered SPPs yields strong directional effects in SPP propagation, which are observed in the SPP leakage radiation pattern.

In light of what we have demonstrated in the previous chapters (see in particular Secs. 3.3 and 4.2), we may interpret our results on the STM-excitation of plasmonic crystals shown above in the following way. Firstly, the local excitation of SPPs using the inelastic electron tunneling under the STM tip and the detection of the resulting SPP leakage radiation in the transparent substrate give access to the out-of-plane component of the local density of SPP states (z-SPP-LDOS) in the plasmonic crystals. Secondly, the real-space image recorded using the optical microscope reveals the dependence of the z-SPP-LDOS on the SPP propagation direction and, most interestingly, the persistence of the observed beaming effects beyond the boundaries of the plasmonic crystals. Thirdly, the Fourier-space image shows the momentum-dependence of the z-R-EMLDOS, i.e., the out-of-plane component of the local density of radiative electromagnetic states, including the light emitted from the tunnel junction, the SPP leakage radiation, and the SPP scattering into light at the nanodisks.

Finally, our numerical simulations of the Fourier-plane images show the interest in spectrally filtering the detected light in order to highlight the bandgap structure of the energy-momentum dispersion of the SPPs in plasmonic crystals, which is smeared out in a panchromatic detection due to the broad power spectrum of the inelastic electron tunneling effects. In the next section, such a filtering is used to reveal the energy-momentum dispersion of the SPPs excited in another widely studied system in plasmonics, i.e., a M-I-M stack. Applications of such stacks in biosensing [START_REF] Lan | Plasmonic rainbow rings induced by white radial polarization[END_REF], superlensing [START_REF] Fang | Sub-diffraction-limited optical imaging with a silver superlens[END_REF][START_REF] Xiong | Two-dimensional imaging by far-field superlens at visible wavelengths[END_REF], radiative decay engineering [START_REF] Sharmistha | Directing fluorescence with plasmonic and photonic structures[END_REF], waveguiding [START_REF] Dionne | Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries[END_REF][START_REF] Verhagen | Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides[END_REF] and tunable light sources [START_REF] Adamo | Light Well: A Tunable Free-Electron Light Source on a Chip[END_REF][START_REF] Fu Feng | Active control of radiation beaming from tamm nanostructures by optical microscopy[END_REF] have been reported. In this context, a simple technique that can be used to obtain the dispersion relation of the optical modes of such systems is indispensable.

Revealing the photonic-plasmonic band-gap structure of a metal-insulator-metal (M-I-M) stack

In principle, the energy-momentum dispersion relation of the modes of the system that couple to light may be retrieved from optical reflectivity measurements, e.g., using plane-wave illumination through a prism in a Kretschmann-Raether (KR) configuration [START_REF] Kretschmann | Radiative decay of nonradiative surface plasmons excited by light[END_REF]. However, prism-based KR experiments generally require sweeping the incidence angle and beam wavelength over a wide range of values-a single-shot, broadband measurement, on the other hand, would be more practical. This, however, is not possible in a standard prism-based KR experiment. In theory, such a measurement may be carried out by simultaneously illuminating the sample at all angles using a focused white light source [START_REF] Kano | Excitation of surface-plasmon polaritons by a focused laser beam[END_REF]. In practice, however, tightly focusing a spectrally broad beam of light is difficult due to the inherent abberations of high numerical-aperture lens systems [START_REF] Bouhelier | Excitation of broadband surface plasmon polaritons: Plasmonic continuum spectroscopy[END_REF]. Nonetheless, such issues may be overcome through the use of a local source, in which case both the spatial extent and the power spectrum of the excitation may be controlled.

Various different strategies have been used to obtain a local source of light, e.g., the use of an optical fiber or a scattering tip in a scanning nearfield optical microscope [START_REF] Hecht | Local excitation, scattering, and interference of surface plasmons[END_REF][START_REF] Lalouat | Subwavelength imaging of light confinement in high-Q/small-V photonic crystal nanocavity[END_REF][START_REF] Lalouat | Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe[END_REF][START_REF] Dellinger | Hyperspectral optical near-field imaging: Looking graded photonic crystals and photonic metamaterials in color[END_REF][START_REF] Jäger | Au nanotip as luminescent near-field probe[END_REF], sometimes in combination with a plasmonic or photoluminescent nanoparticle [START_REF] Schell | Scanning single quantum emitter fluorescence lifetime imaging: Quantitative analysis of the local density of photonic states[END_REF][START_REF] Da Cao | Mapping the radiative and the apparent nonradiative local density of states in the near field of a metallic nanoantenna[END_REF][START_REF] Rabouw | Europium-doped NaYF 4 nanocrystals as probes for the electric and magnetic local density of optical states throughout the visible spectral range[END_REF][START_REF] Salas-Montiel | Local density of electromagnetic states in plasmonic nanotapers: spatial resolution limits with nitrogenvacancy centers in diamond nanospheres[END_REF]. Nevertheless, the excitation spectra of these techniques is often narrow compared to the frequency range of interest (the visible and near infrared) for most studies of plasmonic systems. On the other hand, the truely local and spectrally broad excitation of optical modes is possible using the high-energy (∼ 30 keV) electron beams of a scanning [START_REF] Coenen | Angle-resolved cathodoluminescence spectroscopy[END_REF] or transmission [START_REF] Kociak | Mapping plasmons at the nanometer scale in an electron microscope[END_REF] electron microscope. In this case, the electron-matter interactions produce light via cathodoluminescence [START_REF] García De Abajo | Optical excitations in electron microscopy[END_REF]. Among other studies, this approach has been used to investigate the optical modes of plasmonic multilayer stacks [START_REF] Mohtashami | Nanoscale Excitation Mapping of Plasmonic Patch Antennas[END_REF][START_REF] Adamo | Light Well: A Tunable Free-Electron Light Source on a Chip[END_REF][START_REF] Jan | Experimental Verification of n=0 Structures for Visible Light[END_REF]. The main drawback of these excitation techniques is the vacuum environment and associated cost of the necessary high energy electrons.

In contrast, inelastic electron tunneling (IET) through a nanometer-scale tunnel junction provides a spectrally broad excitation source using low energy electrons [START_REF] Lambe | Light emission from inelastic electron tunneling[END_REF][START_REF] Rendell | Surface plasmons confined by microstructures on tunnel junctions[END_REF]. Advantageously, this approach is compatible with ambient conditions, uses low voltage and low current, and can be implemented using a scanning tunneling microscope (STM) operating in air [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF][START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF]. The spatial selectivity of the electrical excitation of optical modes with an STM tip is well beyond the diffraction limit of light [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. On the scale of visible wavelengths, the excitation source may indeed be considered a point-like electric dipole [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF][START_REF] Wang | Plasmon scattering from holes: from single hole scattering to Young's experiment[END_REF][START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]. The emission of this point source continuously ranges from the infrared to visible frequencies and the power spectrum of the excitation source is determined by the probability of inelastic tunneling, the applied voltage and the optical response of the tip-surface nanocavity [START_REF] Bharadwaj | Electrical Excitation of Surface Plasmons[END_REF][START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]. When a non-plasmonic tip is used, as is the case here where we use a tungsten tip, no sharp tip-surface nanocavity resonances are present [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF].

Results and discussion. In this section, we show that an "STM-nanosource" coupled to an optical microscope may be used to measure the dispersion relation of the propagating modes in a plasmonic multilayer stack. The STM-nanosource results are compared to optical reflectivity measurements (acquired using a focused laser beam)

and to theoretical calculations of the energy-momentum dispersion relations. In this way we demonstrate that only a single image is required for the broadband characterization of the hybrid plasmonic-photonic TM modes of a metalinsulator-metal stack consisting of a silicon oxide layer [START_REF] Melissa Konzelmann | Interaction of orbital angular momentum light with Rydberg excitons: Modifying dipole selection rules[END_REF][START_REF] Dregely | 3D optical YagiUda nanoantenna array[END_REF] or 310 nm thick) between two gold films (each with a thickness of 30 nm).

The electrical excitation of the existing optical modes through inelastic electron tunneling between the tip and the sample is modeled using a point-like oscillating electric dipole located in the tip-sample gap. The oscillating dipole is orthogonal to the sample surface restricting the light emission to the p polarization. Figure 5.6(a) shows a schematic of the modeled system. The spherical-wave emission from the vertical dipole is expressed in terms of a continuous sum of plane waves using the Sommerfeld expansion (see refs. [START_REF] Lukosz | Light emission by magnetic and electric dipoles close to a plane interface. I. total radiated power[END_REF][START_REF] Chance | Molecular Fluorescence and Energy Transfer Near Interfaces[END_REF][START_REF] Novotny | Allowed and forbidden light in near-field optics. I. a single dipolar light source[END_REF]). Then, the Poynting vector or energy flux per unit time and per unit area of the emitted light through the multilayer stack is expressed in terms of the Fresnel transmission coefficients of the entire stack, which are calculated using Abèles transfer matrix algorithm in Bethune's implementation [START_REF] Bethune | Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques[END_REF]. The dispersion graphs are calculated by representing the intensity of the transmitted flux of the electromagnetic wave on a grid of the real in-plane wavevector k ρ k 0 and of the energy ̵ hω.

Finally, the nature of the excited optical modes is inferred from the electric field profile along the direction orthogonal to the stacks. This last result is obtained using Bethune's transfer matrix algorithm (for more detail, see [START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]).

In a system such as a MIM stack, the different optical modes that exist are expected to have a specific energywavevector relation, i.e., a mode of a certain energy will have a particular wavevector. Since the optical Fourier space corresponds to "k-vector" or "wavevector" space, a Fourier-space image of the emission from the excited modes will give information on their wavevector distribution. 1" of the experimental setup introduced in Fig. 2.4(b) is used. The detected light is not spectrally filtered, i.e., the signal is integrated over the broad power spectrum of the excitation source, weighted by the detection efficiency of the instrument. Due to the symmetry of the excitation and of the system, the resulting image is seen to be independent of direction in the k x k y -plane, indicating that the STM locally excites out-going circular waves in the MIM stack which propagate isotropically away from the tunnel junction. In Fig. 5.6(c), a polarizer is set in front of the CCD camera with its transmission axis parallel to the x-axis. The total extinction of the transmitted light along the k y -axis demonstrates that the emitted light is purely p-polarized (i.e., TM or radially polarized). Simulations of the corresponding Fourier-space images are shown in Figs. 5.6(d) and 5.6(e), respectively. In both the experimental and calculated images, a sharp ring of radius k ρ k 0 = 1.03 and a comparatively fainter and broader ring that extends from k ρ k 0 = 1 to the collection limit of the microscope objective (i.e., k ρ k 0 = 1.49), are seen. Such rings are the result of the excitation of the optical modes of the MIM stack. These modes may be plasmonic or photonic, or a hybridization of the two. A step towards identifying the nature of the excited modes is to determine the energy-wavevector (or energy-momentum dispersion) relations. While this could be carried out by repeating the above "configuration 1" experiment with different filters in front of the detector (see an example of such an experiment in Fig. 5.7), a more efficient one-shot measurement is performed using "configuration 2" of the set-up presented in Fig. 2.4(b). To obtain this data, the Fourier-space image is projected onto the entrance slit of the imaging spectrometer using lenses, so that the k y -axis is parallel to the slit and the origin of Fourier space, i.e., (k x , k y ) = (0, 0), is in the center of the slit. Thus, the slit selects a narrow band of light along index is seen to be very different: in one case the curve is practically vertical on the graph, corresponding to a mode with little dispersion (i.e., weak energy dependence of the mode effective index on energy), while in the other, the dispersion is significant (the dependence of the mode effective index on energy may not be ignored). Such dispersion relations are typical of SPP and waveguided (WG) photonic modes, respectively.

Though difficult to see in the experimental images, a minimum in the mode density between the two observed a lower value of the Rabi splitting is estimated (about 0.33 eV), and the optical bands are comparatively broader, presumably due to losses from surface roughness and inexact values for the permittivity of gold and titanium.

In order to determine the nature of the excited modes, the electric field in the different layers of the sample may be calculated [START_REF] Sharmistha | Directing fluorescence with plasmonic and photonic structures[END_REF][START_REF] Dionne | Planar metal plasmon waveguides: frequencydependent dispersion, propagation, localization, and loss beyond the free electron model[END_REF][START_REF] Smith | Field profiles of coupled surface plasmon-polaritons[END_REF][START_REF] Chen | Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides[END_REF][START_REF] Ditlbacher | Coupling dielectric waveguide modes to surface plasmon polaritons[END_REF]. This is carried out theoretically by illuminating the structure with a plane wave from the glass substrate. Figure 5.9 shows the z-dependence of the electric field modulus as a function of energy for different values of the in-plane wavevector component k ρ k 0 .

At a value of k ρ k 0 just below that of an SPP-mode on an air/gold interface [see Fig. 5.9(a) and (b)], a single mode is present. The presence of significant electric field in both the air and SiO 2 layers demonstrates that the mode is a hybridized SPP/photonic waveguide mode. With the particularly strong electric field in air, especially for the stack with the thicker SiO 2 layer [part (b)], we can conclude that this mode is of dominantly SPP character.

For a value of k ρ k 0 just above that of an SPP-mode on an air/gold interface [see Fig. 5.9(c) and (d)], two modes are found. These modes are of the same character as previously. As k ρ k 0 is increased further, however, [see Fig. 5.9(e) and (f)], the field in the SiO 2 layer increases relative to that in air. In other words, as would be expected, as k ρ k 0 becomes significantly larger than that of an SPP-mode on an air/gold interface, the waveguide character of the hybrid mode increases. Indeed, the photonic waveguide mode dominates for the highest values of k ρ k 0 shown in Fig. 5.9(g) and Fig. 5.9(h). filter transmitting light at 625 nm with a bandwidth of 26 nm is set in front of the CCD camera. Note that the STMnanosource Fourier-space images are displayed using a reversed intensity scale (i.e., the darker the color, the more The experimental data in wavelength has been converted to energy using a Jacobian transformation [START_REF] Mooney | Get the basics right: Jacobian conversion of wavelength and energy scales for quantitative analysis of emission spectra[END_REF][START_REF] Mooney | Correction to "get the basics right: Jacobian conversion of wavelength and energy scales for quantitative analysis of emission spectra[END_REF]. Reprinted with permission from [START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]. Copyright (2019) Optical Society of America. intense the emitted light), so that the optical modes stand out against a bright background in all cases. Two main differences may be easily observed when the Fourier-space images obtained under optical and electrical excitation are compared (Fig. 5.10). The first is the fact that while complete rings are observed in the STMexcitation images, only partial arcs are present in the case where the sample is illuminated by a focused laser beam.

The second is that while the same rings or arcs appear in the k x -axis direction for both types of excitation (labels 1 and 2), the rings or arcs in the k y -axis direction do not correspond (i.e., they are located at different values of k y , see arcs with the label 3). This analysis is confirmed by the intensity cross-sections of Figs. 5.10(c) and 5.10(f).

These results may be understood by recalling that since the incident laser beam is linearly polarized, the incident illumination is s-polarized in one plane and p-polarized in the other when it is focused on the sample surface. As shown in Fig. 5.6(c), the STM-nanosource excites p-polarized or transverse magnetic (TM) modes. This is confirmed when taking into account that the experimental laser polarization is such that the incident light is p-polarized in the x direction -indeed, along k x , the optical and electrical excitation results are equivalent. In the k y -axis direction, the incident illumination is s-polarized: we may thus conclude that the modes present in the optically excited image along the k y -axis are s-polarized or transverse electric (TE) modes. Note that these TE modes may not be excited by the STM-nanosource, which may be considered as a vertical oscillating electric dipole.

For the MIM stack with d SiO 2 = 190 nm, the signature of the detected TE mode lies within the subcritical angular range. Thus the incident light is transmitted through the MIM stack and propagates away in the air above the sample.

The drop in reflectance may thus be understood as a transmission resonance of the MIM stack (such as in a Fabry-Perot resonator) and the radial width of the dark arcs in Fourier space is determined by the reflection coefficients at the gold-silicon oxide interfaces. For the MIM stack with d SiO 2 = 310 nm, however, the reflectance dip of the TE mode occurs at a supercritical angle and its radial width is comparatively narrow. This excited TE mode must be an optical waveguide mode that propagates in the plane of the MIM stack.

Note that in general, the detection of emitted light over a dark background generally results in more sensitive measurements than the detection of the absorption of light (i.e., the inverse contrast) in a bright field. This is because of the difficulty of illuminating the sample with a spatially and spectrally homogeneous optical field. As seen in Figs. [START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF].10(a) and 5.10(d), the inhomogeneous illumination pattern (despite the use of a spinning diffuser in front of the laser source) complicates the distinction between artifactual and real features and the quantitative measurement of the reflectivity variations; in comparison, the baseline of the electrically excited light is flat. Thus, with electrical excitation, even comparatively faint features occurring at high angles close to the maximum acceptance angle of the microscope objective (i.e., where the objective's transmission drops) may be detected. For instance, the peak/dip at k ρ k 0 = 1.45 (the objective's NA is 1.49) in Fig. 5.10(f) is identified with difficulty in the reflected light data, whereas it clearly distinguishes itself from the background in the STM-induced light data [see the arrow numbered 2 in Fig. 5.10(e)]. In addition, recent theoretical work [START_REF] Brissinger | Unguided plasmon-mode resonance in optically excited thin film: exact modal description of Kretschmann-Raether experiment[END_REF][START_REF] Akimov | Kretschmann-Raether configuration: Revision of the theory of resonant interaction[END_REF][START_REF] Akimov | Optical resonances in Kretschmann and Otto configurations[END_REF][START_REF] Vinogradov | Exciting surface plasmon polaritons in the Kretschmann configuration by a light beam[END_REF] has shown that reflectivity measurements in the Kretschmann configuration may be less accurate for the determination of the dispersion relations of the propagating modes in plasmonic stacks than techniques based on the leakage radiation of the excited modes such as the STM-technique described above.

Nonetheless, the STM-based technique used in this study also has several drawbacks as compared to far-field and near-field optical techniques. On a flat horizontal surface, the excitation source resulting from the inelastic tunnel current flowing between the tip and the surface invariably behaves like a vertical oscillating electric dipole.

As a result, only TM optical modes of the sample may be excited (i.e., TE modes may not be detected). It may, however, be possible to overcome this difficulty via the functionalization of the tip with a plasmonic nanoparticle in such a way that a tilted electric dipole may be generated [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. Such an excitation could then couple to both TE and TM modes. In addition, the flux of emitted photons is fundamentally limited by the electronic current passing through the junction in the tunneling regime (in the nA range) and the electron-to-optical mode conversion efficiency (theoretically in the 10 -6 -10 -4 range [START_REF] Johansson | Light emission from a scanning tunneling microscope: Fully retarded calculation[END_REF]). On average, this yields photon fluxes at the detector in the range of 10 3 to 10 5 s -1 . Therefore, exposure times of several minutes are often necessary to record typical values of 100 -1000 counts per pixel of the CCD camera. Here also, a solution may be found in the use of a specific tip design, e.g., a plasmonic tip engineered in a way so as to increase the local density of modes inside the tip-sample gap [START_REF] Bigourdan | Nanoantenna for Electrical Generation of Surface Plasmon Polaritons[END_REF].

Conclusions and outlooks.

To conclude, the inelastic electron tunnel current from the tip of an STM provides an extremely local and spectrally broad excitation source which may be used to probe the density of optical modes in a plasmonic multilayer stack, e.g., a metal-insulator-metal or MIM sample. The energy-momentum dispersion relations of the propagating modes is determined from the angle-resolved optical spectrum in transmission. This transmitted flux is measured using an optical microscope and an imaging spectrometer coupled to the STM head.

Thus, the hybrid plasmonic-photonic TM modes of a sample may be characterized from a single image. This approach may naturally be extended to the measurement of the optical band structure in systems exhibiting spatial periodicity in the lateral direction, i.e., plasmonic and photonic crystals and metasurfaces.

The STM-based technique introduced here has several advantages over existing far-field and near-field optical characterization methods. Its true deep-subwavelength spatial selectivity and its ability to provide STM topography images with nanoscale spatial resolution are strong assets for the study of nanostructured or surface-functionalized systems. In principle our technique is fully compatible with STM at the liquid-solid interface, where submolecular resolution may be attained even at room temperature (see, for example [START_REF] Sylvain Le Liepvre | Fluorescent Self-Assembled Molecular Monolayer on Graphene[END_REF]). In addition, our excitation source has a broader power spectrum than most optical probes based on a quantum nanoemitter (e.g., a semiconductor nanocrystal or an NV center in a nanodiamond), without resorting to the use of a tunable or supercontinuum laser source as in, for example, previous aperture near-field optical microscopy studies [START_REF] Bakker | Near-field, broadband optical spectroscopy of metamaterials[END_REF][START_REF] Dvořák | Imaging of near-field interference patterns by aperture-type SNOM -influence of illumination wavelength and polarization state[END_REF]. In principle, the spectral distribution of the excitation source is only limited in energy by the applied bias voltage [START_REF] Lambe | Light emission from inelastic electron tunneling[END_REF], which makes it well suited for studies in the near infrared [START_REF] Michael | Infrared emission from tunneling electrons: The end of the rainbow in scanning tunneling microscopy[END_REF]. Moreover, the well-controlled electric dipole orientation (orthogonal to the sample plane) of the STM excitation is best suited to the excitation of TM modes, e.g. surface plasmon polaritons, and provides a source of circular surface waves, isotropically propagating away from the excitation point [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF].

The main drawbacks of the electrical excitation of optical modes using the STM are the weakness of the resulting optical signal and the difficulty of detecting TE and nonradiative modes. Nonetheless, these issues could be overcome by implementing various strategies, e.g., based on the engineering of the tip.

Finally, we anticipate that the STM-based technique introduced in this article may be applied to a number of different fields, including, among many others, the characterization of optical modes in nanoresonators, stacked nanoantennas [START_REF] Esteban | Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances[END_REF], and multilayer stacks incorporating semiconductors [START_REF] Symonds | Emission of Tamm plasmon/exciton polaritons[END_REF]. Combining our technique with polarimetry would lead to the characterization of the optical response of chiral nano and microstructures [START_REF] Gorodetski | Generating far-field orbital angular momenta from near-field optical chirality[END_REF]. Beyond optical mode characterization, our technique may be used as an interferometric tool to determine the phase in the optical response of nanostructures, as introduced in [START_REF] Wang | Scattering of electrically excited surface plasmon polaritons by gold nanoparticles studied by optical interferometry with a scanning tunneling microscope[END_REF]. It is also a valuable tool for the testing and design of integrated plasmonic microstructures in view of their integration in optoelectronic microdevices, as proposed in [START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF].

In the next chapter (Chap. 6), we show that the same experimental setup may also be used to probe the excitons in two-dimensional semiconductors and to distinguish between electroluminescence from bright (spin-allowed) and dark (spin-forbidden) excitonic transitions based on the distribution of STM-induced light in Fourier space [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF].

Thus, applications to semiconductor physics may be numerous too, including in the rapidly growing field of valleytronics. Finally, a recent report of time-correlated photon pair generation from the tunnel junction of an STM [START_REF] Leon | Photon superbunching from a generic tunnel junction[END_REF] suggests that future experiments in the field of quantum optics are also possible with this technique.

85

Chapter 6

Application in excitonics: electroluminescence nanospectroscopy of two-dimensional semiconductors

In the present chapter, we show that the use of an STM coupled to an optical microscope allows one to locally and spectroscopically probe the excitons of two-dimensional (2D) semiconductors. This was a long sought-after goal in the STM community, notably in view of electrically controlling the emission from point defects in such materials. The excitation and emission mechanisms may involve a combinaison of energy transfer and electric charge carrier injection into the electronic bands of the semiconductor, the creation of quasiparticles called excitons (i.e. electron-hole pairs bounded through Coulombic interaction), and internal conversion processes into various excitonic species. Below, we report the first observation of STM-induced excitonic luminescence from transition-metal dichalcogenide monolayers, of molybdenum diselenide (MoSe 2 ) on a transparent conducting substrate. We compare the results with photoluminescence measurements to identified the emission mechanism. The dependence of the STM-induced luminescence on the bias voltage is investigated in order to determine the excitation mechanism. Thus, we demonstrate a new technique for investigating the excitonic and optoelectronic properties of 2D semiconductors and their heterostructures at the nanometer scale. (2019) by the American Physical Society. [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF] Context and motivation. Two-dimensional (2D) semiconductors such as transition metal dichalcogenides (TMD, MX 2 , M=Mo, W; X=S, Se, Te) exhibit strong light-matter interactions, room-temperature excitonic effects and direct bandgap emission in the monolayer limit [START_REF] Mak | Atomically Thin MoS 2 : A New Direct-Gap Semiconductor[END_REF][START_REF] Splendiani | Emerging Photoluminescence in Monolayer MoS2[END_REF][START_REF] Fai | Photonics and optoelectronics of 2d semiconductor transition metal dichalcogenides[END_REF][START_REF] Victor | New Discoveries and Opportunities from Two-Dimensional Materials[END_REF][START_REF] Wang | Colloquium: Excitons in atomically thin transition metal dichalcogenides[END_REF][START_REF] Victor | Emerging photonic architectures in two-dimensional opto-electronics[END_REF]. With such assets, TMDs are of enormous interest for photonic and optoelectronic applications in miniaturized photodetectors and light-emitting devices [START_REF] Geim | Van der Waals heterostructures[END_REF][START_REF] Cheng | Electroluminescence and Photocurrent Generation from Atomically Sharp WSe 2/ MoS 2 Heterojunction pn Diodes[END_REF][START_REF] Furchi | Photovoltaic Effect in an Electrically Tunable van der Waals Heterojunction[END_REF][START_REF] Ross | Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 pn junctions[END_REF][START_REF] Clark | Single Defect Light-Emitting Diode in a van der Waals Heterostructure[END_REF][START_REF] Jariwala | Hybrid, Gate-Tunable, van der Waals pn Heterojunctions from Pentacene and MoS 2[END_REF][START_REF] Liu | Nanocavity Integrated van der Waals Heterostructure Light-Emitting Tunneling Diode[END_REF][START_REF] Binder | Sub-bandgap voltage electroluminescence and magneto-oscillations in a wse2 light-emitting van der waals heterostructure[END_REF]. Investigating the optoelectronic response of 2D semiconductors at the nanometer scale may not only provide fundamental insights into their rich exciton manifold and complex exciton dynamics but also lead to novel quantum devices. In this context, electroluminescence has recently been reported in TMD-based p-n junctions [START_REF] Furchi | Photovoltaic Effect in an Electrically Tunable van der Waals Heterojunction[END_REF][START_REF] Ross | Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 pn junctions[END_REF][START_REF] Zhang | Electrically Switchable Chiral Light-Emitting Transistor[END_REF][START_REF] Britton | Optoelectronic devices based on electrically tunable p-n diodes in a monolayer dichalcogenide[END_REF],

STM-induced excitonic luminescence of monolayer

tunnel junctions [START_REF] Binder | Sub-bandgap voltage electroluminescence and magneto-oscillations in a wse2 light-emitting van der waals heterostructure[END_REF] and quantum-light emitting diodes [START_REF] Palacios-Berraquero | Atomically thin quantum light-emitting diodes[END_REF]. However, in these studies, spatial control over exciton formation was typically limited to the micrometer scale due to the size of the devices. Achieving such control down to the nanoscale is a major challenge that has only been tackled using tip-enhanced optical excitation until now [START_REF] Park | Hybrid Tip-Enhanced Nanospectroscopy and Nanoimaging of Monolayer WSe 2 with Local Strain Control[END_REF][START_REF] Park | Radiative control of dark excitons at room temperature by nano-optical antenna-tip Purcell effect[END_REF]. One particularly promising approach that suppresses the need for optical excitation is the use of a scanning tunneling microscope (STM), since the tunnel current is an extremely local, low-energy, electrical excitation [START_REF] Qiu | Vibrationally Resolved Fluorescence Excited with Submolecular Precision[END_REF][START_REF] Zhang | Visualizing coherent intermolecular dipoledipole coupling in real space[END_REF][START_REF] Imada | Realspace investigation of energy transfer in heterogeneous molecular dimers[END_REF][START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF]. Nonetheless, STM-induced excitonic luminescence, i.e., the radiative recombination of STM-excited excitons in a monolayer TMD has not been reported. In previous attempts, the emission of light resulted from the radiative decay of the STM-excited plasmonic modes of the nanocavity formed between a gold tip and a gold surface [START_REF] Krane | Electronic Structure and Luminescence of Quasi-Freestanding MoS 2 Nanopatches on Au(111)[END_REF]. About one year after the publication of our results in Ref. [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF], two other groups have reported the observation of STM-induced excitonic luminescence from monolayer TMDs, i.e., WSe 2 [START_REF] Javier | Tunneling-current-induced local excitonic luminescence in p-doped WSe 2 monolayers[END_REF] and MoSe 2 monolayers [START_REF] Péchou | Plasmonic-induced luminescence of MoSe 2 monolayers in a scanning tunneling microscope[END_REF], on gold surfaces. Earlier, the creation of excitons had also been invoked by another group to explain the STM-induced emission of light from graphene on ITO-coated glass [START_REF] Beams | Electroluminescence from graphene excited by electron tunneling[END_REF]. Results and discussion. In this section, we report the first observation of STM-induced excitonic luminescence from a 2D semiconductor, i.e., monolayer MoSe 2 , using a non-plasmonic tip and a non-metallic transparent conducting substrate. All experiments are carried out under ambient conditions, i.e., in air at room temperature, and the emitted light is collected in transmission using an optical microscope. The observed luminescence is attributed to the radiative recombination of bright A excitons in MoSe 2 . The photon emission quantum efficiency depends on the bias voltage V s . The onset of photon emission is at values of eV s close to the optical bandgap of MoSe 2 , i.e., more than 0.5 eV lower than its electronic bandgap. The proposed excitation mechanism is resonance energy transfer from the tunneling current to the excitons in the semiconductor; thus, excitons are created through virtual photon coupling [START_REF] Andrews | The role of virtual photons in nanoscale photonics[END_REF]. This fundamentally differs from the charge injection mechanism inferred for the most part in previous electroluminescence studies [START_REF] Cheng | Electroluminescence and Photocurrent Generation from Atomically Sharp WSe 2/ MoS 2 Heterojunction pn Diodes[END_REF][START_REF] Furchi | Photovoltaic Effect in an Electrically Tunable van der Waals Heterojunction[END_REF][START_REF] Ross | Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 pn junctions[END_REF][START_REF] Clark | Single Defect Light-Emitting Diode in a van der Waals Heterostructure[END_REF][START_REF] Jariwala | Hybrid, Gate-Tunable, van der Waals pn Heterojunctions from Pentacene and MoS 2[END_REF][START_REF] Liu | Nanocavity Integrated van der Waals Heterostructure Light-Emitting Tunneling Diode[END_REF]. Additional mechanisms (including charge injection) may come into play for bias voltages that are higher than the electronic bandgap. Our results demonstrate a new technique for locally probing the elementary interactions between electrons, excitons and photons in 2D semiconductors; such studies are not possible using on-chip electroluminescent devices. focal planes of the objective on the camera (real-space and Fourier-space imaging), respectively [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF][START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Lieb | Single-molecule orientations determined by direct emission pattern imaging[END_REF].

Luminescence spectra are measured using an optical imaging spectrometer. In addition, photon mapping of the STM-induced luminescence (STL) is obtained by simultaneously scanning the sample surface with the STM tip and recording the optical signal using an avalanche-photodiode (APD) single-photon counting module. The photon emission quantum efficiency is obtained by dividing the optical signal by the measured current and expressing this ratio as a number of emitted photons per tunneling electron.

In Fig. 6.2(d), the STM tip locally excites a monolayer MoSe 2 domain [same area as the one framed in Fig. 6.2(b)] and the spatial distribution of the resulting light is measured in real space using the optical microscope. An intensity profile taken along a line crossing the location of the STM tip is shown in the inset. Not only is STL emitted from below the STM tip, but also from a microscale area around the tip, as defined by the flake boundaries. In addition, localized emission from several "hot spots", one to two micrometers away from the tip, is detected. Such observations confirm that excitons in monolayer TMDs at room temperature may diffuse micrometers away from the excitation source before radiatively decaying [START_REF] Mouri | Nonlinear photoluminescence in atomically thin layered WSe 2 arising from diffusion-assisted exciton-exciton annihilation[END_REF][START_REF] Kato | Transport dynamics of neutral excitons and trions in monolayer WS 2[END_REF][START_REF] Kulig | Exciton diffusion and halo effects in monolayer semiconductors[END_REF]. Hot spots at the flake edges and along folds and cracks in the flake may result from longer exciton residence times, or trapping. Below, the emission mechanism of STL is investigated using optical spectroscopy.

The STL and PL spectra from monolayer MoSe 2 shown in Fig. 6.2(e) are similar to each other. At a sample bias V s = 2 V and current setpoint of 10 nA, an STL peak at 1.57 eV (λ = 788 nm) is observed, the full width of which is 74 meV at half maximum (FWHM). Lower FWHM are measured at lower currents, i.e., 55 meV at 0.1 nA for the 1.5 -3.0 V bias range. Likewise, the PL spectrum of monolayer MoSe 2 exhibits an emission peak at 1.58 eV, the FWHM of which is 45 meV. These values are typical of the neutral A exciton in MoSe 2 at room temperature [START_REF] Froehlicher | Charge Versus Energy Transfer in Atomically Thin Graphene-Transition Metal Dichalcogenide van der Waals Heterostructures[END_REF].

The peaks in both spectra in Fig. 6.2(e) are asymmetric on the low energy side, due to additional contributions from charged excitons (trions) [START_REF] Wang | Colloquium: Excitons in atomically thin transition metal dichalcogenides[END_REF] and/or vibronic transitions [START_REF] Christiansen | Phonon sidebands in monolayer transition metal dichalcogenides[END_REF][START_REF] Niehues | Strain control of exciton-phonon coupling in atomically thin semiconductors[END_REF]. Such contributions cannot be resolved at room temperature. In addition, the semilog plot shown in Fig. 6.2(e) clearly shows the existence of a secondary peak blueshifted by [START_REF] Giannini | Plasmonic Nanoantennas: Fundamentals and Their Use in Controlling the Radiative Properties of Nanoemitters[END_REF][START_REF] Li | Directional light emission from propagating surface plasmons of silver nanowires[END_REF][START_REF] Shegai | Unidirectional Broadband Light Emission from Supported Plasmonic Nanowires[END_REF][START_REF] Novotny | Antennas for light[END_REF][START_REF] Ahmed | Directivity enhanced raman spectroscopy using nanoantennas[END_REF][START_REF] Aouani | Plasmonic Antennas for Directional Sorting of Fluorescence Emission[END_REF][START_REF] Aouani | Ultrasensitive Broadband Probing of Molecular Vibrational Modes with Multifrequency Optical Antennas[END_REF][START_REF] Zhu | Direct observation of beamed raman scattering[END_REF][START_REF] Lu | Plasmonicenhanced molecular fluorescence within isolated bowtie nano-apertures[END_REF][START_REF] Taminiau | Enhanced directional excitation and emission of single emitters by a nano-optical Yagi-Uda antenna[END_REF][START_REF] Dregely | 3D optical YagiUda nanoantenna array[END_REF] meV with respect to the A exciton. This shift matches the energy splitting of the valence band due to spin-orbit coupling in monolayer MoSe 2 [START_REF] Wang | Colloquium: Excitons in atomically thin transition metal dichalcogenides[END_REF]; thus, we ascribe the blue-shifted peak to hot luminescence from the B exciton [START_REF] Froehlicher | Charge Versus Energy Transfer in Atomically Thin Graphene-Transition Metal Dichalcogenide van der Waals Heterostructures[END_REF]. The match between the PL and STL spectra shown in Fig. 6.2(e) is evidence that they result from the same emission mechanism. Thus, the dominant emission process of STL from monolayer MoSe 2 on ITO is the radiative recombination of A excitons in MoSe 2 . Other emission mechanisms such as black-body radiation or radiative electronic transitions between tip and surface states may be ruled out because of the close match of the results to the PL spectrum. As shown in Fig. 6.3(f), the experimental radial profile clearly differs from that of an out-of-plane electric dipole. In contrast, excellent agreement with the in-plane dipole model shown in Fig. 6.3(e) is found, in particular within the subcritical angular range and for the angle of maximum emission, without the use of any fitting parameters. These observations confirm that the detected light is not due to a nanocavity mode of the tip-surface junction, since such a mode would exhibit an emission pattern similar to that of an out-of plane dipole [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. These results also confirm that we measure the luminescence of the bright exciton in monolayer MoSe 2 , which has an in-plane transition dipole (unlike the dark exciton) [START_REF] Schuller | Orientation of luminescent excitons in layered nanomaterials[END_REF]. Here, bright and dark excitons refer to the spin-allowed and spin-forbidden excitons that result from the conduction band splitting due to spin-orbit coupling, respectively. In molybdenum-based TMDs, bright A excitons have lower energy than their dark counterparts; therefore, PL from monolayer MoSe 2 is due to bright A excitons [START_REF] Wang | Colloquium: Excitons in atomically thin transition metal dichalcogenides[END_REF]. Thus, we conclusively demonstrate that the electrical excitation from the STM induces luminescence from the same excitons as those responsible for the photoluminescence of MoSe 2 . In our work, no interaction with a plasmonic tip [START_REF] Park | Radiative control of dark excitons at room temperature by nano-optical antenna-tip Purcell effect[END_REF] or substrate [START_REF] Zhou | Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons[END_REF] renders the dark excitons optically active. Neither the substrate nor the STM tip used support surface plasmons within the investigated frequency range (the real parts of the dielectric permittivities of tungsten and ITO are positive). lateral resolution, which is not attainable in standard optical microscopy. In particular, the quantum efficiency map exhibits a sharp transition between the bilayer and monolayer areas, over less than 20 nm. The two areas differ by 0.9 nm in STM height, i.e., close to the expected thickness of one MoSe 2 layer (i.e., 0.65 nm). The photon emission quantum efficiencies measured on the two areas differ from each other by two orders of magnitude. Thus, detection limit @ I t = 10 nA

I t = 0.1 nA I t = 10 nA
Quantum efficiency (photon / electron) Sample bias voltage (V) detection limit @ I t = 0.1 nA optical gap Figure 6.5: Photon emission quantum efficiency (i.e., the number of emitted photons per tunneling electron) versus the sample bias voltage, obtained from STM-induced luminescence spectra of monolayer MoSe 2 measured at current setpoints of 0.1 nA and 10 nA (see spectra in SM). The detection limit is defined from the standard deviation of the dark current of the CCD camera and the STM setpoint current. A vertical dotted line indicates the optical gap energy of monolayer MoSe 2 . Reprinted with permission from [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF]. Copyright (2019) by the American Physical Society. monolayer versus bilayer MoSe 2 may be identified without ambiguity. Furthermore, the imaging of nanoscale defects is demonstrated, e.g., on folds that form in monolayer MoSe 2 flakes due to the deposition process and which may extend over micrometers. As shown in Fig. 6.4(a), such folds are 1.7 ± 0.1 nm in height (compared to the rest of the monolayer) and 10 to 100 nm in lateral width. In standard optical microscopy, such structures appear as onedimensional objects. In contrast, the map shown in Fig. 6.4(b) reveals lateral variations of STL on a 10 to 20 nm scale, with a decrease of the photon emission quantum efficiency on the folds. Moreover, STL makes it possible to uncover geometrical features such as a "domain boundary" in Fig. 6.4(b) (see profile P 3), i.e., presumably a nanometer-wide crack in the monolayer, which is almost undetectable in the STM topography image. This domain boundary has a strong effect on the photon emission quantum efficiency, which drops by a factor of about 5 over a distance of 10 to 20 nm.

In order to elucidate the excitation mechanism through which excitons are electrically created in MoSe 2 , we examine the dependence of the STL on the bias voltage. To this purpose, a series of STL spectra from monolayer MoSe 2 is measured at current setpoints of 0.1 nA and 10 nA and sample biases V s varying within the 1.3-4.0 V range. The photon emission quantum efficiency is obtained from the area beneath the STL peaks and the simultaneously-measured tunnel current integrated over the acquisition time. Figure 6.5 shows a plot of the photon emission quantum efficiency versus bias voltage. At V s = 4 V, about 3 × 10 -8 photons per electron are detected, which corresponds to 10 -7 photons per electron after correction for the detection efficiency (i.e., 31% at λ 0 = 783 nm).

At both current setpoints 0.1 nA and 10 nA, the onset of luminescence occurs at electron energies close to 1.5 eV, matching the optical gap of monolayer MoSe 2 [START_REF] Wang | Colloquium: Excitons in atomically thin transition metal dichalcogenides[END_REF][START_REF] Ugeda | Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor[END_REF][START_REF] Koperski | Optical properties of atomically thin transition metal dichalcogenides: observations and puzzles[END_REF]. The latter observation is a strong indication that the luminescence is excited by resonance energy transfer from the tunneling current to the excitons, i.e., through virtual photon coupling. A classical picture of the proposed excitation mechanism is that the tunnel current generates an oscillating electric dipole in the tip-surface gap which transfers energy to the semiconductor via near-field electromagnetic coupling. In a diode-like excitation mechanism, however, where electrons and holes are injected in the bands of the semiconductor, the onset of luminescence would occur at an electron energy higher than the "free particle" electronic bandgap of monolayer MoSe 2 [START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF]. The energy of the electronic bandgap of monolayer MoSe 2 exceeds that of its optical bandgap by more than 0.5 eV [START_REF] Wang | Colloquium: Excitons in atomically thin transition metal dichalcogenides[END_REF][START_REF] Ugeda | Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor[END_REF][START_REF] Koperski | Optical properties of atomically thin transition metal dichalcogenides: observations and puzzles[END_REF]; thus, the two possible excitation mechanisms are distinguished by determining the lowest bias voltage at which luminescence is detected. Nevertheless, at sufficiently high electron energies eV s above the electronic bandgap, the two processes (energy transfer and charge injection) may be present.

In the present work, we describe the excitation mechanism in terms of virtual photon coupling because energy transfer from the tunnel current to the excitons occurs without the participation of an intermediary optical mode such as a localized surface plasmon polariton [START_REF] Kröger | Fano description of singlehydrocarbon fluorescence excited by a scanning tunneling microscope[END_REF]. In a different context, i.e., STM electroluminescence of single molecules, a comparable excitation mechanism has recently been reported in terms of inelastic electron-molecule scattering [START_REF] Chen | Spin-triplet-mediated up-conversion and crossover behavior in single-molecule electroluminescence[END_REF]. Below, we discuss in more detail the bias and current dependence of the STL spectra. show a series of spectra measured from monolayer MoSe 2 at current setpoints of 0.1 nA and 10 nA, respectively, and sample biases V s varying within the 1.3 -4.0 V range. The STL spectra are recorded while scanning the tip on a 500 × 50 nm 2 area on monolayer MoSe 2 for averaging. The photon emission quantum efficiency plotted versus V s in Fig. 6.5 is obtained by dividing the area beneath the emission peaks by the integrated measured current.

The STL peak position and lineshape are nearly independent of V s at a current setpoint of 0.1 nA. The emission peak remains at 1.572 ± 0.005 eV in energy and at about 55 meV in FWHM within the 1.5 -3.0 V bias range. Stronger spectral dependence on V s is found at a current setpoint of 10 nA compared to 0.1 nA [see Fig. 6.6(b)]. The emission peaks increasingly broaden and redshift as the sample bias is raised from 2 to 4 V. A quantitative analysis of the red-shift versus V s is shown in Figure 6.6(c).

A general tendency is observed in Fig. 6.6(c), where both the A and B exciton energies redshift by roughly 30 meV V -1 as the sample bias is increased within the 2 -4 V range. Nevertheless, the data recorded at each bias voltage exhibit a statistical variation, with a standard deviation that increases at higher sample bias. This biasdependent distribution is observed because each spectrum is measured on a "fresh" area of the sample, where no STM-induced luminescence experiments have been carried out before. Our motivation for proceeding in this way is to prevent any effect from possible non-reversible modifications of the luminescent sample by the STM tip.

The scanned areas on the sample may exhibit slight geometrical differences, e.g., in roughness or in density of Reprinted with permission from [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF]. Copyright (2019) by the American Physical Society.

V s = 4 V 2.5 V 2.25 V 2 V 1.75 V 1.6 V 1.5 V 1.4 V STM-LE
I t = 10 nA V s = 4 V 2.5 V 2.25 V 2 V 1.75 V 1.6 V 1.5 V 1.4 V 3 V ← A
defects. In addition, different areas on the sample may exhibit slightly different coupling to the underlying ITO layer, which exhibits some spatial heterogeneity in surface conductivity on the sub micrometer scale, due to its granular geometry. Consequently, the effect of the strong electric field in the tip-substrate junction on the energy positions of the excitons may differ from an area to another. Such variations are inherent of the experimental method used,

where the experiments are carried out in air on samples that are not controlled at the atomic scale; nonetheless, it is expected that such variations would not occur if similar experiments were carried out in surface science conditions, in vacuum on an atomically flat surface.

The increasing spectral broadening and the red shift of the emission peaks when the sample bias is raised from 2 V to 4 V may be explained in several ways. First, exciton-exciton annihilation and exciton interactions with charge carriers may yield such spectral modifications of the emission peaks. Due to the low current (0.1 -10 nA) and the low efficiency of the electrical excitation process, exciton and charge carrier densities are expected to be much lower than in previous photoluminescence and electroluminescence studies. Nevertheless, since the excitation is comparatively much more localized in our case, exciton-exciton annihilation and exciton interactions with charge carriers cannot be excluded. Secondly, the observed spectral broadening and red shift of the emission peaks may result from the Stark effect due to the strong electric field in the tip-substrate junction. However, the contribution of the Stark effect is difficult to model or to distinguish from other effects in the present case, because all STM experiments are carried out in constant current mode (not constant height) and the spatial distribution of the inplane and out-of-plane components of the electric field in and around the tip-substrate junction may be highly heterogeneous. Finally, the observed spectral broadening and red shift of the emission peaks may also result from local heating effects, due to the electronic current.

In addition, overbias (hν > eV s ) emission is visible in Figs. [START_REF] Dürig | Near-field optical scanning microscopy[END_REF].6(a) and 6.6(b) at low sample bias (V s ≤ 1.6 V), both at 0.1 nA and 10 nA. Light is emitted up to 200 meV above the quantum cutoff (eV s ) at V s = 1.4 V. The highenergy tail of the emission peak exceeds the quantum cutoff in energy by an amount that apparently decreases when increasing the sample bias. This is similar to previous STL studies [START_REF] Pechou | Cutoff anomalies in light emitted from the tunneling junction of a scanning tunneling microscope in air[END_REF]. Nonlinear electronic processes involving surface plasmons [START_REF] Schull | Electron-Plasmon and Electron-Electron Interactions at a Single Atom Contact[END_REF][START_REF] Schneider | Hot electron cascades in the scanning tunneling microscope[END_REF][START_REF] Xu | Overbias Light Emission due to Higher-Order Quantum Noise in a Tunnel Junction[END_REF]] cannot be invoked here, since the tip and the substrate are made of non-plasmonic materials. Instead, overbias emission may be due to phonon-assisted upconversion processes in the TMD [START_REF] Jones | Excitonic luminescence upconversion in a two-dimensional semiconductor[END_REF][START_REF] Jadczak | Room temperature multi-phonon upconversion photoluminescence in monolayer semiconductor WS2[END_REF], exciton-exciton Auger scattering [START_REF] Manca | Enabling valley selective exciton scattering in monolayer WSe 2 through upconversion[END_REF][START_REF] Han | Exciton States in Monolayer MoSe 2 and MoTe 2 Probed by Upconversion Spectroscopy[END_REF], or local heating effects under the STM tip. In general, overbias emission in electroluminescence relies on excitation mechanisms involving several electrons.

Nevertheless, the data shown in Fig. 6.5, which have been measured at setpoint currents of 0.1 nA and 10 nA, may not be used to confirm a nonlinear dependence of the overbias emission on the current. Additional experiments on the current dependence of the overbias emission are necessary to address this specific issue [START_REF] Chen | Spin-triplet-mediated up-conversion and crossover behavior in single-molecule electroluminescence[END_REF].

Before concluding, we would like to insist on the advantages of a plasmon-less excitation. In this work, the absence of surface plasmons is crucial for two reasons. First, the absence of surface plasmons means that the "native" properties of the emitter, and not the properties of the emitter coupled to a plasmonic tip, a plasmonic surface, or a tip-surface plasmonic cavity, may be probed. This is key in the present study, since the previous STMinduced luminescence studies on 2D semiconductors have not shown native excitonic properties; instead, only plasmonic emission was observed, which does not reveal the excitonic properties of the 2D semiconductors [START_REF] Krane | Electronic Structure and Luminescence of Quasi-Freestanding MoS 2 Nanopatches on Au(111)[END_REF].

Moreover, the presence of a localized surface plasmon in the tip-surface gap is expected to strongly modify the emission processes by enhancing (by orders of magnitude) the radiative rate of the out-of-plane modes of the emitter, as compared to the in-plane modes [START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. As a result, the emission may be dominated by (otherwise dark) excitons that have an out-of-plane transition dipole moment, to the expense of (otherwise bright) excitons that have an in-plane transition dipole moment [START_REF] Park | Hybrid Tip-Enhanced Nanospectroscopy and Nanoimaging of Monolayer WSe 2 with Local Strain Control[END_REF][START_REF] Park | Radiative control of dark excitons at room temperature by nano-optical antenna-tip Purcell effect[END_REF]. Secondly, the mechanisms previously considered to explain STMinduced luminescence from semiconducting nanostructures and organic molecules involve the excitation of localized surface plasmons in the tip-surface gap, which makes it difficult to identify the elementary excitation processes [START_REF] Dong | Generation of molecular hot electroluminescence by resonant nanocavity plasmons[END_REF].

Our work shows that an energy transfer from the tunnel current to the emitter may occur directly, through virtual photons, without any coupling to a plasmonic mode.

Conclusions and outlooks.

The local electrically-excited excitonic luminescence from a 2D semiconductor in the tunnel junction of an STM has been detected using a non-metallic, transparent substrate (ITO-coated glass) and a non-plasmonic (tungsten) tip, combined with high-numerical-aperture collection optics (i.e., an oil-immersion microscope objective). In particular, the emitted light is unambiguously identified as the radiative decay of bright A excitons in monolayer MoSe 2 . This origin is fundamentally different from that reported in a previous STM study of gold-supported monolayer MoS 2 [START_REF] Krane | Electronic Structure and Luminescence of Quasi-Freestanding MoS 2 Nanopatches on Au(111)[END_REF], where the emitted light is from plasmons. Our approach, based on the absence of coupling to a plasmonic tip or nanocavity, makes it possible to probe locally the "native" excitonic properties of a 2D semiconductor. In addition, in our study, the onset of luminescence at electron energies as low as the optical bandgap of monolayer MoSe 2 is consistent with a resonance energy transfer mechanism from the tunneling current to excitons in the 2D semiconductor. Real-space optical microscopy images reveal that the excited excitons may diffuse over micrometers from the STM tip before radiatively decaying, i.e., light may be emitted from a microscale area. Nonetheless, the exciton creation process itself is highly localized, which yields a lateral resolution on the order of 10 to 20 nm in photon maps recorded upon raster scanning the STM tip across the sample. The present work demonstrates the use of STL as a tool to study exciton dynamics and the optoelectronics properties of 2D semiconductors at the nanometer scale. In particular, with this technique, such investigations may be carried out in air under ambient conditions, i.e., in the environment where devices based on these materials will operate.

We anticipate that such investigations will become crucial in the studies of van der Waals heterostructures [START_REF] Parzefall | Light from van der Waals quantum tunneling devices[END_REF][START_REF] Massicotte | Photothermionic effect in vertical graphene heterostructures[END_REF][START_REF] Ma | Fast MoTe 2 waveguide photodetector with high sensitivity at telecommunication wavelengths[END_REF] and TMD superlattices and quantum-well based optoelectronic devices [START_REF] Su | Quantum wells formed in transition-metal dichalcogenide nanosheet-superlattices: stability and electronic structures from first principles[END_REF][START_REF] Azizi | Spontaneous Formation of Atomically Thin Stripes in Transition Metal Dichalcogenide Monolayers[END_REF][START_REF] Xie | Coherent, atomically thin transition-metal dichalcogenide superlattices with engineered strain[END_REF]. They will also be of importance for the local control of exciton energies and dynamics in strained TMDs [START_REF] Kuate Defo | Strain dependence of band gaps and exciton energies in pure and mixed transition-metal dichalcogenides[END_REF][START_REF] Cordovilla Leon | Exciton transport in strained monolayer WSe 2[END_REF] and the localization of excitons in point-like defects and their non-classical emission properties [START_REF] Palacios-Berraquero | Atomically thin quantum light-emitting diodes[END_REF].

What is next? In the following of the work presented above, we have started a new project, which aims at tailoring the optoelectronic properties of semiconductors on the nanometer scale. Our project is based on hybrid systems of TMD monolayers and plasmonic nanostructures. Currently, such hybrid systems are being actively considered as potential single-photon nanosources at room temperature for, e.g., integrated quantum technologies.

However, the fundamental physics behind such systems is poorly understood, notably due to the lack of experimental investigations combining high-resolution temporal and spatial studies of the exciton dynamics. In our project, we will During the last decade, our group has reported on a number of experiments using inelastic electron tunneling under the tip of an STM as a nanosource of photons [START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF][START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF][START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF], surface plasmons [110, 113, 116, 153-157, 159, 161, 162], and excitons [START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF], as shown in the previous four chapters (see Chaps. 3 to 6). Some of these experiments may inspire future concepts of integrated nanosources; however, these sources have very low temporal coherence (broad spectrum) compared to, e.g., electrically driven nanolasers [START_REF] Service | Ever-Smaller Lasers Pave the Way for Data Highways Made of Light[END_REF][START_REF] Ding | Fabrication challenges of electrical injection metallic cavity semiconductor nanolasers[END_REF][START_REF] Jeong | Electrically driven nanobeam laser[END_REF][START_REF] Ma | Applications of nanolasers[END_REF]. As well, inherent instabilities of STM operations in air hinder atomic or molecular-scale control of the excitation [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF]. In Chap. 7, I introduce an on-going project, started in 2015 to initiate a new direction in the group, which targets the highest structural and electronic control of light-and exciton-emitting nanostructures and a comprehensive understanding of the excitation and emission processes. In particular, it builds on the experience of the group in low-temperature STM in UHV and the excitation of molecules using inelastic electron tunneling [START_REF] Baffou | State selective electron transport through electronic surface states of 6 H-SiC(0001)-3 × 3[END_REF][START_REF] Yang | STM imaging, spectroscopy and manipulation of a self-assembled PTCDI monolayer on epitaxial graphene[END_REF][START_REF] Yang | Single-molecule light emission at room temperature on a wide-band-gap semiconductor[END_REF].

From a technological point of view, the local excitation of molecular luminescence with electrons tunneling from an STM tip represents a crucial step for the emergence of a new generation of optoelectronic devices. While the STM itself cannot participate in a device, the use of similar planar tunnel junctions is extremely promising [START_REF] Wang | Molecular electronic plasmonics[END_REF][START_REF] Shamai | Spectroscopy of molecular junctions[END_REF].

Pushing device technology toward this direction requires a better understanding of this excitation method. During the last two decades, a number of publications have reported light emission from single organic molecules or molecular nanostructures under the tip of an STM [START_REF] Kuhnke | Atomic-Scale Imaging and Spectroscopy of Electroluminescence at Molecular Interfaces[END_REF][START_REF] Qiu | Vibrationally Resolved Fluorescence Excited with Submolecular Precision[END_REF][START_REF] Rossel | Luminescence experiments on supported molecules with the scanning tunneling microscope[END_REF][START_REF] Hoffmann | Tunneling-induced luminescence from adsorbed organic molecules with submolecular lateral resolution[END_REF][START_REF] Deng | Stm-induced photon emission from self-assembled porphyrin molecules on a cu(100) surface[END_REF][START_REF] Dong | Vibrationally Resolved Fluorescence from Organic Molecules near Metal Surfaces in a Scanning Tunneling Microscope[END_REF][START_REF] Ćavar | Fluorescence and phosphorescence from individual c 60 molecules excited by local electron tunneling[END_REF][START_REF] Schneider | Light emission from a doubledecker molecule on a metal surface[END_REF][START_REF] Schneider | Plasmonic excitation of light emission and absorption by porphyrine molecules in a scanning tunneling microscope[END_REF][START_REF] Lutz | Molecular Orbital Gates for Plasmon Excitation[END_REF][START_REF] Merino | Exciton dynamics of C 60 -based single-photon emitters explored by hanbury brown-twiss scanning tunnelling microscopy[END_REF]. The use of STM-induced luminescence to image single molecules has been pioneered by the group of Richard Berndt in 1993 with C 60 on Au(110) [START_REF] Berndt | Photon Emission at Molecular Resolution Induced by a Scanning Tunneling Microscope[END_REF]. Ten years later, the group of Wilson Ho measured STM-induced luminescence from Zn-TPP molecules on Al 2 O 3 /Ni [START_REF] Wang | Excitation of propagating surface plasmons with a scanning tunnelling microscope[END_REF] with submolecular spatial resolution [START_REF] Qiu | Vibrationally Resolved Fluorescence Excited with Submolecular Precision[END_REF]. Since then and until the last few years (about 2016), STM-induced luminescence from various molecules on different surfaces has been reported [START_REF] Rossel | Luminescence experiments on supported molecules with the scanning tunneling microscope[END_REF], yet without clearly establishing the excitation and emission mechanisms. Indeed, the research was mainly focused on strategies for electronically decoupling the organic molecules from their metallic substrate, with the hope of observing intrinsic spectral lines of the molecules in STM-induced luminescence. Inorganic insulating layers of metal oxides have been used as spacers [START_REF] Qiu | Vibrationally Resolved Fluorescence Excited with Submolecular Precision[END_REF][START_REF] Wu | Intramolecular photon emission from a single molecule in a scanning tunneling microscope[END_REF][START_REF] Chen | Viewing the Interior of a Single Molecule: Vibronically Resolved Photon Imaging at Submolecular Resolution[END_REF]. Various other strategies, based on organic multilayers [START_REF] Dong | Generation of molecular hot electroluminescence by resonant nanocavity plasmons[END_REF][START_REF] Ino | Luminescence from 3,4,9,10-perylenetetracarboxylic dianhydride on Ag(111) surface excited by tunneling electrons in scanning tunneling microscopy[END_REF][START_REF] Izabela | Light emission from PTCDA bilayer on Au(111) induced in scanning tunneling microscopy[END_REF], chemical engineering of the molecules [START_REF] Zhu | Self-Decoupled Porphyrin with a Tripodal Anchor for Molecular-Scale Electroluminescence[END_REF], inclusion of porphyrin units in a suspended wire [START_REF] Reecht | Electroluminescence of a Polythiophene Molecular Wire Suspended between a Metallic Surface and the Tip of a Scanning Tunneling Microscope[END_REF][START_REF] Michael | Narrow-line single-molecule transducer between electronic circuits and surface plasmons[END_REF], or three-dimensional tubular structures of porphyrin [START_REF] Meng | Tunneling electron induced molecular electroluminescence from individual porphyrin j-aggregates[END_REF], were reported. Still, the excitation and emission mechanisms could not be established without ambiguity.

A first and fundamental distinction to be made is whether the emitted light results from electronic transitions between molecular states (i.e., molecular luminescence) or between tip and substrate surface states [START_REF] Kuhnke | Atomic-Scale Imaging and Spectroscopy of Electroluminescence at Molecular Interfaces[END_REF][START_REF] Dong | Vibrationally Resolved Fluorescence from Organic Molecules near Metal Surfaces in a Scanning Tunneling Microscope[END_REF][START_REF] Schneider | Light emission from a doubledecker molecule on a metal surface[END_REF].

Then, further distinctions may be made based on the different elementary processes via which the molecules are excited and deexcite. In general, photoexcited molecular luminescence refers to radiative electronic transitions between the lowest unoccupied (LUMO) and highest occupied (HOMO) molecular orbitals of a neutral molecule (in agreement with Kasha's rule). However, it was suggested in early STL studies [START_REF] Wu | Intramolecular photon emission from a single molecule in a scanning tunneling microscope[END_REF] that molecular luminescence in an STM may result from LUMO + 1 → LUMO transitions, i.e., between higher-energy molecular states of negatively charged molecules. The reasoning was that STL requires the transient injection of an extra electron in the LUMO of the molecule; thus, the excited molecule is electrically charged, unless a hole is created in the HOMO before the molecule returns to the ground state. In 2009, the group of Z.-C. Dong reported the observation of hot electroluminescence from electrically neutral molecules in an STM, i.e., LUMO → HOMO transitions from excited vibronic states [START_REF] Dong | Generation of molecular hot electroluminescence by resonant nanocavity plasmons[END_REF]. They interpreted this result as an effect of ultrafast resonance energy transfer between the molecule and the plasmonic nanocavity formed by the STM tip on the gold substrate. In 2012, the group of R. Berndt reported that STL from molecules may be observed without injecting electrons in the molecular orbitals [START_REF] Schneider | Plasmonic excitation of light emission and absorption by porphyrine molecules in a scanning tunneling microscope[END_REF]. In 2016, the group of Guillaume Schull demonstrated the STM-excitation of molecular luminescence via energy transfer from the tip-surface gap plasmon (excited by inelastic electron tunneling) to a molecule in the neutral state under the STM tip [START_REF] Michael | Narrow-line single-molecule transducer between electronic circuits and surface plasmons[END_REF].

Furthermore, the origin of spatial resolution in STL of molecules has received various interpretations. In early studies, submolecular resolution was ascribed to the spatial distribution of the higher-energy molecular state [START_REF] Qiu | Vibrationally Resolved Fluorescence Excited with Submolecular Precision[END_REF][START_REF] Wu | Intramolecular photon emission from a single molecule in a scanning tunneling microscope[END_REF] and the dependence of the transition probability on the lateral position of the tip with repect to the transition dipole moment of the molecule [START_REF] Chen | Viewing the Interior of a Single Molecule: Vibronically Resolved Photon Imaging at Submolecular Resolution[END_REF]. It was generally admitted that the tip-surface gap plasmon is comparatively delocalized, at the scale of individual molecules [START_REF] Schneider | Plasmonic excitation of light emission and absorption by porphyrine molecules in a scanning tunneling microscope[END_REF]; whereas localized charge injection from the last few atoms of the tip is primarily responsible for submolecular resolution. Indeed, when a simplified geometry of the tip end is considered (i.e., a sphere), the electromagnetic field of the gap plasmon is expected to extend over √ 2Rd in the lateral direction [START_REF] Rendell | Role of local plasmon modes in light emission from smallparticle tunnel junctions[END_REF], where R is the curvature radius at the tip apex and d is the tip-sample distance, i.e., √ 2Rd equals a few nanometers for typical STM parameters, considerably larger than the size of a single porphyrin molecule.

However, a handful of papers published from 2013 shed new light on STM-induced molecular luminescence and, thus, gave this research field new momentum. In particular, the excitation mechanism and the electronic decoupling issues were partly solved. In 2013, the group of Z.-C. Dong imaged the inner structure of a single porphyrin (H 2 TBPP) molecule at a spatial resolution below 1 nm using tip-enhanced Raman scattering microscopy (TERS) [START_REF] Zhang | Chemical mapping of a single molecule by plasmon-enhanced raman scattering[END_REF], a technique that was so far limited in spatial resolution to 3 -15 nm [START_REF] Anderson | Nanoscale Vibrational Analysis of Single-Walled Carbon Nanotubes[END_REF][START_REF] Steidtner | Tip-enhanced raman spectroscopy and microscopy on single dye molecules with 15 nm resolution[END_REF]. Dong et al obtained such resolution by using a plasmonic (silver) tip in a low-temperature STM under UHV conditions and by tuning the spectral resonance of the tip-surface gap plasmons to the investigated Raman transitions to obtain the strongest tip enhancement effect [START_REF] Zhang | Chemical mapping of a single molecule by plasmon-enhanced raman scattering[END_REF]. Since TERS primarily relies on the local enhancement of the excitation field, Dong's results

were interpreted as evidence that the nanocavity formed by the STM tip and the surface can concentrate the incident light at the scale of a single atom. Shortly after, in 2015, this interpretation was theoretically confirmed by atomistic quantum mechanical calculations of the electric field distribution in Ångström-scale gaps between plasmonic nanocristals upon illumination with plane waves [START_REF] Barbry | Atomistic near-field nanoplasmonics: Reaching atomic-scale resolution in nanooptics[END_REF]. Such a geometry has strong similarities with the tip-surface gap of an STM. The results of these calculations suggested that the "natural" atomic protrusions of plasmonic tips or nanoparticles could be harnessed to attain atomic-scale spatial resolution in nano-optics. From this emerged rapidly a new (and currently very active) subfield of nano-optics based on plasmonic picocavities [START_REF] Benz | Single-molecule optomechanics in "picocavities[END_REF][START_REF] Urbieta | Atomic-scale lightning rod effect in plasmonic picocavities: A classical view to a quantum effect[END_REF]. Finally, a series of seminal papers, published at short intervals during the years 2016-2017 by the groups of Z.-C.

Dong [START_REF] Zhang | Visualizing coherent intermolecular dipoledipole coupling in real space[END_REF][START_REF] Zhang | Electrically driven single-photon emission from an isolated single molecule[END_REF][START_REF] Zhang | Sub-nanometre control of the coherent 167 interaction between a single molecule and a plasmonic nanocavity[END_REF], Yousoo Kim [START_REF] Imada | Realspace investigation of energy transfer in heterogeneous molecular dimers[END_REF][START_REF] Imada | Single-molecule investigation of energy dynamics in a coupled plasmon-exciton system[END_REF] and G. Schull [START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF], established a new understanding and theoretical framework for STM-induced molecular luminescence. A decisive breakthrough was achieved with the use of ultrathin alkali-halide films (islands, 1 -4 monolayers in thickness) that almost perfectly decouple the electronic states of the adsorbed molecules from those of the underlying metallic surface, while still allowing STM operation at low temperature under UHV. Thus, emission bands of single molecules on surfaces could be measured at a spectral width of a few tens of meV at half maximum [START_REF] Kröger | Fano description of singlehydrocarbon fluorescence excited by a scanning tunneling microscope[END_REF], approaching the long-sought-after goal of observing intrinsic spectral lines of molecules in STM-induced luminescence. In addition, coherent energy transfer from the tip-surface gap plasmon excited by the tunneling current to a nearby molecule, laterally off-centered by a few nanometers from the tip apex, was demonstrated [START_REF] Zhang | Sub-nanometre control of the coherent 167 interaction between a single molecule and a plasmonic nanocavity[END_REF]. As the tip was laterally moved and brought closer to the molecule, the contribution of the molecular luminescence grew at the expense of the background light emitted by the empty tunnel junction (i.e., the radiative decay of the gap plasmon). Eventually, only the molecular luminescence remained when the tunneling current flowed through the orbitals of the molecule, as if the molecule had absorbed all the energy stored in the tip-surface nanocavity. This phenomenon exhibits some analogy to the principle of cavity-enhanced absorption spectroscopy [START_REF] Fiedler | Incoherent broad-band cavity-enhanced absorption spectroscopy[END_REF], scaled down to the level of a single molecule in a plasmonic nanocavity. Since then, a number of papers, mostly from the same three research groups, have laid the foundations for a new STM-based single-molecule optical spectroscopic method capable of visualizing elementary molecular processes (e.g., vibra-tional transitions [START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF], resonance energy transfer [START_REF] Zhang | Visualizing coherent intermolecular dipoledipole coupling in real space[END_REF][START_REF] Imada | Realspace investigation of energy transfer in heterogeneous molecular dimers[END_REF], charge state transitions [START_REF] Doppagne | Electrofluorochromism at the single-molecule level[END_REF], tautomerization [START_REF] Doppagne | Single-molecule tautomerization tracking through space-and time-resolved fluorescence spectroscopy[END_REF],

exciton delocalization [START_REF] Luo | Electrically driven singlephoton superradiance from molecular chains in a plasmonic nanocavity[END_REF]) at a submolecular scale in real space. Part of this research activity focuses on the growth and the structural, electronic and optical characterization of thin insulating films and nanoscale systems of organic molecules (from individual molecules to large aggregates and ordered layers) [START_REF] Husseen | Reaction kinetics of ultrathin NaCl films on Ag(001) upon electron irradiation[END_REF][START_REF] Humberg | Hydrogen-bonded one-dimensional chains of quinacridone on Ag(100) and Cu(111): The role of chirality and surface bonding[END_REF]. The other part aims at controlling and understanding the electroluminescence processes of these molecules and molecular systems under the tip of an STM. Below, I present the most significant results obtained in our collaboration with the group of Guillaume Schull and I give a glimpse of our ongoing and future directions of research.

My

Single molecule electroluminescence and vibrational spectroscopy

Context and motivation.

A fascinating aspect of STL, when operated under ultrahigh vacuum (UHV) conditions and at low temperature, is that it combines the atomic-scale resolution of STM and the selectivity of photoluminescence (PL) spectroscopy [START_REF] Kuhnke | Atomic-Scale Imaging and Spectroscopy of Electroluminescence at Molecular Interfaces[END_REF][START_REF] Zhang | Visualizing coherent intermolecular dipoledipole coupling in real space[END_REF][START_REF] Imada | Realspace investigation of energy transfer in heterogeneous molecular dimers[END_REF][START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF][START_REF] Doppagne | Electrofluorochromism at the single-molecule level[END_REF][START_REF] Doppagne | Single-molecule tautomerization tracking through space-and time-resolved fluorescence spectroscopy[END_REF][START_REF] Luo | Electrically driven singlephoton superradiance from molecular chains in a plasmonic nanocavity[END_REF]. The vibronic structure of organic molecules measured using low-temperature PL spectroscopy is extremely sensitive to electronic and vibrational interactions with the environment, e.g., the substrate and neighboring molecules. However, in general, such information is averaged over a large ensemble of molecules, which may have a slightly different environment (e.g, non-equivalent adsorption sites). This is a drawback of the diffraction limit of light, which makes it difficult to address a single molecule in a well controlled environment. Indeed, the smallest spot into which a light beam may be focused (or the finest details that may be spatially resolved using an optical microscope) is orders of magnitude larger than most organic molecules. On the contrary, STL under UHV and at low temperature allows one to selectively excite a single molecule; thus averaging effects (i.e., inhomogeneous broadening of the emission lines) may be avoided. On a crystal surface, STM imag-ing also allows one to control the atomic-scale environment or adsorption site of the excited molecule. Moreover, since the excitation may be spatially localized on the scale of the molecular orbitals, vibrational spectroscopy at submolecular resolution becomes a reality [START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF].

Equally fascinating is the study of the excitation and emission mechanisms underlying the STL of organic molecules, which may differ from the well-established mechanisms underlying their PL. The electronic nature and extreme proximity of the excitation source, as well as the coupling of the molecule to the plasmonic nanocavity formed by the tip and the substrate, may yield hot-carrier and multielectronic processes and may strongly modify the dynamics of the excited states. Only a few different molecules have been considered since the first STL experiments on ultrathin alkali-halide films have been reported, and a number of different excitation mechanisms have already been identified, which in addition are far from being fully understood [START_REF] Doppagne | Vibronic spectroscopy with submolecular resolution from stm-induced electroluminescence[END_REF][START_REF] Kröger | Fano description of singlehydrocarbon fluorescence excited by a scanning tunneling microscope[END_REF][START_REF] Chen | Spin-triplet-mediated up-conversion and crossover behavior in single-molecule electroluminescence[END_REF][START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF][START_REF] Rai | Boosting Light Emission from Single Hydrogen Phthalocyanine Molecules by Charging[END_REF]. Most intriguing is the recent observation of so far unreported near-infrared luminescence from one of the most studied and well known aromatic molecule, i.e., perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA, a red dye and organic semiconductor used in industry) [START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF]. The PL spectrum of PTCDA molecules adsorbed on alkali halides have been investigated before, under "surface science" conditions, and the very fine effects of the adsorption site and molecular interactions on the vibronic structure are well documented in the literature [START_REF] Müller | Fluorescence spectroscopy of ultrathin molecular organic films on surfaces[END_REF][START_REF] Müller | Exciton and polarization contributions to optical transition energies in an epitaxial organic monolayer on a dielectric substrate[END_REF][START_REF] Müller | Finite size line broadening and superradiance of optical transitions in two dimensional long-range ordered molecular aggregates[END_REF][START_REF] Müller | Spectroscopy of isolated PTCDA molecules on the KCl(100) surface: Vibrational spectra and azimuthal orientation[END_REF][START_REF] Paulheim | Fluorescence spectroscopy of PTCDA molecules on the KCl(100) surface in the limit of low coverages: site selection and diffusion[END_REF][START_REF] Paulheim | Inhomogeneous and Homogeneous Line Broadening of Optical Spectra of PTCDA Molecules Adsorbed at Step Edges of Alkali Halide Surfaces[END_REF][START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF][START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF][START_REF] Eisfeld | Superradiance from Two Dimensional Brick-Wall Aggregates of Dye Molecules: The Role of Size and Shape for the Temperature Dependence[END_REF]. Upon laser excitation, PTCDA monomers may exhibit a narrow emission band in the blue-green region of the spectrum (λ 0 ≈ 500 nm), which results from the purely electronic (0, 0) transition between the first singlet excited electronic state and the ground state of the molecule. In the vibronic structure accompagnying the (0, 0) line, each peak has been assigned to a vibrational mode of the molecule [START_REF] Müller | Spectroscopy of isolated PTCDA molecules on the KCl(100) surface: Vibrational spectra and azimuthal orientation[END_REF][START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF] or a coupling to phonons in the substrate [START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF]. Subtle energy shifts of these peaks have been observed, depending on the adsorption sites of the molecules, e.g., on terraces and on step edges of the alkali-halide film, which may result from a slight deformation of the molecular structure due to electrostatic interactions with the substrate [START_REF] Paulheim | Inhomogeneous and Homogeneous Line Broadening of Optical Spectra of PTCDA Molecules Adsorbed at Step Edges of Alkali Halide Surfaces[END_REF]. Inevitably, as such PL investigations are carried out on macroscopic ensembles of molecules, their interpretation relies on hypotheses about the homogeneity of these ensembles, and may require statistical analysis based on STM images. In this context, STL spectroscopy would have a crucial asset if it offered the same level of sensitivity as PL spectroscopy under similar UHV and low-temperature conditions, since such fine investigations could be carried out on individual molecules, with direct atomic identification of the local environment of the molecule.

Below, I present preliminary results of an on-going collaboration with G. Schull's group in Strasbourg. All experiments are carried out under UHV using a low-temperature STM operated at 4 K (liquid helium cooling). We consider individual PTCDA molecules adsorbed on thin alkali halide films (NaCl and KCl) on single crystals of silver.

We focus our research efforts on the excitation mechanisms of STL, the effect of the alkali halide film thickness, and the analysis of the vibronic structure in the STL spectra. This work is inspired by the recent publication by Y.

Kim's group on the STL of PTCDA [START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF] and has a twofold objective, i.e., developing a better understanding of their observations and preparing future experiments in our group on larger molecular structures. Table 7.1: Apparent thickness of the NaCl and KCl thin films, as determined from the STM heights of the alkali halide islands with respect to the metal surface, measured on NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] and KCl/Ag(001) at V s = -2.5 V and I t = 5 -10 pA, as a function of the island thickness in atomic monolayer (ML). 7.1 and 7.2. In particular, Table 7.1 shows that the apparent thickness of one atomic NaCl (KCl) layer at V s = -2.5 V is about 125 nm (150 nm), whereas the "true" distance between two (001) planes in bulk NaCl (KCl) is 282 nm (318 nm) [START_REF] Pivetta | Local work function Moiré pattern on ultrathin ionic films: NaCl on Ag(100)[END_REF][START_REF] Ploigt | Local work function changes determined by field emission resonances: NaCl/Ag(100)[END_REF]. Moreover, Table 7.2 shows that the apparent height of a PTCDA molecule with respect to the underlying silver or alkali-halide surface increases with the number of atomic layers of alkali halide (NaCl or KCl), e.g., from 70 pm on bare Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] to 720 pm on 4 ML of NaCl on Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF]. The apparent height increase of PTCDA observed in STM may be related to the increasing electronic decoupling of the molecular orbitals from the metal surface states by the alkali-halide thin film. [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF]. We find that the energy positions of the peaks do not change significantly when varying the tip-sample distance (through the current setpoint), which indicates that the electric field in the tunnel junction has a negligible effect, i.e., the voltage drop is primarily between the molecule and the tip. A detailed analysis of dI dV STM spectra of this system may be found in Refs. [START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF][START_REF] Cochrane | Pronounced polarization-induced energy level shifts at boundaries of organic semiconductor nanostructures[END_REF], where the authors Table 7.2: Apparent height of the PTCDA molecules, as defined as their STM heights with respect to the underlying (metal or alkali halide) surface, measured on NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] and KCl/Ag(001) at V s = -2.5 V and I t = 5 -10 pA, as a function of the alkali halide thickness in atomic monolayer (0 ML refers to bare metal).

# atomic layers PTCDA/NaCl/Ag(111) PTCDA/KCl/Ag(001) 0 ML 70 ± 5 pm 100 ± 5 pm 2 ML 360 ± 5 pm 310 ± 5 pm 3 ML 530 ± 5 pm 460 ± 5 pm 4 ML 720 ± 5 pm conclude that the PTCDA molecule is negatively charged. The charged state of PTCDA on NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] is pivotal in the STL mechanism devised by Kimura et al [START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF] to explain the near-infrared emission of PTCDA. Interestingly, we observe on 2 -4 ML NaCl/Ag(111) similar near-infrared emission of PTCDA as reported by Kimura et al [START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF] but not on KCl/Ag(001), where no STL could be measured within the investigated range of STM parameters. This discrepancy might indicate that PTCDA is not negatively charged on KCl/Ag(001), possibly due to a higher work function of the substrate as compared to NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF]. However, it might also be that the tip-molecule distance is shorter on PTCDA/KCl/Ag(001) than on PTCDA/NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF], e.g., due to different electronic density distributions in NaCl and KCl thin films, which could result in a comparatively stronger tip-induced quenching of the emission in the case of PTCDA/KCl/Ag(001).

In order to test the latter hypothesis, we estimate the difference in tip-molecule distance of the two considered systems. Firstly, in Table 7.3, the STM heights (in second column) are compared to the theoretical ("true") heights of the PTCDA/alkali halide systems (in third column), which are obtained as follows: The distance between two nearest (001) atomic planes in bulk NaCl (KCl) is 282 pm (318 pm). The vertical center-to-center distance between a PTCDA molecule and the ions of the underlying NaCl or KCl layer is 340 pm, according to previous calculations [START_REF] Aldahhak | Single PTCDA molecules on planar and stepped KCl and NaCl(100) surfaces[END_REF]. The vertical center-to-center distance between a PTCDA molecule and the atoms of the underlying Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] or Ag(001)

surface is been estimated at 281 pm, based on available normal-incidence X-ray standing-wave data [START_REF] Hauschild | Normal-incidence x-ray standing-wave determination of the adsorption geometry of PTCDA on Ag(111): Comparison of the ordered room-temperature and disordered low-temperature phases[END_REF][START_REF] Bauer | Role of func-tional groups in surface bonding of planar π-conjugated molecules[END_REF].

Secondly, we retrieve from the heights given in Table 7.3 the variation of the tip-sample distance when the tip is moved from bare silver onto a PTCDA molecule that is on NaCl and KCl thin films. As shown in Table 7.4, the vertical distance between the tip and the underlying molecule on PTCDA/KCl/Ag(001) and PTCDA/NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] only differs by less than 30 pm. Therefore, we cannot ascribe a tip-induced quenching effect to the fact that we have not observed STL on PTCDA/KCl/Ag(001). Instead, we suggest that we did not detect near-infrared STL from this system either because the charge state of the molecule is different compared to PTCDA/NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] or the sample-bias threshold beyond which this emission occurs on PTCDA/KCl/Ag(001) is beyond the investigated range.

Moreover, we could observe STL from the electrically neutral PTCDA (i.e., at λ 0 ≈ 500 nm) from neither of the two systems, most probably because the density of photonic modes in the tunnel junction was comparatively very low.

Indeed, we had engineered the tip end (through controlled tip contacts on the silver surface) to tune the resonance of the tip-induced gap plasmon in the near infrared, in order to attain the highest possible enhancement of radiative Table 7.3: STM height of the PTCDA molecules with respect to the surface of the metal, measured on NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] and KCl/Ag(001) at V s = -2.5 V and I t = 5 -10 pA, as a function of the alkali halide thickness in atomic monolayers (0 ML refers to bare metal). The STM heights (in second column) are compared to the theoretical ("true") heights of the PTCDA/alkali halide systems (in third column), which are taken from the literature. -238 ± 10 pm emission in this range, and the STL of the empty tip-substrate junction was negligible at λ 0 ≈ 500 nm.

#
In the following, we investigate the STL properties of PTCDA/NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] in the near infrared and we consider two different excitation ways. First, we examine the STL spectra measured when the STM tip is close to (≈ 2 nm)

but not above a PTCDA, i.e., the case where the tunneling current does not flow through the orbitals of the PTCDA molecule. peak is observed at a photon energy of about 1.33 eV, which spectrally matches the near-infrared STL previously reported by Kimura et al [START_REF] Kimura | Selective triplet exciton formation in a single molecule[END_REF]. We observe this peak when the tip is located along the long axis of the molecule [see chemical structure in Fig. 7.2(a)]; however, the peak is absent when the tip-molecule axis is orthogonal to the long axis of the molecule. Moreover, the difference between the two spectra (see blue curve) reveals that the peak has an asymmetric profile, which is characteristic of a Fano-like interference. These observations are consistent with a nonradiative energy transfer from the nanocavity plasmon (which is excited through inelastic electron tunneling) to the molecule by near-field optical coupling (i.e., via the evanescent field). In first approximation, this coupling is a Therefore, if the charged state of the molecule is key in the STL mechanism that yields the peak at 1.33 eV, the PTCDA molecule must be charged negatively on NaCl/Ag(111) even when the electrons do not tunnel between the tip and the orbitals of the molecule.

Secondly, we measure STL spectra of PTCDA molecules on NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] with the STM tip "on" the PTCDA molecule, i.e., electrons may tunnel between the tip and the molecular orbitals. Figure 7.3 shows the resulting STL spectra measured for NaCl thicknesses of 2, 3 and 4 ML, when the STM tip is located at the position marked by a white cross in Fig. 7.3(a). Unlike in Fig. 7.2, here, the spectrally broad contribution of the nanocavity plasmon is not observed. Instead, the sharp peak in the near infrared range remains and its amplitude is much enhanced compared to the case where the tip is not above the molecule. Table 7.5 gives the STL peak energies and full widths at half maximum (FWHM) retrieved from the spectra shown in Table 7.5: Simple peak analysis of the STL spectra of PTCDA/NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] shown in Fig. 7.3(a).

# NaCl thickness Peak energy FWHM 2 ML 1.330 eV 3.7 meV 3 ML 1.333 eV 0.9 meV 4 ML 1.337 eV 0.5 meV a spectral narrowing and a blue shift of the emission. These three effects are consistent with a reduction of the damping rate in an harmonic dipolar oscillator, which we ascribe to the increasing electronic decoupling of the molecular orbitals from the Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] surface states by the NaCl thin film [START_REF] Aguilar-Galindo | Unveiling the anisotropic behavior of ultrafast electron transfer at the metal/organic interface[END_REF][START_REF] Aguilar-Galindo | Ultrafast dynamics of electronic resonances in molecules adsorbed on metal surfaces: A wave packet propagation approach[END_REF]. Note, however, that the STL peaks shown in Fig. 7.3(a) are not Lorentzian and exhibit an asymmetrical profile; thus FWHM may not be related to the excited state lifetime only.

Finally, we examine the series of secondary peaks that accompagnies the (0, 0) line in the STL spectra. 7.6, we compare the energy shifts of these secondary peaks with respect to the (0, 0) line to the energy shifts that are reported in the literature for experimentally measured PL spectra of PTCDA on thick (≈ 10 ML) NaCl films on Ag(001) [START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF]. Remarkably, an excellent matching is obtained, which allows one to assign the secondary peaks in the STL spectra to the vibrational modes known from PL spectroscopy. Note that, in previous PL studies, the vibronic structure of PTCDA is measured in the visible range; whereas, using STL, we measure the vibronic structure of PTCDA in the near infrared.

In PL, the energies and Franck-Condon factors of the vibrational modes depend on slight deformations of the Table 7.6: Comparison between the energy shifts (expressed in cm -1 ) of the STL and PL peaks with respect to the (0, 0) line, where we consider the STL spectra of PTCDA on 2 -4 ML NaCl/Ag [START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] shown in Fig. 7.3(b) and the PL spectra of PTCDA on ≈ 10 ML NaCl/Ag(001) from Ref. [START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF]. Mode assignment is based on Refs. [START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF][START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF]. t and s sites refer to adsorption sites of PTCDA on NaCl terraces and at NaCl step edges, respectively. The "-" in the PL on t sites column denotes that the modes are not experimentally observed. To classify the modes, we use the same nomenclature as in Ref. [START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF], where (A) -(D) refer to the vibrational modes of PTCDA in the gas phase [(A ′ ) is an overtone of (A)] and (L 1,2 ) refer to modes that are active when the molecule is adsorbed on a surface, due to the lowering of the system symmetry. We note ν ′ the emission from excited vibrational states, i.e., at negative energy shifts with respect to the (0, 0). NaCl, PTCDA exhibits a different bending of its squeleton and of its functional groups on terraces (t sites) and on step edges (s sites) [START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF][START_REF] Aldahhak | Single PTCDA molecules on planar and stepped KCl and NaCl(100) surfaces[END_REF]. The molecules adsorbed on t and s sites belong to the C 2v and C 1 symmetry groups, respectively; whereas undistorted PTCDA is of the D 2h group [START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF]. This difference translates into a different expression of the vibrational modes in the PL spectrum, as shown in the fifth and sixth columns of Table 7.6, which in principle may be used to distinguish between these two adsorption sites of the molecules [START_REF] Paulheim | Surface induced vibrational modes in the fluorescence spectra of PTCDA adsorbed on the KCl(100) and NaCl(100) surfaces[END_REF]. The STL spectra used to extract the energy of the vibrational modes are measured on PTCDA molecules adsorbed on terraces.

Mode

Interestingly, the detected modes and their energy are in agreement with the PL data of PTCDA molecules on t sites. Mostly, we find STL/PL discrepancies by about 15 cm -1 in energy for the A and D modes, which correspond to a breathing mode along the long axis of the PTCDA molecule and bending vibrations of its hydrogen atoms, respectively [START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF]. Most of the modes that are active only for PTCDA molecules on s sites are silent in the STL spectra of PTCDA on terraces. Exceptions are the presence of the ν A + ν 1 line, which is a combination of modes that are active on t sites, and the absence of the L 2 mode, which corresponds to vibrations of the hydrogen atoms toward the surface [START_REF] Hochheim | Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl[END_REF].

From the STL/PL similarities reported above, we infer that the presence of the STM tip above one end of the PTCDA molecule [see white cross in Fig. 7.3(a)] does not significantly modify its adsorption geometry and symmetry.

Thus, we conclude that STL may be an attractive vibrational spectroscopy method to investigate the effects of adsorption geometry on the vibrational modes of individual molecules. Nevertheless, further investigations on the observed discrepancies (in energy shift and relative intensity) between the vibronic structure measured using STL and PL spectroscopy may reveal so far ignored aspects of the excitation and emission mechanisms in play in STL.

For instance, we observe in our STL spectra two vibrational lines at negative energy shifts with respect to the (0, 0) line, which may be ascribed to hot luminescence [START_REF] Dong | Generation of molecular hot electroluminescence by resonant nanocavity plasmons[END_REF], i.e., radiative decay from excited vibrational states.

This effect, which is not observed in PL spectroscopy, may indicate that the rate of energy transfer from the excited molecule to the tip-surface nanocavity is high enough to compete with the vibrational relaxation rate of the molecule.

An interesting consequence is that the area ratio between the ν ′ 1 and ν 1 peaks in the STL spectra must depend on the lifetime of excited electronic state. Thus, in Fig. 7.3(b), the relative increase of the ν ′ 1 peak when decreasing the NaCl layer thickness from 4 ML to 2 ML reveals the lifetime shortening due to the stronger electronic coupling to the underlying metallic surface [START_REF] Aguilar-Galindo | Unveiling the anisotropic behavior of ultrafast electron transfer at the metal/organic interface[END_REF][START_REF] Aguilar-Galindo | Ultrafast dynamics of electronic resonances in molecules adsorbed on metal surfaces: A wave packet propagation approach[END_REF].

The effect of the NaCl layer thickness on the energy shifts and spectral width of the vibrational peaks also requires a finer analysis. We note that the vibrational peaks exhibit a similar spectral narrowing as the (0, 0) line when the NaCl layer thickness is increased (see Fig. 7.3). However, the spectral resolution and signal-to-noise ratio in the considered STL data do not allow one to conclusively demonstrate a systematic lowering of the vibrational mode energy at 4 ML compared to 2 ML of NaCl, since the shift variations reported in Table 7.6 (i.e., about 5 cm -1

for the A and D modes) are within the uncertainties.

What is next? The STL spectroscopy technique described above is of particular interest for technological prospects, to investigate extended excitonic systems, e.g., semiconducting organic thin films, molecular aggregates, supramolecular networks or two-dimensional organic-inorganic hybrid architectures. This is precisely the direction of our research project for the future coming years. Experimental work has been started already in this direction at ISMO and in collaboration with our partners. Our long-term goal is to explore a novel approach, based on molecular excitonics, to engineer integrated active devices. The key idea is the use of molecular aggregates to electrically generate coherently delocalized molecular excitations (Frenkel excitons). A crucial advantage is that molecular excitonics allows the design of active optical components that have spectrally narrow optical response and nanometric dimensions compatible with on-chip integration with state-of-the-art nanoelectronics. In the short term, components based on molecular aggregates could be used to feed integrated photonic circuits with coherent light. Temporal coherence (i.e. spectral narrowness) is mandatory for highly multiplexed inter-chip communications or for on-chip processing and filtering of optical signals using high-quality-factor photonic structures (i.e. components with narrow bandwidth). In the longer term, the Frenkel excitons themselves could advantageously be used as a novel, charge-neutral, information vector, for intra-chip communications without the fundamental limitations of light diffraction. Abstract: The scanning tunneling microscope (STM) is not only a surface science tool capable of producing atomically resolved images of crystal surfaces; it is also an extraordinary tool for nano-optics. Indeed, the inelastic tunneling current between the STM tip and the sample surface leads to an extremely local excitation of the existing optical modes. Thus, the tip-sample junction may behave as a nanosource of photons, surface plasmon polaritons, or excitons, depending on the nature of the sample. In this dissertation, I introduce some of the unique studies, in particular in plasmonics and excitonics, that this tool may be applied to when STM and optical microscopy are combined in the same instrument. Examples from my research involve the investigation of the eigenmodes of individual plasmonic nanoparticles, the response of plasmonic micro-optical components, the energymomentum dispersion of polaritons in metasurfaces, and the excitonic properties of two-dimensional semiconductors. Future research directions include a recent collaborative work on single-molecule luminescence spectroscopy in a low-temperature STM under ultrahigh vacuum.

Université Paris-Saclay

Espace Technologique / Immeuble Discovery Route de l'Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France

I

  owe a lot to Moritz Sokolowski and Anne Sentenac, who have believed in me enough to hire me as a postdoc in 2007 and 2009, respectively, and to Gérald Dujardin who has supported my application to the CNRS in 2011. I have learnt from them most of what I know about good research practices.

Figure 2 . 1 :

 21 Figure 2.1: (a,b) Schematics illustrating the light emission induced by inelastic tunnelling in the junction of a scanning tunneling microscope (STM). The emitted light can be detected (a) from the tip side or (b) at through the sample.(c) Energy diagram showing the tip-to-surface junction polarized at a voltage V and the passage of an electron by elastic (ET) and inelastic (IET) tunnelling accompanied by the emission of a photon of energy hν ≤ eV . Adapted from[START_REF] Rossel | Luminescence experiments on supported molecules with the scanning tunneling microscope[END_REF] with permission from Elsevier. Reprinted from[START_REF] Le | La nano-optique sous la pointe d´un microscope à effet tunnel[END_REF], published under the conditions of the Creative Commons Attribution License CC-BY.

Figure 2 . 2 :

 22 Figure 2.2: Pictures of the experimental setup in a glove box. The setup consists of an STM/AFM head (Veeco/Bruker Bioscope II) mounted on an inverted optical microscope (Zeiss Axio Vert). Light emission from the sample is collected using an oil-immersion objective lens of high numerical aperture (NA) and focused on a cooled CCD camera using two lenses (the tube and Bertrand lenses) so as to image the light pattern that forms in the back focal plane of the objective lens (Fourier image). Removing the Bertrand lens allows recording a standard real-plane image.

Figure 2 .

 2 Figure 2.3(a) shows a schematic of the experimental setup used for the studies of the STM-induced light emission reported in Secs. 3.1, 3.2 and 4.1. The setup consists of a commercial STM/AFM head operating in air in ambient

Figure 2 . 3 :

 23 Figure 2.3: (a) Fourier imaging of the STM-induced light emission from metallic nanostructures on a transparent substrate. (b) Darkfield optical spectroscopy of single nanostructures upon illumation with polarized white light in grazing incidence. In both setups, light is collected through the substrate. Inscriptions on the housing of the objective lenses indicate immersion medium and numerical aperture. Reprinted with permission from Ref. [160]. Copyright (2016) by the American Physical Society.

Figure 2 .Figure 2 . 4 :

 224 Figure 2.4 shows schematically the different excitation and detection configurations used in the studies reported in Secs. 3.3, 4.2, 4.3 and in Chaps. 5 and 6.All experiments are carried out using an inverted optical microscope (Nikon Instruments, Eclipse Ti-U) equipped with an oil-immersion, high numerical aperture (NA = 1.49), 100× objective lens (Nikon CFI Apochromat TIRF objective). The microscope is coupled to a cooled CCD camera (Andor, iKon-M) and an imaging spectrometer (Horiba Jobin Yvon, iHR320 spectrometer and Synapse CCD detector). A pair of achromatic doublet lenses arranged in a telescope configuration is used to image the back focal plane of the microscope objective on the CCD detector. The resulting Fourier-space image reveals the angular distribution of the collected light, which is related to the wavevectors of the excited propagating waves in the sample. Using a removable mirror, the Fourier-space image may be projected onto the entrance slit of the imaging spectrometer.

  This chapter primarily presents the results of a long-standing and very fruitful collaboration with Andrey G. Borisov (ISMO) and Sylvie Marguet (CEA NIMBE), to whom I am much indebted. Their support, inspiration, and scientific contributions have been key to the work discussed below.

Figure 3 .Figure 3 . 1 :

 331 Figure 3.1: (a) Schematic of the setup consisting of an STM mounted on an inverted optical microscope, which is introduced in more detail in Sec. 2.1). The sample consists of NPs on an ITO-coated glass slide. (b) Top view SEM image with magnification of 97590× giving a top view of the NP and, in inset, a schematic showing its truncated bitetrahedral shape. (c) Schematic top view of a NP showing the definitions used for its geometrical characteristics. (d) STM image of a NP, superimposed with equilateral triangles (dotted line) indicating NP's mean dimensions (mean edge length taken from SEM statistics). (e) False-color CCD-camera Fourier image showing the angular emission pattern and (f) the associated real-plane image showing the spatial distribution of the emitted light from an STM-excited NP. In both cases, the STM excitation is above the center of the NP. In the Fourier image, the center is associated with emission along the optical axis (polar angle θ = 0) while the circles labeled NA = 1 and NA = 1.45 (black and white dotted lines) show the critical angle of the air/glass interface (θ c = 41 ○ for n glass = 1.52)and the maximum acceptance angle of the objective lens (θ max = 72 ○ for n glass = 1.52), respectively. Adapted with permission from[START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. Copyright(2013) American Chemical Society.

Figure 3 .

 3 Figure 3.2 shows how the angular emission pattern varies as the STM tip is moved with respect to the NP.

Figure 3 .

 3 Figure 3.2(a) shows an STM image of the NP and the different positions along one of the three medians of its triangular face where the measurements are acquired. As illustrated in Fig. 3.2(b), we position the STM tip at a

Fig. 3 .

 3 Fig. 3.2(f) shows the experimental (filled black curve) and corresponding simulated polar angle distributions (red line) along the direction of the median (see white dotted line in Fig. 3.2(c)). A red arrow represents the orientation of the dipole in the model. The emission pattern is anisotropic and this anisotropy changes when the tip is moved from close to the edge (base) to close to the vertex of the triangular upper face. In Figs. 3.2(c) and 3.2(e), we see

Figure 3 . 2 :

 32 Figure3.2: (a) STM image of the NP (overlay: tip positions (numbered 1 to 4) along the median for which Fourier images are provided in panel c). On the STM image, the dashed edge contour represents the statistical mean edgelengths previously determined from SEM images. (b) Schematics of the experimental configuration with the STM tip above the NP on the ITO-coated substrate; the Fourier image is a projection of the angular emission pattern; intensity profiles along a cross-section of the Fourier image may be plotted in a polar graph, thus providing the distribution of the emission intensity versus polar angle θ. (c) False-color experimental Fourier images obtained with the STM tip at positions 1 to 4 of panel a. (d) Graphic representation of the simple analytical model that is used to interpret the experimental results: the Fourier images and the angular distribution of the emitted light are compared to those of a point dipole emitter located on an air-glass interface, with the dipole orientation defined by the azimuthal Φ and polar Θ angles with respect to horizontal and vertical axes, respectively. (e) Theoretical Fourier images calculated with this simple model. The appropriate polar dipole orientation angle Θ is determined by calculating different theoretical images while varying Θ in steps of 5 ○ until the best theoretical image with respect to the experimental Fourier image is found. Φ is chosen so that the dipole has same azimuthal orientation as the median of the NP's triangular face. (f) Polar plot of the intensity versus polar angle Θ, obtained from the intensity profiles along the median (dotted line in Fourier image) on both the experimental (filled curve) and theoretical (red line) Fourier images. Dotted lines at θ max = ±72 ○ help visualize the collection cone of the objective lens. For the experimental images, a short-pass filter (cutoff wavelength 842 nm or 1.47 eV) is placed in front of the CCD camera. Adapted with permission from[START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. Copyright(2013) American Chemical Society.

Figure 3 . 3 :

 33 Figure 3.3: FDTD calculations of the electric field components E x (a,d) and E z (b,e) at a given time in the xz plane. The tip and the vertical dipole are located at either (a,b) x = 0, right above the center of the NP, or (d,e) laterally shifted to x = 60 nm, above the vertex of the NP. The red and blue color scale corresponds to field amplitudes of opposite sign, while white represents zero amplitude. Schematics (c) and (f) depict the charge displacement at a given time, as deduced from (a,b) and (d,e) respectively, as well as the corresponding polarization of the NP.Reprinted with permission from[START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]. Copyright(2013) American Chemical Society.

Figure 3 . 4 :

 34 Figure 3.4: (a) Scanning electron micrograph of a gold nanotriangle and (b) sketch of its truncated bitetrahedral shape. (c,d) Calculated (crosses and dashed lines) and experimental (circles) light scattering spectra for vertical (p z ) and in-plane (p x ) incident light polarization. Experimental data are obtained by dark-field optical microscopy upon polarized white light illumination of an individual NP. Experimentally observed resonances are fitted with single Lorentzian profiles yielding 2.15 eV, and 1.88 eV for the vertical (p z ) and in-plane (p x ) dipolar LSP resonances, respectively. (e) Theoretical distribution of the vertical component of the electric field (E z ) in the horizontal (x, y) plane 0.5 nm above the NP. Results are shown for the excitation of the p z and p x dipolar LSPs. Inset: sketch of the simplified NP geometry used in the E z calculations. Reprinted with permission from [160]. Copyright (2016) by the American Physical Society.

Figure 3 . 5 :

 35 Figure 3.5: (a,b) Tilt angle Θ of the "effective emission dipole". (c) Schematic of the NP-tip system, showing the truncated bitetrahedral shape of the NP. Shaded areas indicate tip positions where the tip apex is above a tilted side face (light grey) or outside the NP (dark grey), i.e., inelastic electron tunneling cannot be modeled as a vertical electric dipole in these regions. Comparisons between theoretical and experimental results in (a,b) are only relevant in the unshaded regions. (d) Theoretical emission intensity I in the substrate calculated using the three approaches described in the text (inset: NP shape used in the calculations). In (a,b,d), results are shown as a function of the tip position along the median of the upper NP triangular face (0 corresponds to the center). Symbols with error bars are experimental data taken from Ref.[START_REF] Le Moal | An electrically excited nanoscale light source with active angular control of the emitted light[END_REF]; circles (⊙) are the complete calculations including the full NP-tip geometry; diamonds (⟐) are model calculations of the NP excited by the point dipole with no tip (i.e., Green's function of the NP); solid dots and line (-• -) are model calculations based on E z maps of plasmonic eigenfields. Reprinted with permission from[START_REF] Le Moal | Engineering the emission of light from a scanning tunneling microscope using the plasmonic modes of a nanoparticle[END_REF]. Copyright (2016) by the American Physical Society.

Figure 3 .

 3 Figure 3.5(d) shows the theoretical variation of the intensity of emitted light I versus tip position, as calculated using the three approaches discussed above. Again, the model (ii) based on the calculation of the point dipole excitation of the NP (Green's function of the NP with no tip) and the (iii) simple model using E z maps of plasmonic NP fields are in relative agreement with each other. As well, both models reproduce the (i) complete calculation of the NP-tip system on a semi-quantitative level, correctly capturing all the main trends. An intensity minimum is found at the center of the upper (triangular) NP face and first and secondary maxima are found close to its vertex and basis, respectively.

  Figures 3.6(a) and 3.6(b) show a scanning electron micrograph and a three-dimensional projection of an STM topography image of such a nanostructure. The triangles considered here have side lengths L ranging from 600 to 900 nm and are 20 nm thick. The STM-based experiments are carried out with an STM head mounted on an inverted optical microscope, which is described in detail in Sec. 2.2. A non-plasmonic tungsten tip is used in order to avoid plasmonic nanocavity resonances of the tip-sample junction; thus we expect to excite the inherent resonances of the sample.

Figure 3 .

 3 Figure 3.6(c) shows the resulting experimental spectra of the light emitted when the STM-nanosource is placed in the center of the upper facet (dotted curves) or in the middle of the edge (continuous curves) of the triangular platelet (see panels d and e of the figure for a schematic of the tip position). When the excitation is centered on a platelet of side length L = 600 nm, two broad overlapping resonances may be observed in the light emission at about 730 and 910 nm. When the excitation is located on the edge of the same triangle, three different overlapping resonances are apparent at wavelengths of about 670, 760, and 870 nm. The connection between these experimental spectra and

Figure 3 . 6 :

 36 Figure 3.6: (a) Scanning electron micrograph and (b) 3D projection of a scanning tunneling microscopy image of a colloidal, triangular, gold platelet. Typical side lengths L of the studied particles are 600 to 900 nm. The platelets are 20 nm thick. For the STM image, a voltage of 0.5 V is applied and the set-point current is 0.1 nA (constant current mode). (c) Experimental spectra obtained by placing the STM excitation in the center of the top face of a triangular platelet (dotted curves) or along the triangle edge (continuous curves). Triangle side lengths of L = 600, 800, and 900 nm have been investigated. The spectra are normalized by their maximum values. STM parameters are I t = 0.5 nA and V s = 2.8 V and the acquisition time is 300 s. (d) and (e): schematics of the excitation geometries. (f) Calculated light emission spectra for different excitation positions and triangular platelet sizes. Dotted lines: results for the STM tip located in the center of the triangle face. Continuous curves: results for the STM tip located in the center of the triangle edge. The platelets side lengths are varied from L = 600 to 800 nm, as indicated in the inset.(g,h) Surface charge density induced at a wavelength of (g) 620 and (h) 860 nm for the tip location indicated in the insets. The calculations are performed with a tip (curvature radius 40 nm, length 400 nm) placed 2 nm above the platelet surface (substrate index of refraction is 2). Adapted with permission from[START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]. Copyright (2020) American Chemical Society.

Figure 3 . 7 :

 37 Figure 3.7: (a,b) Photon yield maps obtained by dividing the simultaneously acquired photon images by their corresponding STM current maps. Either a 750 40 nm (in panel a) or a 900 40 nm bandpass filter (in panel b) is placed before the detector. (c,d) Electron energy loss results. A high energy electron beam scans the particle and the energy lost by the electrons passing through the sample is measured. In (c) the number of electrons having lost energy in the 1.5 -1.8 eV range as a function of e-beam position is plotted, while in (d) the energy loss range is 1.1 -1.4 eV. These results match the STM-excitation images qualitatively. The triangle side length is L ≈ 630 nm.(e) Calculated energy-resolved maps of the EM-LDOS, R-EM-LDOS, and of the intensity of the light emitted by the tunneling STM-nanosource when scanned over a triangular platelet with side length L = 650 nm. The EM-LDOS is calculated 1 nm above the upper face of the platelet. The STM tip scans the upper face of the platelet at a constant tipsurface distance of 2 nm. Different columns correspond to the maps obtained for different radiation wavelengths as indicated. Adapted with permission from[START_REF] Cao | Probing the radiative electromagnetic local density of states in nanostructures with a scanning tunneling microscope[END_REF]. Copyright(2020) American Chemical Society.

  Figures 3.7(a) and 3.7(b) show photon yield maps that are obtained by dividing the simultaneously acquired photon images by their corresponding STM current maps. The result is thus an efficiency in terms of the number of photons emitted per tunneling electron. We use the spectral results shown in Fig. 3.6(c) to select two different wavelength windows for the light emission mapping experiments. A 750 40 nm bandpass filter, in Fig. 3.7(a), or 900 40 nm bandpass filter, in Fig. 3.7(b), is placed before the detector. The two resulting images exhibit noticeable differences. Indeed, we can easily visualize the general trend observed in the experimental and simulated spectra shown in Fig.3.6: the highest intensity modes for excitation in the center of the top face are found at high energy (short wavelength) while the highest intensity modes for excitation on the edge are at low energy (or long wavelength). In addition, similar experiments are performed using EELS. Looking at the EELS data in Fig.3.7(c) and 3.7(d) for a similar triangular platelet, we obtain a result that shows similar trends as in the case of the STM-nanosource excitation: considering a high energy/short wavelength range, a strong signal is measured when the excitation (a high energy (100 keV) electron beam) is incident on the flat upper surface of the triangle platelet; for a low energy/long wavelength range, the signal is most significant when the excitation is along the triangle edge.

Figure 4

 4 Figure 4.1: (a) Schematics of the experiment: the local, electrical excitation of the SPs on a plasmonic lens using the tip of an STM leads to the emission of a cylindrical light beam with radial polarization (inset: scanning electron micrograph of the plasmonic lens). (b) Real-plane optical image in false color of the emitted light collected through the substrate with a high-NA (1.45) objective lens. (c) Same as (b) but filtered with a linear polarizer (the white double arrow indicates the transmission axis). Reprinted from [157] with permission from AIP Publishing.

Figures 4. 1

 1 Figures 4.1 and 4.2 show experimental results obtained with a 5-ring circular grating plasmonic lens with an

  Figures 4.1and 4.2 show experimental results obtained with a 5-ring circular grating plasmonic lens with an inner diameter D in = 5 µm (i.e. outer diameter is 11.2 µm). The real-plane image in Fig. 4.1(b) shows the spatial distribution of the emitted light obtained when the STM tip is located in the center of the plasmonic lens. The light

Intensity 0 1 Figure 4 . 2 :

 142 Figure 4.2: (a)-(d) Fourier-plane optical images in false color of the light detected from the same five-slit cicular grating plasmonic lens as in Fig. 4.1. These results are obtained under the same conditions, but for four different lateral positions of the STM excitation on the central disk region. X is the distance from the center of the plasmonic lens. Dotted white circles indicate the maximum acceptance angle (NA = 1.45, ≈ 73 ○ ) and the critical angle (NA = 1.00, ≈ 41 ○ ). The polar plot below each Fourier-plane image is obtained by measuring the intensity profile along the white dotted, horizontal line. In the polar plots are indicated the polar angle of emission θ and the angular spread of the beam, defined as the half width at half maximum (HWHM), rounded to the unit. (e-h) Same as (a-d) filtered with a linear polarizer (the white double arrow indicates the transmission axis). Reprinted from [157] with permission from AIP Publishing.

  4.2(b)).

Figure 4 .

 4 2(f) shows the same experiment, but with a linear polarizer placed in front of the CCD camera. These results clearly demonstrate the emission of a highly collimated beam of purely radial polarization propagating perpendicularly to the sample plane. From the polar plot below Fig 4.2(b), the angular spread of the beam is measured at ±3.8 ○ (half width at half maximum of the intensity profile)

Figure 4 . 3 :

 43 Figure 4.3: (a) Experimental and theoretical Fourier-plane images in false color of the light from a five-slit circular grating (top row) and a single circular slit (second row) of inner diameters D in = 6 µm, 4 µm and 2 µm, when the STM excitation is centered on the plasmonic lens. The dotted white circle indicates the maximum acceptance angle (NA = 1.45, ≈ 73 ○ ). (b) Experimental and theoretical angular spread of the emission from a five-slit circular grating and a single circular slit, versus the inner diameter of the central disk D in (STM excitation in the center; solid spheres: experimental data; dashed lines: model). Adapted from [157] with permission from AIP Publishing.

  . 4.2(a)-(d) show the angular distribution of the light emitted below the substrate.The lateral position of the STM tip on the central disk of the plasmonic lens is varied in parts (a) to (d). We also obtain Fourier-plane images under similar conditions but with a linear polarizer in front of the CCD camera, as shown in Fig.4.2(e)-(h). When the tip is 0.5 µm from the center, the emitted light beam is tilted by 2 ○ from the normal and its collimation and radial polarization are preserved (see Figs. 4.2(a) and (e)). With the tip at 1.2 µm from the center (Fig 4.2(c))

Fig. 4 .

 4 Fig. 4.2(h) reveals a quite intricate polarization pattern, with several azimuthally polarized lobes below the critical angle, and an essentially radially polarized supercritical contribution.

Figure 4 .

 4 Figure 4.3 shows the importance of having a plasmonic lens that consists of a circular grating rather than just a single circular slit. The effect of the inner diameter is also investigated. Figure 4.3(a) shows the Fourier-plane

Figure 4 .

 4 3(a) shows the Fourier-plane images measured for plasmonic lenses consisting of either a five-slit circular grating (top row) or a single circular slit (second row) of inner diameter D in = 6 µm (first column), 4 µm (second column) or 2 µm (third column).

Figure 4 .

 4 3(a) (fourth column) shows the resulting Fourierplane images calculated for the five-slit circular grating and for the single circular slit, with a inner diameter D in = 2 µm. These calculated results reproduce well the experimental Fourier-plane images (third column, Fig. 4.3(a)).

Figure 4 .

 4 Figure 4.3(b) shows good agreement between the experimental and theoretical angular spread of the light emitted

  Collaborators: Jean-Paul Hugonin and Jean-Jacques Greffet (Laboratoire Charles Fabry, University of Paris Saclay -IOGS, Palaiseau), Aurélien Drezet and Serge Huant (Institut Néel, Grenoble). Students involved: Shuiyan Cao (PhD, ISMO) and Florian Bigourdan (PhD, IOGS). Florian, Jean-Paul and Jean-Jacques performed the numerical simulations. I derived the simplified analytical model to predict the spectral dependence of the angular emission pattern. Shuiyan did the STM-based experiments under my guidance. The plasmonic structures were fabricated by Jean-François Motte and Gwénaëlle Julie at the NanoFab facility in Grenoble.This section is adapted with permission from Shuiyan Cao, Eric Le Moal, Florian Bigourdan, Jean-Paul Hugonin, Jean-Jacques Greffet, Aurélien Drezet, Serge Huant, Gérald Dujardin, and Elizabeth Boer-Duchemin. Revealing the spectral response of a plasmonic lens using low-energy electrons. Phys. Rev. B, 96:115419, Sep 2017. Copyright (2017) by the American Physical Society.[START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]

  5 -1.0 -0.5 0.0 0.5 1.0 1.Intensity (counts) Fourier-space coordinate k // / k 0

Figure 4 .

 4 Figure 4.4: (a) Fourier-space optical image, in false color, revealing the angular emission pattern in the substrate.The plasmonic lens is a five-slit circular grating of period 700 nm and inner diameter 5 µm. For this image, light is collected using an objective lens of NA = 1.49, the full emission spectrum is used (no spectral filtering) and the image resolution is 0.0098 k 0 per pixel (i.e. the NA = 1.5 circle has a diameter of 306 pixels). The STM bias is U b = 2.8 V, the current setpoint is I t = 6 nA and the acquisition time is 600 s. (b) Intensity profiles taken from the Fourier image in panel a, along the direction of the Fourier-space vectors k x and k y . The profile along k y is vertically offset for clarity. The Fourier-space coordinates (k ∥ stands for k x or k y ) are normalized by the wavevector corresponding to the spectral peak wavelength in free space k 0 . The angular spread of the emitted beam is defined as the difference in angle corresponding to the two peaks observed in the intensity cross-sections in Fourier space. (c-j) Spectrally filtered Fourier-space optical images, in false color, of the light emitted in the substrate. The collected light is filtered using bandpass filters that have the following central wavelengths / bandwidths: (c) 550 88 nm, (d) 600 14 nm, (e) 650 13 nm, (f) 700 13 nm, (g) 750 40 nm, (h) 800 40 nm, (i) 850 40 nm and (j) 900 40 nm. Intensity profiles taken from the Fourier images are shown below each image in a polar plot. For these images, light is collected using an objective lens of NA = 1.45 and the image resolution is 0.027 k 0 per pixel (i.e., the NA = 1.5 circle has a diameter of ≈ 108 pixels) and the acquisition time is 300 s. Reprinted with permission from[START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society.

Figure 4 .

 4 Figure 4.5(a) illustrates the principle of the simple two-dimensional scalar model used. We consider only two adjacent slits which scatter the incoming SPPs into light in the substrate, and model these slits as two coherent point

Figure 4 . 5 :

 45 Figure 4.5: (a) Sketch of the scattering of SPPs into light at two slits etched in a gold film on glass. The SPPs propagate from the left-hand side of the figure.The light emitted in the substrate from the two slits interferes constructively in the direction denoted by the angle θ. δ is the optical path difference for the light emitted at θ at the two slits. If the period P of the slit grating is longer than the SPP wavelength λ SP P , then the SPPs scattered into light interfere constructively in the forward direction. For P < λ SP P , constructive interference is in the backward direction. Only first-order diffraction is considered here. [(b) to (d)] The experimental values of the angular spread [see Fig.4.4(b) for definitions] measured for three different five-slit circular gratings are compared with the angle of constructive interference θ (red line) calculated using the model shown in a. The grating period is P = 700 nm in b, P = 600 nm in c and P = 800 nm in d. The inner diameter of the plasmonic lens is D = 5 µm in b and D = 6 µm in c and d. The theoretical lower bound for the angular spread due to the finite size of the slit grating is shown by the black line. L is the outer diameter of the plasmonic lens. The experimental data are obtained from the analysis of spectrally filtered Fourier-space images following the method described in Fig.4.4. Reprinted with permission from[START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society.

  Figures 4.5(b) to4.5(d) show the results of this simple model (see red line) along with the experimental data for three different slit grating periods: P = 600, 700 and 800 nm. As a second step, we introduce in the model the effect of the finite size of the slit grating by including a lower bound to the angular spread. Within the far-field approximation (Fraunhofer diffraction), the radiation pattern from the source has an angular spread ∆k limited by the source size L through the relation L∆k ≳ 2π. Here, light is emitted from the slits etched in the gold film; thus the source size L is the outer diameter of the N -slit circular grating, i.e., L = D + 2(N -1)P + 2W , where W is the slit width. Light is mainly emitted orthogonally to the gold film, i.e., along the optical axis of the microscope; therefore, ∆k is equivalent to the width of the doughnut-shaped spot observed in the Fourier-space images. The above relation thus leads to a lower bound for the angular spread of the light beam from the plasmonic lens:

Figure 4 .

 4 Figure 4.6 shows the angularly-resolved spectroscopy results obtained using configuration 2 of the experimental setup shown in Fig. 2.4(b). By projecting the Fourier-space image obtained from the emitted light on the entrance slit of the spectrometer, we spectrally resolve the collected light along a line in the Fourier plane. The relative position

Figure 4 . 6 :

 46 Figure 4.6: Angular and spectral distributions of the light emitted upon STM excitation of (a) an unstructured 50nm gold film on glass, (b-d) a five-slit plasmonic lens of inner diameter D = 4 µm and period (b) P = 700 nm, (c) P = 800 nm and (d) P = 600 nm, and (e) a single circular slit of inner diameter D = 5 µm, etched in a 200-nm gold film on glass. These experimental data are measured by projecting the Fourier-space image of the emitted light on the partly-closed entrance slit of the spectrometer [see Fig. 2.4(b), configuration 2]. The STM bias is U b = 2.8 V, the current setpoint I t = 3 to 4 nA and the acquisition time is 300 s. On the left of panels a and b are the Fourier-space images that are obtained when the spectrometer entrance slit is at its largest width and the image is acquired using the zeroth order of the diffraction grating (acquisition time: 100 s). Dotted lines indicate the selected area when the entrance slit is partially closed for spectral measurements. The partially-closed entrance slit gives rise to a spectral resolution of about 8 nm (i.e., ≈ 0.02 eV at λ 0 = 700 nm). Along the vertical axis (k y k 0 ), the resolution is limited by the CCD pixel size to 0.018 per pixel. Reprinted with permission from[START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society.

Figure 4 . 7 :

 47 Figure 4.7: Spectral distribution of the light emitted upon STM excitation of a five-slit (N = 5) circular grating of different inner diameters D and periods P , etched in a 200-nm gold film on glass.The spectral dependence on D with (a) P = 700 nm and (b) P = 800 nm is examined (a vertical dotted line indicates λ 0 = P to guide the eye). In (c), the effect of varying P while keeping D fixed is studied. For comparison purposes, the spectra obtained for an unstructured 50-nm gold film and for a single (N = 1) circular slit etched in a 200-nm gold film are also plotted in panels b and c (black lines), respectively. All spectra are corrected for the spectral response of the instrument, which includes the transmission of the microscope objective, the scattering efficiency of the diffraction grating and the quantum efficiency of the CCD camera used in the spectrometer. Spectra are vertically offset for clarity. The STM bias is U b = 2.8 V, the current setpoint is I t = 3 to 4 nA and the acquisition time is 300 s. Reprinted with permission from[START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society.

Figure 4 . 8 :

 48 Figure 4.8: [(a) and (b)] Theoretical SPP reflection and transmission coefficients, R = r 2 and T = t 2 , and (c) phase shift at reflection, i.e., the argument of the complex amplitude reflection coefficient, arg(r), of a slit grating with period P = 700 nm. The results are shown for a number of slits N = 5, N = 10, N = 20 and [only for R and arg(r)] N = ∞, i.e., an infinite number of slits. (d) Dispersion relation (in red) for the slit grating with P = 700 nm. The black dashed lines labeled light lines correspond to the folded dispersion lines of photons propagating in air and glass along directions parallel to the air-glass interface, respectively. (e) SPP reflection coefficient [same data as shown in (a)], plotted with same Y-axis as that of the dispersion curves. A horizontal dashed line indicates the energy position of the upper gap edge. Calculation methods are described in Refs.[START_REF] Cao | Stable and efficient bloch-mode computational method for one-dimensional grating waveguides[END_REF] and[START_REF] Paul | Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization[END_REF]. Reprinted with permission from[START_REF] Cao | Revealing the spectral response of a plasmonic lens using low-energy electrons[END_REF]. Copyright (2017) by the American Physical Society.

  4.7(c)]. As well, if P remains the same and D is modified [see Figs. 4.7(a) and 4.7(b)]

  Collaborators: Aurélien Drezet and Serge Huant (Institut Néel, Grenoble), Jean-Paul Hugonin (IOGS, Palaiseau). Students involved: Shuiyan Cao (PhD, ISMO) and Quanbo Jiang (PhD, Institut Néel). Jean-Paul and Aurélien Drezet performed the numerical simulations and I derived the analytical model of the antenna. Shuiyan did the STM-based experiments under my guidance. The plasmonic structures were fabricated by Jean-François Motte and Gwénaëlle Julie at the NanoFab facility in Grenoble. This section is adapted from S. Cao, E. Le Moal, Q. Jiang, A. Drezet, S. Huant, J. P. Hugonin, G. Dujardin, and E. Boer-Duchemin. "Directional light beams by design from electrically driven elliptical slit antennas." Beilstein J. Nanotechnol., 9:2361, 2018. Open Access article under the terms of the Creative Commons Attribution License.

Figure 4 .

 4 [START_REF] Betzig | Combined shear force and near-field scanning optical microscopy[END_REF] shows schematics of the experiment performed. All experiments are carried out using the same set-up as in Sec. 4.2, which is described in detail in Sec. 2.2. Circular or elliptical slits are etched in an optically thick (200 nm) gold film deposited on a glass coverslip. The inelastic effects of the tunnel current between the STM tip and the surface of the gold film generate circular SPP waves which propagate

Figure 4 . 9 :

 49 Figure 4.9: A single (a) circular or (b) elliptical slit etched in a 200nm gold film on glass is used as an electrical light beam microsource. Inelastic electron tunneling from the tungsten tip of an STM excites SPPs at the air-gold interface. These SPPs propagate isotropically away from the tip to the slit where they scatter into light. Excitation at (a) the center of the circle or (b) at a focus of the ellipse yields (a) radially polarized cylindrical vector beams orthogonal to the plane or (b) oblique light beams in a specific direction as determined by the eccentricity of the ellipse. Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

x 2 a 2 + y 2 b 2 = 1 ,

 21 where a and b are the semi axes of the ellipse. If a > b and the ellipse is centered at (0, 0), the focii are at F (-c, 0) and F ′ (c, 0), where c 2 = a 2 -b 2 .

φFigure 4 . 10 :

 410 Figure 4.10: At a planar surface, the phase of the electric field of an incident light beam in (a,c) orthogonal or (b,d) oblique incidence is spatially (a,c) independent or (b,d) dependent, respectively. If this spatial phase distribution is reproduced on a planar surface, an extended planar light source can emit a beam of light in a particular direction out of the plane. (e) Such a light source is obtained when an elliptical slit antenna is fed by circular surface waves at one of its focii. The scattered light from the slit has the same spatial phase distribution at the surface as a light beam arriving at oblique incidence. The eccentricity of the ellipse determines the emission angle of the beam. Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

Figure 4 .

 4 Figure 4.11: (a) The intersection of a cylinder and a plane is an ellipse; however, elliptical slit antennas do not necessarily emit cylindrical beams. (b) This is in analogy to a cylindrical beam with a circular section that becomes elliptical after refraction at the interface between two media with different refractive indices. (c) Similarly, due to different propagation speeds of light in the superstrate, of light in the substrate and of the surface waves at the interface, elliptical slit antennas emit non-cylindrical light beams at angles that depend on the upper and lower media refractive indices. Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

Figure 4 .

 4 Figure 4.12: (a-c) Transmission optical images under white light illumination, (d-f) experimental and (g-i) theoretical Fourier-space images of the light emitted upon electrical excitation of Structure 1, 4 and 6, respectively (see Tab. 4.1). The STM tip is located in the center of Structure 1, and at the focus F (-c, 0) of Structures 4 and 6. (j) Intensity profiles taken from theoretical Fourier-space images along k x , as well as the measured experimental emission angle (in red) and the calculated theoretical emission angle (in black) are shown. The calculated emission angle is determined from Eq. 4.6. The intensity profiles are normalized and vertically offset for clarity. (k) Polar plot of the angular emission pattern retrieved from an experimental Fourier-space image of the light emitted upon electrical excitation of Structure 8 (see Tab. 4.1) at the focus F (-c, 0). Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

Figure 4 .

 4 Figure 4.13: (a) Schematic of the experiment (in inset, a transmission optical image under white light illumination). (b-f) Experimental and (g-k) theoretical Fourier-space images of the light emitted upon electrical excitation of Structure 8 (see Tab. 4.1) at (from b to f) F ′ (c, 0), ( c 2 , 0), (0, 0), (-c 2 , 0) and F (-c, 0), respectively. Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

Figure 4 .

 4 Figure 4.13 shows the effect of the SPP source location on the far-field emission pattern. The emission of light from an elliptical slit (Structure 8 in Tab. 4.1) is obtained using the STM-nanosource at different positions along the major axis of the ellipse, namely: on the focii F (-c, 0) and F ′ (c, 0), in the center O(0, 0), and at intermediate positions, (-c 2 , 0) and ( c 2 , 0). The corresponding experimental and theoretical Fourier-space images are shown in Fig. 4.13. Intricated interference patterns, covering broad polar and azimuthal angular ranges, are produced when

  b/a angular spread ratio ∆k x /∆k y (b)

Figure 4 .

 4 Figure 4.14: (a) Half width at half maximum (HWHM) of the angular distribution of the light emitted in glass. This data is obtained from experimental Fourier-space images along the k x and k y axes for Structures 1 to 8. Here the HWHM is plotted versus the eccentricity of the ellipse. (b) Ratio of the minor and major semi-axes (b a) and of the angular spread along k x and k y as a function of the ellipse eccentricity. Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

Figure 4 .

 4 Figure 4.15: (a-h) Theoretical emission patterns from the elliptical slit antennas upon excitation by a z-oriented oscillating electric dipole located at the focus F (-c, 0) of the ellipse. These patterns are calculated at a vacuum wavelength of λ 0 = 700 nm for Structures 1 to 8 (see Tab. 4.1). Adapted from [159] (Open Access article under the terms of the Creative Commons Attribution License).

Figure 4 . 8 (

 48 Figure 4.15(a-h), the flux of the Poynting vector per unit solid angle is represented in real space for Structures 1 to 8 (see Tab. 4.1). Electrical excitation at F (-c, 0) is modeled as a monochromatic (λ 0 = 700 nm) z-oriented oscillating

  Collaborators: Hervé Dallaporta (CINaM, Marseille) and Xavier Quélin (GEMaC, UVSQ, Université Paris-Saclay). Postdoc/student involved: Damien Canneson (postdoc, ISMO) and Shuiyan Cao (PhD, ISMO). Damien, Shuiyan and I carried out the experiments. Damien and Xavier performed the numerical calculations using the Lumerical software. The plasmonic structures were designed by Hervé and fabricated at the technological platform for nano and microfabrication Planète, which is part of the Technological Center of the Région Provence-Alpes-Côtes-d'Azur.

Figure 5 . 1 :

 51 Figure 5.1: (a) Schematics of the experimental setup. Local electrical excitation of the sample is carried out using inelastic electron tunneling from the tip of an STM. The resulting light for real-space and Fourier-space imaging is collected and recorded on a CCD camera. (b) 1 × 1 µm 2 STM topography image of the gold nanodisk array on a gold film that has a square 450×450 nm 2 unit cell. Nanodisks are 170 nm in diameter and 50 nm high. The apparent width of the nanodisks in the image is increased due to the convolution with the STM tip (radius of curvature ≈ 50-100 nm).Reprinted with permission from[START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF]. Copyright (2016) Optical Society of America.

Figure 5 .Figure 5 . 2 :

 552 Figure 5.2: (a) The electrical excitation of SPPs on a thin (50 nm) gold film on glass (no nanodisks). The leakage radiation detected beneath the substrate is isotropic, no preferred propagation directions for the SPPs are observed. (b) The electrical excitation of SPPs on a gold nanodisk square array on a 50 nm-thin gold film (unit cell 450 × 450 nm 2 ). The leakage radiation signal shows four preferred SPP propagation directions. (c) Intensity ratio obtained when the data of part (b) is divided by the data of part (a). A factor of ≈ 1.5 increase in the intensity for particular directions is clearly seen when the array is present. In order to obtain part (c) of this figure, the data of parts (a) and (b) are first normalized with respect to the maximum intensity of the respective images. Reprinted with permission from [154]. Copyright (2016) Optical Society of America

Figure 5 .

 5 Figure 5.2 shows real-space optical images recorded upon STM excitation of SPPs on (a) a featureless 50 nmthin gold film and on (b) the square plasmonic crystal introduced above, and (c) the intensity ratio of the two latter images. Whereas SPP emission on unstructured gold is isotropic in the plane, it is enhanced in four specific directions on the nanodisk array, which coincide with the diagonals of the square array.

Figure 5 .

 5 3 shows real-space optical images recorded when the STM excitation is positioned in the center, on the middle of a side, and at a corner of the square array. (Note that in all cases the tip is centered on the top face of a nanodisk.) Bright-field transmission images of the same area [see Figs. 5.3(a) to 5.3(c)] are also shown, where the shadow of the tip may be seen. The in-plane angular distribution of emitted SPPs is retrieved from the analysis of the real-space optical images through radial integration of the intensity. The result is shown in Figs. 5.3(g) to 5.3(i), where the intensity integrated within (black curve) and outside (red curve) the NP array area are distinguished.

Figure 5 . 3 :

 53 Figure 5.3: [(a) to (c)] Bright-field optical microscopy images measured upon white-light illumination of the sample (in transmission) with the STM tip present. The shadow of the tip end reveals its lateral position: in the center of the array in panel (a), in the middle of the right edge in panel (b) and at the top right corner of the array in panel (c).[(d) to (f)] Real-space images acquired when the excitation position is (d) in the center, (e) on the side and (f) at the corner of the array. In this figure, all the data has been obtained on a square array of 450 × 450 nm 2 unit cell on a 50nm-thin gold film (the array consists of 40 × 40 gold nanodisks). Images in panels (d) to (f) are in false color and saturated (intensity is given in photon counts). Exposure times range from 600 to 1800 s. STM bias is 2.8 V and the tunnel current setpoint is in the 0.1 -6 nA range. The real-space axes are defined with respect to the array axes. [(g) to (i)] Polar plots obtained from the analysis of the real-space images shown in panels (d) to (f), respectively, and [(j) to (l)] schematics showing the preferential SPP propagation directions. In (g) to (i), we use a polar coordinate system where ρ is the lateral distance from the tip apex and φ is the polar angle in the surface plane. In each graph, the two plots correspond to the radially-integrated intensity over two different ranges of ρ, i.e., from 10 µm to 15 µm (black curve) and from 26 µm to 31 µm (red curve). In (g), these ranges of ρ correspond to an area within the NP array (but far enough from the source to solely detect propagating SPPs) and an area just outside the NP array, respectively. The numbers on the graph are the full angular width at half maxima (FWHM) of the intensity peaks after the isotropic background is subtracted. Dashed lines in (h) and (i) indicate the directions of the array edges. In (j) to (l), thin and thick arrows indicate that angularly narrow (FWHM = 8 ○ to 10 ○ ) and broad (FWHM ≈ 20 ○ ) SPP beams are observed in these directions, respectively. Adapted with permission from[START_REF] Canneson | Surface plasmon polariton beams from an electrically excited plasmonic crystal[END_REF]. Copyright (2016) Optical Society of America

  5.3(h) and 5.3(k)]. When the local excitation position is located at the corner of the array [see Figs. 5.3(f), 5.3(i) and 5.3(l)], a narrow (yet weaker) SPP beam starting at this corner and continuing diagonally through the array is created. As well, broader SPP beams are seen in the three other diagonal directions, similar to the case where the excitation is on the side of the array.

Figures 5 .Figure 5 . 4 :Figure 5 . 5 :

 55455 Figures 5.5(e) to 5.5(g) are FDTD calculations of the Fourier plane obtained for a monochromatic source. They are obtained by taking the numerical Fourier transform of images similar to those shown in Fig. 5.4(e). The complex electric field is Fourier transformed and its squared modulus is displayed. A weighted sum of this series is then used to obtain the equivalent of a polychromatic Fourier-space image in Figs. 5.5(c) and 5.5(d). The signal above

  [START_REF] Betzig | Near field scanning optical microscopy (NSOM): Development and biophysical applications[END_REF].5(a) to 5.5(d); instead, the Fourier images differ from those of an unstructured gold film by the increased intensity of the SPP ring in the four directions where SPP beaming occurs.

Collaborators:

  Georges Raşeev (ISMO) and Philippe Gogol (C2N, Université Paris-Saclay). Students involved: Shuiyan Cao (PhD, ISMO), Moustafa Achlan (PhD, ISMO) and Jean-François Bryche (PhD, C2N). Shuiyan did the STM-based experiments under my guidance. Moustafa and Georges derived the analytical model and performed the numerical simulations. The samples were fabricated and optically characterized by Jean-François at the micro-nanotechnology platform of the Center for Nanosciences and Nanotechnologies (C2N-CTU) in Orsay, with assistance from Philippe.This section is adapted with permission from S. Cao, M. Achlan, J.-F. Bryche, Ph. Gogol, G. Dujardin, G. Raşeev, E. Le Moal, and Elizabeth Boer-Duchemin, "An electrically induced probe of the modes of a plasmonic multilayer stack". Opt. Express, 27[START_REF] Lee | Visualizing vibrational normal modes of a single molecule with atomically confined light[END_REF]:33011-33026, Nov 2019. Copyright (2019) Optical Society of America.[START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF] Context and motivation. Stacking dielectric and metallic layers one on top of another is an extremely versatile way to create systems that have novel functionalities since such structures support new kinds of optical modes.

2 Figure 5 . 6 :

 256 Figure 5.6: (a) Schematic of the modeled system (not to scale). A vertical oscillating electric dipole is located at a distance h = 1 nm above a MIM stack. The stack consists of a silicon oxide layer of thickness d SiO 2 sandwiched between two 30 nm-thick gold layers on a glass substrate. A 2 nm-thick titanium layer is used to increase the adhesion of the gold to the glass. [(b),(c)] Experimental Fourier-space images measured upon STM excitation of an Au-SiO 2 -Au MIM system with d SiO 2 = 310 nm (acquisition time 300 s, sample bias 2.8 V, setpoint current 1 nA). In (c), a polarizer is set in front of the CCD camera with its transmission axis along k x . The corresponding theoretical Fourier-space images for parts (b) and (c) are shown in parts (d) and (e) respectively. In the simulations, the spectrally broad excitation has a flat power spectrum ranging in wavelength from λ 0 = 400 to 1000 nm. Reprinted with permission from[START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]. Copyright (2019) Optical Society of America.

  Figure 5.6(b) shows an experimental Fourier-space image recorded upon STM excitation of an Au-SiO 2 -Au MIM stack with oxide thickness d SiO 2 = 310 nm. "Configuration

Figures 5 .

 5 Figures 5.8(a) to 5.8(c) show the experimental dispersion relations obtained from angle-resolved optical spectra measured upon STM excitation of the different MIM stacks with oxide thicknesses of d SiO 2 = 70, 190 and 310 nm acquired using "configuration 2" of Fig. 2.4(b). To obtain this data, the Fourier-space image is projected onto the

Figure 5 . 7 :

 57 Figure 5.7: Experimental Fourier-space images measured upon STM excitation of Au-SiO 2 -Au MIM systems with a SiO 2 layer thickness of 190 nm. Bandpass emission filters are used (central wavelength/bandwidth indicated in inset). Below each experimental images, the corresponding theoretical Fourier-space images. In these simulations, the excitation is modeled with a monochromatic source. Unpublished results.

Figure 5 . 8 :

 58 Figure 5.8: [(a)-(c)] Experimental dispersion relations measured upon STM excitation of Au-SiO 2 -Au MIM stacks with SiO 2 layer thicknesses of (a) 70 nm, (b) 190 nm and (c) 310 nm (acquisition time 300 s, sample bias 2.8 V, setpoint current 1 nA). The white dashed lines are freehand curves added to guide the eye along the maxima of the intensity plot. [(d)-(f)] Theoretical dispersion calculations of the transmitted photon flux for the same MIM stacks as in the experiment. On the horizontal axis, k ρ k 0 = n glass sin θ where k ρ is the in-plane wavevector component, k 0 equals ω c, n glass is the refractive index of glass and θ is the detection angle in glass.The experimental data in wavelength has been converted to energy using a Jacobian transformation[START_REF] Mooney | Get the basics right: Jacobian conversion of wavelength and energy scales for quantitative analysis of emission spectra[END_REF][START_REF] Mooney | Correction to "get the basics right: Jacobian conversion of wavelength and energy scales for quantitative analysis of emission spectra[END_REF]. Reprinted with permission from[START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]. Copyright (2019) Optical Society of America.

Figures 5 .

 5 Figures 5.10(a) and 5.10(d) show experimental Fourier-space images obtained while illuminating the sample from below with a focused laser beam (λ 0 = 632.8 nm) using the experimental set-up of Fig. 2.4(a). The incident electric field is linearly polarized along the x-axis as shown by the double arrow on the top righthand corner of the image. For a MIM sample in this configuration, the incident light is only weakly transmitted and is instead mainly reflected, except for the case where the incident angle and polarization permit the excitation of the optical modes in the sample. This excitation of the optical modes produces dark areas in Fourier-space images acquired in reflection such as those in Figs. 5.10(a) and 5.10(d). Here, the MIM stacks with d SiO 2 = 190 and 310 nm are investigated. Experimental Fourier-space images recorded upon STM excitation of the same two MIM stacks are shown in Figs. 5.10(b) and 5.10(e). The same experimental configuration as in Fig. 5.6(b) is used; however, in order to compare the optical and electrical excitation of the MIM stacks using similar spectral ranges, a bandpass

  Figure 5.9: [(a)-(c)] Experimental dispersion relations measured upon STM excitation of Au-SiO 2 -Au MIM stacks with SiO 2 layer thicknesses of (a) 70 nm, (b) 190 nm and (c) 310 nm (acquisition time 300 s, sample bias 2.8 V, setpoint current 1 nA). The white dashed lines are freehand curves added to guide the eye along the maxima of the intensity plot. [(d)-(f)] Theoretical dispersion calculations of the transmitted photon flux for the same MIM stacks as in the experiment. On the horizontal axis, k ρ k 0 = n glass sin θwhere k ρ is the in-plane wavevector component, k 0 equals ω c, n glass is the refractive index of glass and θ is the detection angle in glass. The experimental data in wavelength has been converted to energy using a Jacobian transformation[START_REF] Mooney | Get the basics right: Jacobian conversion of wavelength and energy scales for quantitative analysis of emission spectra[END_REF][START_REF] Mooney | Correction to "get the basics right: Jacobian conversion of wavelength and energy scales for quantitative analysis of emission spectra[END_REF]. Reprinted with permission from[START_REF] Cao | An electrically induced probe of the modes of a plasmonic multilayer stack[END_REF]. Copyright (2019) Optical Society of America.

Figure 5 . 10 :

 510 Figure 5.10: The experimental data is measured on the Au-SiO 2 -Au MIM stacks with (a)-(c) d SiO 2 = 190 nm and (d)-(f) d SiO 2 = 310 nm. Parts (a) and (d): Fourier-space images acquired in reflection when the sample is backilluminated with a focused laser beam emitting at λ 0 = 632.8 nm. Parts (b) and (e): Fourier-space images acquired using STM excitation of the sample; a bandpass filter centered at λ 0 = 625 nm with a bandwidth of 26 nm is placed before the detector (acquisition time 300 s, sample bias 2.8 V, setpoint current 1 nA). [(c) and (f)] Intensity profiles taken along the k x -axis (dashed lines) in the Fourier-space images shown in (a), (b), (d) and (e), respectively. In (a) and (d), a spinning diffuser is placed in front of the laser source to reduce the speckle of the laser beam in the recorded reflection images. Reprinted with permission from [155]. Copyright (2019) Optical Society of America.

MoSe 2

 2 Collaborators: Stéphane Berciaud and Guillaume Schull (IPCMS, CNRS -Université de Strasbourg). PhD students involved: Delphine Pommier (ISMO), Rémi Bretel (ISMO) and Luis E. Parra Lópes (IPCMS). Delphine carried out most of the experimental work at ISMO. Luis prepared and optically characterized the samples. This section is adapted with permission from D. Pommier, R. Bretel, L. E. Parra López, F. Fabre, A. Mayne, E. Boer-Duchemin, G. Dujardin, G. Schull, S. Berciaud, and Eric Le Moal. "Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor." Phys. Rev. Lett., 123:027402, Jul 2019. Copyright

Figure 6 . 1 :Figure 6

 616 Figure 6.1: Ball-and-stick model of monolayer MoSe 2 . (a) Side and (b) top views of the monolayer. These drawings are made using the Jmol applet (http://www.cryst.ehu.es). Reprinted with permission from [117]. Copyright (2019) by the American Physical Society.

Figure 6 .

 6 Figure 6.2(a) shows the experimental setup and the principle of the experiment. An STM head operating in air

Figure 6 .

 6 2(c) shows a widefield PL microscopy image of the same area as in Fig. 6.2(b). Monolayers of MoSe 2 are unambiguously distinguished from multilayer specimens due to their bright direct-bandgap emission. The emitted light is detected in transmission through the substrate using a highnumerical-aperture (NA = 1.49), oil-immersion microscope objective. Optical images are recorded using a cooled CCD camera. The spatial and angular distributions of the emitted light are resolved by imaging the front and back

  Figure 6.3: (a) Fourier-space optical image of the STL measured on monolayer MoSe 2 . [(b) to (e)] Theoretical emission patterns in Fourier-space, calculated for an oscillating point-like electric dipole on an air-glass interface, for (b) out-of-plane (along z), (c) in-plane along x, (d) in-plane along y and (e) random in-plane orientations of the dipole. (f) Radial profiles taken from images a, b and e. The experimental profile is corrected for apodization [409],i.e., multiplied by cos θ where θ is the emission angle in the substrate. k ∥ k 0 = n sin θ is the normalized in-plane coordinate in Fourier space, where k 0 = ω c is the photon wavevector modulus and n is the refractive index of the substrate. Adapted with permission from[START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF]. Copyright (2019) by the American Physical Society.

Figure 6 .

 6 Figure 6.3 shows a Fourier-space image of the angular distribution of the STL from monolayer MoSe 2 , which is analyzed using the simple analytical model of an oscillating point-like electric dipole on an air-glass interface. This model is relevant to describe the far-field emission pattern resulting from radiative exciton recombination because excitons in monolayer TMDs have a Bohr radius of about 1 nm. The experimental image is juxtaposed with the theoretical emission calculated for two different dipole orientations with respect to the interface[START_REF] Novotny | Principles of Nano-Optics[END_REF]. In Fig.6.3(b), the dipole is oriented out-of-plane, i.e., in the direction perpendicular to the sample, along the z-axis. In Figs.[START_REF] Dürig | Near-field optical scanning microscopy[END_REF].3(c) and 6.3(d), the dipole is oriented in-plane, i.e., in the direction parallel to the sample, along the x and y-axes, respectively. For symmetry reasons, we consider an average over randomly oriented in-plane dipoles [see Fig. 6.3(e)].

  Photon emission quantum efficiency (10 8 count / e-)

Figure 6 . 4 :

 64 Figure 6.4: (a) STM topography of an area featuring bilayer and monolayer MoSe 2 . (b) Photon emission quantum efficiency, i.e., the number of emitted photons per tunneling electron, obtained from the ratio of the STL photon map and STM current simultaneously recorded with the STM topography shown in a. (c) Profiles taken along the same lines in a and b. STM parameters: V s = 4 V, I t = 10 nA. Adapted with permission from [117]. Copyright (2019) by the American Physical Society.

Figures 6 .

 6 Figures 6.4(a) and 6.4(b) show the STM topography and photon emission quantum efficiency maps of an area where both bilayer and monolayer MoSe 2 may be seen. Height and intensity profiles taken along the same lines in Figs. 6.4(a) and 6.4(b) are shown in Fig. 6.4(c). The emission of light is spatially correlated with the presence of monolayer MoSe 2 in the tunnel junction and reveals geometrical features of the sample with deep subwavelength

  Figures 6.6(a) and 6.6(b)

  Photon energy (eV)

Figure 6 . 6 :

 66 Figure 6.6: STM-induced luminescence spectra of monolayer MoSe 2 versus sample bias at current setpoints of (a) 0.1 nA and (b) 10 nA. Arrows and dashed lines indicate the maximum emitted photon energy and the expected quantum cutoff eV s , respectively. Acquisition time is 150 s. All spectra are corrected for the detection efficiency of the apparatus. The spectra are vertically offset for clarity. (c) Analysis of STM-induced luminescence spectra of monolayer MoSe 2 on ITO. Sample-bias dependence of the A and B exciton energy at a current setpoint I t = 10 nA. Exciton energy and uncertainties (error bars) are obtained from the fit of the emission peaks with Voigt profiles.Reprinted with permission from[START_REF] Pommier | Scanning tunneling microscope-induced excitonic luminescence of a two-dimensional semiconductor[END_REF]. Copyright (2019) by the American Physical Society.

  use an original combination of time and spatially resolved optical and electrical nanoprobes, in order to investigate the exciton dynamics with femtosecond and nanometer resolution. The uncovered microscopic mechanisms may eventually be harnessed to optimize optically and electrically driven single photon sources based on 2D materials. This project will be carried out in collaboration with Stéphane Berciaud (IPCMS, CNRS -Université de Strasbourg), Sylvie Marguet (Université Paris-Saclay, CEA, CNRS, NIMBE), Ludovic Douillard and Simon Vassant (Université Paris-Saclay, CEA, CNRS, SPEC).

  research activity on the growth and electroluminescence spectroscopy of molecular systems relies on internal collaborations at ISMO, with Andrey G. Borisov (theory and calculations), Hamid Oughaddou (low-temperature STM), Andrew Mayne (room-temperature STM), Hocine Khemliche (grazing incidence fast atom diffraction -GIFAD) and Aimeric Ouvrard (room-temperature STM and differential reflectance spectroscopy -DRS), and on external collaborations with Mathieu Silly at the SOLEIL Synchrotron Facility (Saint-Aubin), the group of Guillaume Schull at IPCMS in Strasbourg and the group of Moritz Sokolowski at the University of Bonn in Germany. The PhD students involved at ISMO are (or were) Ala Husseen (2015-2018, co-supervized by A. Mayne, S. Le Moal and myself) and Rémi Bretel (2018-2021, supervized by M. Sokolowski and myself).

Collaborator:

  Guillaume Schull (IPCMS, CNRS -Université de Strasbourg). PhD student involved: Benjamin Doppagne (IPCMS, supervisor: G. Schull). Benjamin has carried out most of the experimental work at IPCMS. I have proposed and participated in these experiments on the occasion of a stay at IPCMS in July of 2019 and I have analyzed the data.

Figure 7 . 1 :

 71 Figure 7.1: [(a) and (b)] STM topography images of PTCDA molecules adsorbed on an Ag(111) surface partially covered with NaCl islands. Labels 2 -4 ML indicate NaCl thickness in number of atomic layers. STM parameters: V s = -2.5 V, I t = 5 pA in (a) and I t = 10 pA in (b). [(c) and (d)] atomic representation of the PTCDA molecule. (e) dI dV STM spectra measured on an individual PTCDA molecule on 3 ML NaCl/Ag(111).

#

  atomic layers NaCl/Ag(111) KCl/Ag(001) Results and discussion. Figures 7.1(a) and 7.1(b) show STM topography images of PTCDA molecules adsorbed on an Ag(111) crystal surface that has been partially covered with NaCl islands prior to PTCDA deposition.The NaCl islands have been grown at room temperature and the PTCDA molecules have been deposited at low temperature (4 K) directly inside the STM, from a heated crucible located in front of an opening in the thermal shield of the STM. From their apparent STM height, we infer that the thickness of the NaCl islands locally varies within the range of 2 to 4 atomic monolayers (ML). Thus, the effect of the electronic decoupling of the molecules from the metallic substrate may be compared for three different thicknesses of the insulating spacer, i.e., 2 ML, 3 ML and 4 ML of NaCl. Similar experiments have been carried out on the PTCDA/KCl/Ag(001) system (data not shown here) and the observed discrepancies in the STL behavior of the PTCDA/NaCl/Ag[START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] and PTCDA/KCl/Ag(001) systems are discussed below. Schematics of the atomic structure of PTCDA are shown in Figs. 7.1(c) and 7.1(d). In STM images measured at a sample bias of V s = -2.5 V [e.g., in Fig. 7.1(b)], PTCDA molecules on NaCl exhibit the shape of a yoyo seen edge-on. The two bright lobes are located above the hydrogen atoms and the darker line is oriented along the long axis of the molecule. The same aspect is observed for PTCDA on KCl. The apparent STM heights of the insulating layers and of the molecules, as measured at the same STM parameters (V s = -2.5 V and I t = 5 -10 pA) on NaCl and KCl, are summarized in Tables

Figure 7 .

 7 Figure 7.1(e) shows dI dV STM spectra measured in constant-height mode (i.e., the STM feedback loop is open) on an individual PTCDA molecule on 3 ML NaCl/Ag[START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF]. We find that the energy positions of the peaks do

Figure 7 .

 7 2(a) shows an STM topography image of a single PTCDA molecule on 2 ML NaCl/Ag(111). The STL spectra shown in Fig. 7.2(b) are measured with the STM tip located on the position indicated with a white cross in Fig. 7.2(a), i.e., at about 2 nm away from the center of the molecule [see black curve in Fig. 7.2(b)], and out of area imaged in Fig. 7.2(a), where no molecule is close enough to be excited [see red curve]. In the latter case, the emission is spectrally broad, which results from the excitation of the tip-induced gap plasmon, or nanocavity plasmon, localized in the tip-surface gap. However, near the PTCDA molecule (see black curve), an additional sharp

Figure 7 . 2 :

 72 Photon energy (eV)

Fig. 7 .Figure 7 . 3 :

 773 Photon energy (eV)

Fig- ure 7

 7 .3(b) shows STL spectra measured over a larger spectral range and under similar conditions as those shown in Fig.7.3(a). In Table

Titre:

  Nano-Optique dans un Microscope à Effet Tunnel : Applications à la Plasmonique et à l'Excitonique Mots clés: STM, microscopie optique, plasmon de surface, exciton, semi-conducteur 2D, électroluminescence Résumé: Le microscope à effet tunnel (STM) n'est pas seulement un outil de sciences des surfaces capable de produire des images résolues à l'échelle atomique de surfaces cristallines; c'est aussi un outil extraordinaire pour la nano-optique. En effet, le courant tunnel inélastique entre la pointe du STM et la surface de l'échantillon conduit à une excitation extrêmement locale des modes optiques existants. Ainsi, la jonction pointe-échantillon peut se comporter comme une nanosource de photons, de polaritons de plasmon de surface ou d'excitons, selon la nature de l'échantillon. Dans cette thèse, j'introduis quelques-unes des études uniques, en particulier en plasmonique et excitonique, auxquelles cet outil peut être appliqué lorsque le STM et la microscopie optique sont combinés dans le même instrument. Des exemples de mes recherches impliquent l'étude des modes propres de nanoparticules plasmoniques individuelles, la réponse des composants micro-optiques plasmoniques, la dispersion énergie-vecteur d'onde des polaritons dans des métasurfaces et les propriétés excitoniques des semi-conducteurs bidimensionnels. Les futures directions de recherche incluent un travail collaboratif récent sur la spectroscopie de luminescence de molécule unique dans un STM basse température sous ultra-vide.Title: Nano-Optics in a Scanning Tunneling Microscope: Applications to Plasmonics and Excitonics Keywords: STM, optical microscopy, surface plasmon, exciton, 2D semiconductor, electroluminescence

  Collaborator: Sylvie Marguet (Université Paris-Saclay, CEA, CNRS, NIMBE). Students involved: Samik Mukherjee (M2, ISMO), Benoît Rogez (PhD, ISMO). Sylvie synthesized the gold NPs used in all the work reported in Chap. 3. Samik, Benoît and I did the experiments shown in Sec. 3.1. Benoît and I did the numerical simulations, with technical assistance of Philippe Dos Santos.

This section is adapted with permission from E. Le Moal, S. Marguet, B. Rogez, S. Mukherjee, P. Dos Santos, E. Boer-Duchemin, G. Comtet, and G. Dujardin, "An electrically excited nanoscale light source with active angular control of the emitted light," Nano Lett., 13(9):4198-4205, Sept. 2013. Copyright(2013) American Chemical Society.

  , Codruta and Tatiana did the theoretical work; in particular, the derivation of the model introduced below and the complete electromagnetic calculations are Andrey's work and the numerical simulations using Comsol Multiphysics are Tatiana's work. Benoît, Damien and I did the experimental work.

	AndreyThis section is adapted with permission from E. Le Moal, S. Marguet, D. Canneson, B. Rogez, E. Boer-Duchemin,
	G. Dujardin, T. V. Teperik, D.-C. Marinica, and A. G. Borisov. "Engineering the emission of light from a scanning
	tunneling microscope using the plasmonic modes of a nanoparticle." Phys. Rev. B, 93(3):035418, Jan. 2016.

Borisov and Dana-Codruta Marinica (ISMO), Tatiana V. Teperik (DIPC, San Sebastían, Spain), Sylvie Marguet (NIMBE). Student/postdoc involved: Benoît Rogez (PhD), Damien Caneson (postdoc, ISMO).

Table 4 .

 4 1: Parameters of the elliptical slit antennas. The major axis 2a and the eccentricity e are given (the minor axis is always 2b = 3µm).

	Structure 1	2	3	4	5	6	7	8
	2a (µm)	3 3.05 3.20 3.46 3.92 4.67	6	8.77
	e (µm) arcsin e	0 0.18 0.35 0.51 0.64 0.77 0.87 0.94 0 ○ 10 ○ 20 ○ 30 ○ 40 ○ 50 ○ 60 ○ 70 ○

Table 7 .

 7 4: Variation of the vertical distance between the STM tip and the sample when the tip is on a PTCDA molecule, as compared to the tip-sample distance on bare metal, as a function of the alkali halide thickness in atomic monolayers (0 ML means PTCDA on metal), as retrieved from the difference between the STM and "true" heights shown in Table7.3. STM heights are measured on PTCDA/NaCl/Ag[START_REF] Rogez | The mechanism of light emission from a scanning tunnelling microscope operating in air[END_REF] and PTCDA/KCl/Ag(001) at V s = -2.5 V and I t = 5 -10 pA. The distance variations have a negative sign because the tip is closer to the sample when it is located on a molecule than when it is on the bare metal surface.# atomic layers PTCDA/NaCl/Ag(111) PTCDA/KCl/Ag(001)

	atomic layers	PTCDA/NaCl/Ag(111)	PTCDA/KCl/Ag(001)
		STM height / true height STM height / true height
	0 ML	70 ± 5 pm 281 pm	100 ± 5 pm 281 pm
	2 ML	620 ± 10 pm 904 pm	680 ± 10 pm 976 pm
	3 ML	910 ± 10 pm 1186 pm	990 ± 10 pm 1294 pm
	4 ML	1230 ± 10 pm 1468 pm	-
	0 ML	-211 ± 5 pm	-181 ± 5 pm
	2 ML	-284 ± 10 pm	-296 ± 10 pm
	3 ML	-276 ± 10 pm	-304 ± 10 pm
	4 ML

  bending of the H atoms molecule due to its adsorption geometry. Whereas PTCDA in gas phase is a flat molecule, upon adsorption on

	assignment		STL		PL	from [477]	Characterization
		4 ML	3 ML	2 ML	on t sites on s sites	from [478]
	ν ′ 1 (A) ν ′ A	-237 ± 7 -236 ± 4 -231 ± 5 -52 ± 7 -55 ± 3 -51 ± 6
	ν A	53 ± 7	54 ± 3	55 ± 5	57 ± 5	63 ± 2
	ν B (L 1 )	130 ± 8	130 ± 4	131 ± 8	127 ± 5	94 ± 2	bending of PTCDA anhydride groups
	ν C				¯131 ± 2
	ν D				¯173 ± 2
	ν E (L 2 )				186 ± 5	186 ± 2	H atom vibration twd. the surface
	ν 1 (A)	239 ± 5	240 ± 3	245 ± 6	231 ± 2	233 ± 2	breathing along PTCDA long axis
	ν A + ν 1	294 ± 8	294 ± 4	297 ± 8	¯297 ± 3	combination band
	ν B + ν 1 (L 1 + A)				¯326 ± 5
	ν C + ν 1				¯366 ± 2
	ν 2 (B)				¯394 ± 2	breathing along PTCDA short axis
	ν D + ν 1				¯407 ± 2
	ν E + ν 1 2 × ν 1 (A ′ )	467 ± 7	472 ± 6	477 ± 8	¯420 ± 2 468 ± 2 468 ± 2	1 st overtone of A
	ν 3 (C)	539 ± 5	540 ± 3	539 ± 5	535 ± 2	533 ± 2	skeletal + anhydride deformation
	ν 4 (D)	628 ± 5	630 ± 3	632 ± 6	615 ± 4	615 ± 2

Scientific productions

Acknowledgements

My gratitude goes first to Prof. Dr. Bert Hecht, Prof. Dr. Richard Berndt and Prof. Agnès Maître, who have accepted to review this Habilitation thesis. I am very thankful to Prof. Odile Stéphan, Prof. Renaud Bachelot and Dr. Cyriaque Genet, for accepting my invitation to take on the roles of President and Examiners, respectively.

Function: CNRS researcher (CR-CN: Chargé de Recherche Classe Normale), since 2011 Organization: CNRS -Université Paris-Saclay, Institut des Sciences Moléculaires d'Orsay (ISMO) Research group: 2011-2019: Molecular Nanosciences (leader: Gérald Dujardin / Andrew Mayne), 2020-to date: Nanophysics@Surfaces (leader: Elizabeth Boer-Duchemin) Previous positions 07/2009 -09/2011: Marseille (France), Institut Fresnel -CNRS, Research Assistant (CDD) 09/2007 -06/2009: Bonn (Germany), Institute of Physical and Theoretical Chemistry, Humboldt postdoc fellow 09/2006 -08/2007: Orsay (France), Paris-Sud University -Laboratory of Molecular Photophysics (PPM), Research and teaching assistant (ATER) 09/2003 -08/2006: Paris (France), Pierre-et-Marie-Curie University (UPMC-Paris VI) -ESPCI, Teaching assistant (moniteur) Education 09/2003 -02/2007: PhD thesis in Physics, UPMC-Paris VI -ESPCI https://tel.archives-ouvertes.fr/tel-00164549 2002 -2003: DEA (=M.Sc.) in Experimental atomic and molecular physics, UPMC-Paris VI 2000 -2002: Licence (=B.Sc.) and Maîtrise of Applied physics, University of Versailles-Saint-Quentin-en-Yvelines. 1998 -2000: DEUG in Sciences of Matter, Université de Versailles-Saint-Quentin-en-Yvelines.

Appendix A

Curriculum vitae