Yinping Zhang

Guillaume Demesy

Mohamed Haggui

Davy Gérard

Jérémie Béal

Stephanie Dodson

Qihua Xiong

Jérôme Plain

Nicolas Bonod

Renaud Bachelot
email: renaud.bachelot@utt.fr

Guillaume Demesy $

Qihua Xiong %,#

Jérome Plain

Nanoscale Switching of Near-Infrared Hot Spots in Plasmonic Oligomers Probed by Two-Photon Absorption in Photopolymers

Keywords: nanoplasmonics, nanoantenna, molecular probing, 2-photon isomerization, azopolymer

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Metallic nanostructures offer the possibility to strongly confine light at nanometer scale. [START_REF] Maier | A Plasmonics: fundamental and applications[END_REF][2][3][START_REF] Wei | Plasmonics in composite nanostructures[END_REF][START_REF] Lee | Review on subwavelength confinement of light with plasmonics[END_REF] In general, rational control of the plasmonic nanostructures' geometry and/or incident beam shaping (including phase, polarization state and angle of incidence) can produce a large variety of near-field distributions that can be exploited in photonic computing, [START_REF] Savage | Photonics: Trick of the Light[END_REF][START_REF] Davis | Plasmonic Circuits for Manipulating Optical Information[END_REF] nanophotochemistry, [START_REF] Ueno | Surface Plasmon-Enhanced Photochemical Reactions[END_REF][START_REF] Linic | Photochemical Transformations on Plasmonic Metal Nanoparticles[END_REF][START_REF] Gray | Surface Plasmon-Enhanced Spectroscopy and Phtochemistry[END_REF][START_REF] Deeb | Plasmon-Based Free-Radical Photopolymerization: Effect of Diffusion on Nanolithography Processes[END_REF] optical trapping, [START_REF] Huang | Origin and Future of Plasmonic Optical Tweezers[END_REF][START_REF] Jensen | Optical Trapping and Two-Photon Excitation of Colloidal Quantum Dots Using Bowtie Apertures[END_REF][START_REF] Mivelle | Ultrabright Bowtie Nanoaperture Antenna Probes Studied by Single Molecule Fluorescence[END_REF][START_REF] Juan | Plasmon Nano-Optical Tweezers[END_REF] non-linear nanoptics, [START_REF] Kauranen | Non linear Plasmonics[END_REF][START_REF] Wurtz | Designed Ultrafast Optical Nonlinearity in a Plasmonic Nanorod Metamaterial Enhanved by Nonlocality[END_REF][START_REF] Butet | Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications[END_REF] Surface Enhanced Raman Spectroscopy, [START_REF] Muehlethaler | Review of Surface Enhanced Raman Scattering Applications in Forensic Science[END_REF][START_REF] Schlucker | Surface-Enhanced Raman Spectroscopy: Concepts and Chemical Applications[END_REF][START_REF] Rumyantseva | Nonresonant Surface-Enhanced Raman Scattering of Zno Quantum Dots with Au and Ag Nanoparticles[END_REF] plasmon-assisted light emission (including single photon emission), [START_REF] Stockman | Spasers Explained[END_REF][START_REF] Fort | Surface Enhanced Fluorescence[END_REF][START_REF] Yang | Real-Time Tunable Lasing from Plasmonic Nanocavity Arrays[END_REF][START_REF] Zhou | Two-Color Single Hybrid Plasmonic Nanoemitters with Real Time Switchable Dominant Emission Wavelength[END_REF][START_REF] Schietinger | Plasmon-Enhanced Single Photon Emission from a Nanoassembled Metal-Diamond Hybrid Structure at Room Temperature[END_REF][START_REF] Viste | Enhancement and Quenching Regimes in Metal-Semiconductor Hybrid Optical Nanosources[END_REF][START_REF] Celebrano | Efficient Coupling of Single Photons to Single Plasmons[END_REF] and hot carrier generation and collection. [START_REF] Brongersma | Plasmon-Induced Hot Carrier Science and Technology[END_REF][START_REF] Sundararaman | Theoretical Predictions for Hot-Carrier Generation from Surface Plasmon Decay[END_REF][START_REF] Harutyunyan | Anomalous Ultrafast Dynamics of Hot Plasmonic Electrons in Nanostructures with Hot Spots[END_REF] In this context, plasmonic oligomers are very interesting to efficiently confine and enhance light intensity at deep subwavelength scale within the gaps separating the different plasmonic particles. [START_REF] Hentschel | Plasmonic Oligomers: The Role of Individual Particles in Collective Behavior[END_REF][START_REF] Pasterilli | Self-Assembled Plasmonic Oligomers for Organic Photovoltaics[END_REF][START_REF] Zhao | Large-Area High-Quality Plasmonic Oligomers Fabricated by Angle-Controlled Colloidal Nanolithography[END_REF][START_REF] Knebl | Gap plasmonics of silver nanocube dimers[END_REF] The so-called hot-spots result from the coupling between the localized surface plasmon modes hosted by the individual particles. Multiple hot-spots can be created simultaneously in plasmonic oligomers and their remote control remains challenging.

Trimers of gold nanorods are examples of oligomers that are highly suited to yield strong field enhancements. [START_REF] Roller | Hotspot-mediated non-dissipative and ultrafast plasmon passage[END_REF][START_REF] Zohar | The simplest plasmonic molecules: Metal nanoparticle dimers and trimers[END_REF][START_REF] Funston | Coupling modes of gold trimer superstructures[END_REF] One of the challenges is to switch on or switch off on demand light in the two available gaps. For incident polarization parallel to the trimer axis, the plasmonic bright hot spots result from the excitation of a bonding mode, i.e. when the dipolar moments in the neighboring particles are in phase, while the anti-bonding modes (out-of phase adjacent dipolar moments) are dark. It was first proposed to control the hot spots by tailoring the phase of the incident beam. G. Volpe et al. used Laguerre Gaussian beams to shape the phase of the incident beam and managed to excite anti-symmetric bonding modes in the two particles associated with a nanogap and a symmetric anti-bonding mode in the two particles associated with the other nanogap. [START_REF] Volpe | Controlling the optical near field of nanoantennas with spatial phase-shaped beams[END_REF] Far-field observation based on two-photon induced luminescence supported this approach. A simpler strategy was proposed by Devilez et al., consisting in the simultaneous excitation of the symmetric and anti-symmetric modes in the trimers without shaping the phase of the incident beam. [START_REF] Devilez | Mode-balancing far-field control of light localization in nanoantennas[END_REF] They considered a simple plane wave excitation and showed theoretically that by simply tilting the incidence, it is possible to excite this combination of modes, corresponding to a subradiant mode. The near-field intensity can be almost perfectly vanished in a given gap while strongly enhanced in the other gap, even if they are separated by only a tenth of the incident wavelength. By illuminating the trimer antenna under the opposite incidence angle, the hot spot is switched in the other nanogap. Hence, the position of the electromagnetic hot spot can be controlled at deep subwavelength scale by a simple far-field optical command. This effect is highly promising because it would easily enable rational control of nanometric hot spots for many applications such as those cited at the beginning of the introduction.

Experimental observation and study of this effect at the nanoscale are crucial for its control and optimization. In practice, the near-field investigation of resonant plasmonic nanogaps constitutes a challenging task for several reasons. For example, the use of Scanning Near-field Optical Microscopy (SNOM) [START_REF] Alonso-González | Visualizing the near-field coupling and interference of bonding and anti-bonding modes in infrared dimer nanoantennas[END_REF] is complicated by the presence of the probe, modifying the resonance conditions for hot spot excitation: the observed resonance would mainly result from the coupling between gap modes and the probe, rather than the optical properties of the plasmonic cavity itself. [START_REF] Fisher | Scanning near-field optical microscopy (Chap. 7)[END_REF] Additionally, both the nature of the tip-sample optical interaction and the interpretation of the SNOM images [START_REF] Greffet | Image formation in near-field optics[END_REF] strongly depend on the probe (shape, type, quality, control mode,...) and its environenement, [START_REF] Van Hulst | Evanescent-field optical microscopy: effects of polarization, tip shape and radiative waves[END_REF][START_REF] Gomez | Apertureless scanning near-field optical microscopy: a comparison between homodyne and heterodyne approaches[END_REF] which is pretty difficult to control.

Other methods were recently reported to study plasmonic nanostructures at the nanoscale.

Photon Emission Electron Microscopy (PEEM), [START_REF] Douillard | Short Range Plasmon Resona-tors Probed by Photoemission Electron Microscopy[END_REF][START_REF] Hrelescu | Selective Excitation of Individual Plasmonic Hotspots at the Tips of Single Gold Nanostars[END_REF][START_REF] Word | Direct Coupling of Photonic Modes and Surface Plasmon Polaritons Observed in 2-Photon PEEM[END_REF] based on the photoelectrical effect, has turned out to be highly efficient but requires an electron reservoir. As a result, near-field contrast can be observed only on metal surface and not at zones far from metal. A gap-mode field that is partly delocalized in the dielectric gap medium is not expected to lead to any easily interpretable PEEM contrast, despite some interesting reported data. Additionally, because of the out-of plane electric field used for electron accelerations, this technique is mainly sensitive to out-of plane field components whereas local fields that result from inplane plasmonic coupling are mainly in-plane polarized. This important point will be discussed further. As far as Electron Energy Loss Spectroscopy (EELS) is concerned, [START_REF] Koh | Electron Energy-Loss Spectroscopy Silver Nanoparticles and Dimers: Influence of Beam Damage and Mapping of Dark Modes[END_REF][START_REF] Koh | High-Resolution Mapping of Electron-Beam-Excited Plasmon Modes in Lithographically Defined Gold Nanostructures[END_REF][START_REF] Colliex | Electron Energy Loss Spectroscopy imaging of surface plasmons at the nanometer scale[END_REF][START_REF] Martin | High-Resolution Imaging and Spectroscopy of Multipolar Plasmonic Resonances in Aluminum Nanoantennas[END_REF][START_REF] Hörl | Tomography of Particle Plasmon Fields from Electron Energy Loss Spectroscopy[END_REF][START_REF] Hohenester | Electon Energy Loss spectra of plasmonic nanoparticles[END_REF] contrasts result from local electronic absorption (a metal reservoir is thus also required) and no optical excitation is possible (excitation is purely electronic in EELS). Additionally, it was recently shown that inside the gap region of a coupled plasmonic system, the EELS signal can become zero for the bonding mode and maximal for the antibonding mode. [START_REF] Hörl | Tomography of Particle Plasmon Fields from Electron Energy Loss Spectroscopy[END_REF][START_REF] Hohenester | Electon Energy Loss spectra of plasmonic nanoparticles[END_REF] In general, PEEM and EELS techniques are very efficient but pretty sophisticated and expensive.

Here, we report on the direct near-field observation, based on a simple method, of mode balancing and localization of hot spots in a trimer plasmonic nanoantenna. We used twophoton absorption in Photosensitive Azobenzene-containing Polymer (PAP) for plasmonic nano-imaging of infrared nanoantenna, opening the route to near-field investigation of coupled systems based on molecular probing.

The linear plasmonic trimer antenna under study is presented in Figure 1. It was made by electron-beam lithography and consists of a trimer of gold nanorods (115 nm long, 45 nm wide, and 50 nm high) separated by two 30 nm wide gaps denoted C1 and C2 separated by a 145 nm distance, i.e. /4 (=0/n, where o is the incident wavelength and n is the PAP refractive index). Figure 1(a) shows an image of such a trimer as observed by scanning electron microscopy (SEM). Our main motivation is to experimentally demonstrate that it is possible to switch on and off, on demand, the respective near-field enhancement at each cavity (C1 or C2). We will also pay attention to the extremities E1 and E2 depicted in Figure 1(a), as they can support electromagnetic hot spots as well. The left-hand side of Figure 1(d) shows calculated (see method) absorption spectra of the trimer antenna on glass and coated with a 45 nm-thick PAP film when illuminated by an unpolarized plane wave propagating along the Z axis (illustrated in Figure 1(a)) for different angles of incidence . The absorption spectrum shows a strong optical response in the near-infrared. First, we can observe the strong dependence of the spectrum with respect to the angle of incidence. In normal incidence (=0°), the absorption spectrum features a peak around 0=980nm due to the excitation of the radiant (bright) mode.

This mode corresponds to a situation where the electric dipolar moments associated with each nanoparticle are aligned and in phase, resulting in two gap bonding modes, denoted B-B (see first illustration to the right of the spectrum). To this low absorption is associated a strong scattering efficiency (see supplementary information). One can also observe a secondary peak at 750 nm due to the excitation of the mode for which the dipolar moments are out of phase, resulting in two anti-bonding gap modes, denoted A-A (see third illustration to the right of the spectrum). It is much more pronounced in the absorption spectrum and can be called "dark mode", corresponding to the excitation of a high-order resonance in the nanoantenna. In oblique incidence, with a moderate angle of incidence (=15°), three peaks can be observed.

The radiant and dark modes can again be observed at 0=980nm and 0=750nm respectively, while a subradiant mode is excited at 0=850nm. This mode, described for example by F.

Frimer et al. [START_REF] Frimmer | Signature of a fano resonance in plasmonic metamolecule' local density of optical states[END_REF] and Mirin et al., [START_REF] Mirin | Fano Resonances in Plasmonic Nanoparticle Aggregates[END_REF] corresponds to both in-phase and opposite-phase pairs of dipoles resulting in both anti-bonding and bonding gap modes within the trimer (denoted A-B or B-A, see second illustration to the right of the spectrum). It should be pointed out that A-B and B-A are degenerate modes. When the angle of incidence is increased, the component of the electric field along the trimer axis weakens leading to the cancellation of the radiant mode while the subradiant mode is still excited. Figure 1(d) shows that the gold trimer has strong optical response in the near-infrared. The excitation of this subradiant mode from the far field around 0=850 nm in oblique incidence, especially at an incidence of 30°, opens new routes to tailor the distribution of the near electric field in the two gaps of the trimer antenna. More detailed discussion on trimer modal analysis can be found in supporting information. Based on calculated spectrum in Figure 1(d), the incident wavelength of 900 nm was chosen, in order to be sensitive to both radiant and subradiant modes. We will see later that this wavelength is also suitable for 2-photon absorption in PAP used for near-field probing.

To visualize the optical near-field, we used a specific approach that has been developed over the past decade. [START_REF] Hubert | Near-Field Photochemical Imaging of Noble Metal Nanostructures[END_REF][START_REF] Hubert | Near-Field Polarization Effects in Molecular-Motion-Induced Photochemical Imaging[END_REF][START_REF] Juan | Plasmonic Electromagnetic Hot Spots Temporally Addressed by Photoinduced Molecular Displacement †[END_REF][START_REF] Juan | Multiscale Model for Photoinduced Molecular Motion in Azo Polymers[END_REF][START_REF] Juan | Self-Consistent Model of Light-Induced Molecular Motion Around Metallic Nanostructures[END_REF][START_REF] Haggui | Spatial Confinement of Electromagnetic Hot and Cold Spots in Gold Nanocubes[END_REF][START_REF] Plain | Multiscale optical imaging of complex fields based on the use of azobenzene nanomotors[END_REF][START_REF] Galarreta | Mapping Hot-Spots in Hexagonal Arrays of Metallic Nanotriangles[END_REF][START_REF] Teulle | Photochemical Mapping of the Multimodal Plasmonic Response of 2D Gold Crystals[END_REF] Azobenzene molecules (see Figure 1(c)) that are covalently attached to a polymeric backbone are used as optically driven molecular nanomotors. Light can excite the transcis isomerization in azobenzene-like molecules that are grafted to chains of polymethyl methacrylate (PMMA). This copolymer is usually named PMMA-Dispersed red one (PMMA-DR1) because it looks red since its absorbance is maximum in the range 400-500 nm (see the left-hand side of Figure 1(c)). Upon absorbing a photon in the visible, an isomerization cycle produces a "worm-like" motion that leads to a displacement along the transition moment axis that could be on the order of a nanometer (see right-hand side of Figure 1(c). [START_REF] Lefin | Anisotropy of the photo-induced translation diffusion of azobenzene dyes in polymer matrices[END_REF] Many repeated isomerization cycles ultimately lead to more large-scale mass transport. After exposure to light, an Atomic Force Microscope (AFM) is used to measure the resulting topography that is related to the near-field intensity pattern to be characterized. The azobenzene-like molecules are thus nanomotors that push and pull at the polymer material leading to topographical features after exposure that reflect the underlying near-field intensities. As it will be seen, this method is also sensitive to local field polarization. More details about this optical near-field imaging method in the visible can be found in references. [START_REF] Hubert | Near-Field Photochemical Imaging of Noble Metal Nanostructures[END_REF][START_REF] Hubert | Near-Field Polarization Effects in Molecular-Motion-Induced Photochemical Imaging[END_REF][START_REF] Juan | Plasmonic Electromagnetic Hot Spots Temporally Addressed by Photoinduced Molecular Displacement †[END_REF][START_REF] Juan | Multiscale Model for Photoinduced Molecular Motion in Azo Polymers[END_REF][START_REF] Juan | Self-Consistent Model of Light-Induced Molecular Motion Around Metallic Nanostructures[END_REF][START_REF] Haggui | Spatial Confinement of Electromagnetic Hot and Cold Spots in Gold Nanocubes[END_REF][START_REF] Plain | Multiscale optical imaging of complex fields based on the use of azobenzene nanomotors[END_REF] In particular, in reference [START_REF] Juan | Multiscale Model for Photoinduced Molecular Motion in Azo Polymers[END_REF] we theoretically described optically-induced topographical formation based on a multiscale statistical approach. spectrum of the co-polymer is in the (400-600) nm range (see Figure 1(c)). This feature is the raison why all the near-field studies have been so far done in the visible, which is not relevant for gap mode study because plasmonic couplings generally result in red-shifted plasmon resonance, making a priori impossible the study of the resonant nanoantenna in the infrared.

In order to address this important issue, we propose to follow a two-photon isomerization, which allows us to illuminate the antenna in the near infrared spectrum. We start this study by characterizing the two-photon absorption of a 100 nm thick monolayer of PMMA-DR1 coated on a glass substrate. Figure 2 In particular, it was shown that molecules escape from in-plane polarized light with an inplane motion, resulting in a topography that is the negative image of the intensity distribution on in-plane fields. [START_REF] Hubert | Near-Field Photochemical Imaging of Noble Metal Nanostructures[END_REF] Although 2-photon induced movement in PAP has already been reported, [START_REF] Ishitobi | Two-photon induced polymer nanomovement[END_REF] we used for the first time two-photon absorption in PMMA-DR1 polymer to study the near fields on plasmonic antennas in the near-infrared.

Figure 3 depicts the experimental configuration for near-field investigations of linear plasmonic trimer antennas. A 45-nm thick PMMA-DR1 layer was deposited on the sample by spin coating (see method), resulting in an effective 10 nm thickness at the top on the gold particles and a 45 nm-thickness elsewhere. The apparent height of the particles is thus about 15 nm after spin coating. Figure 1(b) is the AFM image of the PMMA-DR1-coated antenna before exposure. In the following, such an image will not be shown again and all presented photo-induced topographies should be compared to it because each exposure was done from a plasmonic structure covered by a fresh layer of unexposed PMMA-DR1, as illustrated in Figure 5 shows the result of the exposure in the TM case (incident polarization parallel to the main axis of the nanoantenna trimer) at normal incidence (except for Figure 5(g)). The photoinduced topography after exposure displayed in Figure 5(a) confirms that the two hot spots at C1 and C2 are excited. In particular, the field distribution is no longer strictly symmetric relatively to each single gold particle and E1, E2 antenna extremities are not (or poorly) excited. In order to discuss further the experimental observations, calculations were performed at different wavelengths. Figure 6 shows the calculated intensity I1, I2 at gaps C1 and C2

(respectively) as a function of the wavelength for different incidence angles (0°, 15°, 30°) for a TM incident polarization. In the case of normal incidence (=0°), a clear balance between the two gaps is observed (I1=I2) due to the symmetry of the configuration. This balance is in agreement with the symmetric response observed experimentally in Figures 5(a-c). It is worth noticing, again, that the optical response of the plasmonic trimer is both significant and of interest for wavelengths larger than 800 nm, justifying the use of a 900 nm wavelength and the exploration of two-photon absorption in azo-polymers. In particular, for 0>800 nm, a clear distinction can be done between the field of the two nanogaps by tuning the incident angle.

The incidence condition at =30° and 0=900 nm is of great interest: almost zero intensity is predicted at C2 while C1 presents a strong localized field. This situation corresponds to a B-A subradiant mode described in Figure 1(d). We now aim at observing experimentally this phenomenon (see Figure 7).

The sample was illuminated at =30° and 900 nm in TM polarization, and the observation of the molecular motion in Figures 7(a This near-observation constitutes an experimental evidence of a B-A subradiant mode, which is in agreement with Figure 6 that predicts a near-zero intensity I2 at C2 and an I1 intensity (at C1) of about 140. This result shows up the possibility i) to switch on demand and from far field region electromagnetic hot spots at cavities separated by 0/4n, ii) to use this effect for remote activation of azobenzene molecules at the nanoscale. It is worth noticing that a secondary weaker hot spot can be identified in Figures 7(a

show that nanogap C1 is turned off while activation of nanogap C2 is much stronger. This case is clearly symmetrical to the previous one, it corresponds to a A-B subradiant mode. Figures 7(a-f) illustrate well the nanoscale switch between the two gaps.

Figures 7(g) and 7(h) are zoom-out of AFM images in the =30° case, taken before and after exposure respectively. Additionally to the near-field contrast, Figure 7(h) exhibits a topographical modulation that corresponds to a near-field diffraction pattern in the Fresnel zone. This near-field pattern is made of ultra-confined grazing propagating waves able to interfere with each other, reminding us what pioneers observed on metal nanostructures using first version of SNOM. [START_REF] Krenn | Direct observation of localized surface plasmon coupling[END_REF] A multiscale electromagnetic analysis is thus possible.

Figures 7(i-k) show the =-15° case. Again, the C2 nanogap is clearly turned on. It is worth noticing that cavity C1 is also activated: it presents a non-negligible topographical depletion that is about 2.2 times less deep than for nanogap C2. This partial activation is also shown in numerical simulation of lExl (Figure 7(k)). This observed effect is in good agreement with the tendency revealed in Figure 6: tuning  for an accurate tuning of the respective intensities of the different involved electromagnetic hot spots: 0° does not enable any contrast between different hot spots, -/+15° leads to partial contrast, -/+30° allows for full hot spot selection.

In Figure 8 Four locations were considered: the C2 cavity in Figure 7(a), the C2 cavity in Figure 5(a), the C2 cavity in Figure 7(i), and the C2 cavity in Figure 7(d). We have made sure that these three situations i) correspond to the same exposure time and incident power, ii) do not correspond to any saturation of the matter migration, a phenomenon that can for example be suspected in Figure 5(e) where depletion depth > 30 nm were measured. The observed slope of 2 in Figure 8 is the signature of a nanoscale 2-photon absorption and opens up the route towards nearfield intensity quantification based on photo-induced molecular displacement: the measurement of the displaced volume of matter would lead to the assessment of the corresponding near-field intensity. Let us stress that these results are very preliminary in the sense that measuring a nano-volume in a precise way with an atomic force is still a challenge because it strongly depends on tip size and shape.

Finally, Figure 9 summarizes results obtained when considering (E1, C1, C2, E2) as a fourdigit nanosystem. Our motivation is to briefly discuss the possibility to address photonic bits for future data processing and storage. We noticed previously (Figures 5 and7) that the extremities E1 and E2 are also susceptible to support electromagnetic hot spots, although with weaker intensities. As a consequence, migration of matter can also be observed at the extremities of the oligomer. E1, E2, C1, C2 hence constitute a 4-digit system. Figure 9 shows measured topographical depletion at the four digits in four cases corresponding to four incident angles: 0°, 30°, -30°, 15° corresponding to Figures 5(a), 7(a), 7(d), 7(i), respectively.

By applying a threshold, each value of depletion (vd) can be associated to a binary state: 0 or 1. Here we take vd ≥ 4nm  state 1; vd < 4 nm  state 0, resulting in the four binary numbers shown in Figure 9.

With more complex plasmonic structures, any N-digit combination could thus be envisaged, remotely controlled through the angle of incidence and the polarization state of light.

Regarding future application of these switchable hot spots for information processing: azobenzene-containing polymer has only been used for probing electromagnetic hot spots, in order to demonstrate possible different 4-bit digits. This polymer and associated molecular movement are obviously not envisaged for nanophotonic information systems because 2photon induced movement in PAP is pretty slow and irreversible, which is not suitable for the information process.

For practical use in this context, bare trimers could be used and activated with fast switching of incident polarization and angle using for example optoelectronic modulator whose speed can nowadays reach 40 GB/s. The level of the 0/1 optical state would be associated to the local intensity (instead of the local topographical depletion). The bridge between nanoscale hot spots and external modules could be ensured by integrated photonic guiding structure.

Two examples of coupling between optical nanosources and guiding micro and nano structures are described in references. [START_REF] Weeber | Colloidal Quantum Dot Integrated Light Sources for Plasmon Mediated Photonic Waveguide Excitation[END_REF][START_REF] Luo | On-Chip Hybrid Photonic-Plasmonic Light Concentrator for Nanofocusing in an Integrated Silicon Photonics Platform[END_REF] Let us conclude by stressing the most important observations and achievements: i) Hybrid modes in infrared 3-particle linear plasmonic oligomers were imaged with a spatial resolution of about /35 (20 nm resolution, see "Method" section)

ii) A nanoscale and controlled spatial switch of the localized hot spots was

vi)

We also paid attention to the local field enhancement at the extremities of the trimer and discussed the plasmonic oligomer as a 4-bit nanophotonic information system.

These results provide a clear route towards near-field investigation of plasmonic antenna in the near-infrared.

METHODS

Numerical Calculation

The modeling of the scattering problem was performed using a diffracted field formulation of the Finite Element Method (FEM). The main difficulty relies here on the choice of the unknown field that has to satisfy a proper outgoing wave condition. A relevant approach is then to consider a planar reference structure composed of the planar embedding layer, superstrate and substrate only (the trimer is removed). The unknown field of our problem is then the difference between the total (reference and diffracted) field solutions of the diffraction problems when considering first the entire structure described in Figure 3 and, second, the reference planar structure. In that way, the problem is reduced to the calculation of the field radiated by the set of rods of the structure put in the reference field. Standard Cartesian PMLs adapted to the substrate, superstrate, and embedding layer were used to bound the computational domain and absorb the field radiated from the rods. The problem is solved using second order edge elements with a mesh size of 3 nm in and between the rods. Further details can be found in refenrence [START_REF] Demésy | All-purpose finite element formulation for arbitrarily shaped crossed-gratings embedded in a multilayered stack[END_REF] . The model was implemented using the GNU softwares Gmsh and GetDP. [START_REF] Geuzaine | Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities[END_REF][START_REF] Dular | A general environment for the treatment of discrete problems and its application to the finite element method[END_REF]

Photopolymer

The azo dye molecule-containing polymer consists of pseudostilbene azobenzene molecules, disperse red 1(DR1), grafted to a side chain to polymethylmethacrylate (PMMA) in a 30% molar ratio (PMMA-DR1). PMMA-DR1 is dissolved in 1,1,2-trichloroethane concentrated at 20 g/L, after stirring using magnetic stirrer for 5 min and filtering at room temperature, PMMA-DR1 solution is spin-coated on to the trimers with angular acceleration of 4000rmp/s 2 and angular speed of 3000 rmp/s for 30 s. Agilent 5100 AFM measurements (tapping mode) showed that the polymer film is 45 nm thick on the substrate and about 10 nm thick above the top surface of nanoparticles. The same AFM is used for analysis of the photo-induced topography

Exposure

The 900 nm light issued from a Ti: Sa laser is linearly polarized, and focused by 10X nearinfrared objective lens with 18 mm working distance and 0.3 N.A. A landmark fabricated on the sample by Electron Beam Lithography was used to calibrate the position of laser spot and focus relative to the trimers. The entrance objective pupil is partially covered, resulting in a 100 m wide plane wave at the sample surface. In the case of normal incidence, the sample is placed on the sample stage of microscope, Irradiation of the sample is performed with a Z propagating plane wave (cf. figure 3 in manuscript). The power density is measured between the objective lens and the sample. In the case of oblique incidence, a sample stage is used rotate the XZ plane around the Z axis.

It should be pointed out that no modification of the shape of the gold trimers (due to thermal effects) has been observed, which is not surprising. In ref. [START_REF] Bouhelier | Surface Plasmon Characteristics of Tunable Photoluminescence in Single Gold Nanorods[END_REF] , thermal damage was observed from an average intensity of 350 W (=780 nm, spot diameter = 1 micron), corresponding to about 35 kW/cm 2 , which is much bigger than the power density used for our study (typically 300 mW/cm 2 ).

Spatial resolution assessment

Spatial resolution of our approach has been assessed. It is never easy to quantify a spatial resolution in scanning probe microscopy. In our case, this resolution depends on the tip shape and size, the hot spot size, and the response of the azobenzene molecules under local illumination. Let us consider Fig. 7. In Fig. 7 (c) and Fig. 7(f), theoretical hot spot lateral size at extremities E1 and E2 is about 20 nm. Corresponding topographical depletion has a width in the 50-100 nm range, suggesting an effective spatial resolution in the 15-40 nm range. As another example, in Fig. 5(f), the Ey modulus map shows fours central hot spots having a 12 nm spatial expansion. The corresponding depletion is about 20 nm, suggesting a resolution better than 10 nm. As a result, we consider that the spatial resolution is about 20 nm, which can be viewed as a mean value. It should be pointed out that 20 nm corresponds to the typical size of the extremity of the used silicon AFM tip (Nanosensors, PPP-NCLR-50, force constant: 21-98 N/m, resonance frequency: 146-236 kHz)

Figure 1 .

 1 Figure 1. Plasmonic trimer and molecular probe. (a) SEM image of the studied trimer. White scale bar represents 100 nm. (b) Atomic Force Microscope (AFM) image of a gold trimer covered with a 45 nm-thick layer of azobenzene-containing photosensitive copolymer. Apparent height is about 15 nm. White scale bar represents 100 nm. AFM profiles will be shown in the following. (c) Azobenzene molecule used as a nanomotor for near-field probing (see text for details). Left: absorption spectrum and representation of the active molecule. Right: principle of the molecular motion based on 2-photon

Figure 1 (

 1 Figure 1(b) shows an AFM image of a trimer antenna covered by a 45 nm-thick layer of

Figure 2 .

 2 Figure 2. Two-photon absorption of PMMA-DR1. (a) IR absorption spectrum of a 100 nm thick layer of PMMA-DR1 obtained by using a tunable Ti:Sa laser. (b) Induced topography (AFM image) in the case of a focused beam at a 900 nm wavelength. (c) Two-photon scanning optical lithography on PMMA-DR1. (d) Depth of holes as a function of the wavelength. (e) Hole volume as a function of the incident power density (log-log plot).

  (a) shows the absorption spectrum of the monolayer. A strong absorption peak is observed around 900 nm, indicating two-photon absorption in the copolymer film. Figures 2(b) and 2(c) demonstrate that this absorption can result in matter displacement, leading to a clear depletion in the film. In Figure 2(b), we use a laser beam (0=900 nm) focused with an objective lens (N.A=0.3) to print an Airy pattern whose central peak results in a deep depletion. Based on the use of this central depletion, a proper exposure time and intensity can enable scanning lithography of PMMA-DR1, as illustrated in Figure 2(c). Many published works have discussed the origin of this depletion.

  photon nature of the absorption was confirmed by studying the depletion volume of the holes

Figure 1 (

 1 Figure 1 (b). AFM cross-sections taken before and after exposure will be shown for comparison.

Figure 3 .Figure 4

 34 Figure 3. Experimental configuration used for near-field imaging of gold trimers. 900 nm wavelength was used (see text for details).

Figure 4 .

 4 Figure 4. Result of the exposure for TE polarization at normal incidence (=0° except for calculated Figure 4(d) for which =30°. Exposure wavelength is 900 nm. (a) AFM image after exposure. (b) Distribution of absolute value of each field component calculated with Finite Element Method (FEM). (c) Y cross sections above one particle, taken before and after exposure. In all the cross sections throughout the article, height scale was set so that 0

Figure 4 (

 4 Figure 4(b) shows the calculated absolute value of each field component for a realistic

Figure 5 .

 5 Figure 5. Result of the exposure for TM polarization at normal incidence (=0° except for calculated Figure 5(g) for which =30°. Exposure wavelength is 900 nm. (a) AFM image after exposure. b,c) X Cross sections above the trimer, taken along the axes (A) and (B) respectively. (A) and (B) are shown in Figure 5(a). (d) AFM image taken after weaker intensity exposure. (e) AFM image taken after higher intensity exposure. (f) Calculated absolute value of each component. (g) Calculated absolute value of Ex field for =30° showing the influence of the incident angle.

Figure 5 (

 5 a) is a near-field map of the radiant B-B mode described in Figure1(d).

Figure 5 (

 5 f) shows the calculated absolute value of each field component. Again, it shows pretty weak XY and very weak XZ depolarization. In the case of a TM excitation, the plasmon field is localized within the gaps and mainly X polarized: photo-activated matter principally moved parallel to the involved near-field leading to a topographical depletion at high intensity zones. This depletion is shown in Figure5(b): matter migrated from cavities C1 and C2 and was partly accumulated at the top of particles, at the edges of the trimer, as shown in Figure5(c). In other words, Figure5(a) is, at the first approximation, a snapshot of the Xpolarized near-field coupling in the plasmonic trimer. However, it turns out that Figure5(a)hides some features that are the signature of weak Y-polarized near-fields. Weaker exposure (300 mW/cm 2 for 30 s.) led to the optically induced topography shown in Figure5(d). This topography presents features that are the signature of Y-polarized field map (see second calculated image of Figure5(f)). On the other hand, for higher exposure dose (600 mW/cm 2 for 60 s.) Ex dominates (see Figure5(e)) and even local field enhancement at the trimer extremities (E1, E2) are visible. We explain this behavior by assuming that molecular motion along Y is easier due to free space requirement: 58 at low intensity, probability of molecular absorption is very weak for both Ex and Ey fields. As there is free space along the Y direction (no Au particles are expected to block this motion), only Ey leads to molecular motion, resulting in Figure5(d). At higher dose, the influence of Ex becomes visible and the final topography looks like Ex distribution, masking the contribution of Ey. Again, let us stress that, in principle, PEEM would have been poorly sensitive to the involved Ex, Ey fields. Figure5(g)is the calculated absolute value of the Ex field at oblique incidence (=30°). Unlike for the TE case, it shows a clear modification of the field distribution: energy is concentrated at gap C1, to the detriment of C2, illustrating the possibility of mode balancing in the plasmonic oligomer.

Figure 6 .

 6 Figure 6. Calculated near-field intensity I1 and I2 at gaps C1 and C2 respectively, for different angles of incidence, in the case TM polarization.

  ) and 7(b) reveals that the nanogap C1 was turned on (23 nm topographical depletion) while activation of nanogap C2 is very weak (3 nm depletion).

  ) and 7(b) at the trimer left extremity E1, opposite to the incident direction, which is confirmed by the calculated modulus of the Ex field component in Figure 7(c). Let us now induce the switch of the hot spot location by illuminating the sample with an opposite incidence at =-30°. Both molecular motion and calculations displayed in Figures 7(d),

Figure 7 .

 7 Figure 7. Result of the exposure for TM polarization at oblique incidence. Exposure wavelength is 900 nm. (a),(b),(c) Case of =30°. (a) AFM image. (b) X Cross sections above the trimer. (c) Calculated map of the absolute value of the Ex field component. (d),(e),(f) Case of =-15°. (d) AFM image. (e) X Cross sections above the trimer. (f) Calculated map of the absolute value of the field X component. (g), (h) zoom out AFM image for the =30° case: (g) AFM image before exposure. (h) AFM image

  the obtained near-field data are analyzed in a more quantitative way. The volume of the nanometric topographical depletion measured at three different locations was plotted, using a ln-ln scale, as a function of corresponding calculated integrated intensity of the x,y component of the electric field.

Figure 8

 8 Figure 8 Analysis of the data. Measured Volume of nano topographical depletion in four cases as a function of calculated integrated intensity of the in-plane (x,y) component of the electric field (ln-ln plot).

Figure 9 .

 9 Figure 9. Near-field data summarized as 4-digit information: topographical depletion at different locations and corresponding binary 4-digit numbers.

  Fig. 5(a) Fig. 7(a) Fig. 7(d) Fig. 7(i) 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 E2 C2 C1 E1

ACKNOWLEDGMENTS

The authors thank the Agence Nationale de la Recherche (ANR), under Grants TWINS, NATO, HAPPLE and ACTIVE-NANOPHOT. R. B. thanks Ludovic Douillard for fruitful discussion about PEEM technique. Plasmonic samples were fabricated in the Nano'mat Platform (www.nanomat.eu). This work has been carried out in the context of the Labex ACTION project


L Maillé

M A Dourges

S Le Ber

P Weisbecker

F Teyssandier

Y Le Petitcorps

R Pailler

STUDY OF THE NITRIDATION PROCESS OF TiSi 2 POWDER

Keywords: CMC, milling, powder, XRD

This paper reports on the nitriding process of TiSi 2 micro/submicrometer-sized powders. TiSi 2 powders were treated under nitrogen flow, at 1100°C, during various durations. The composition and morphology of the nitride powders are characterized by X-ray diffraction and observed on cross-section, prepared using ion polishing system by scanning electron microscopy whereas the chemical composition is analyzed by energy dispersive X-ray spectroscopy. All these analyses revealed that under nitrogen flow, TiSi 2 grains are first transformed into a core-shell structure composed of TiN, surrounding by Si. Long nitriding treatments result in the complete transformation of Si 3 N 4 . These results are discussed in terms of various diffusion limitation phenomena.

INTRODUCTION

Ceramic Matrix Composites are developed for aeronautic and spatial applications [1]. Due to their refractoriness and their low density they are used in the hot parts of engines. These composites are usually elaborated by infiltrating a weaved preform by chemical vapor infiltration to form a ceramic matrix. Other processes can also be used to form the matrix. In particular ceramic processes in which a slurry impregnation including filler powder and liquid polymer impregnation can be used [2][3][4][5][6][7]. The active fillers are aimed at reducing the volume shrinkage resulting from the pyrolytic conversion of polymer to ceramic [8][9]. Titanium disilicide (d=4.01g/cc) is identified as interesting active filler: under nitrogen atmosphere, the nitridation of TiSi 2 starts in a temperature range around 1000°C to form TiN (d=5.43g/cc) and Si 3 N 4 (d=3.19g/cc) [10]. This reaction generates a 57% volume increase. In this paper, we explore the influence of temperature and duration on the nitriding rate of a micro and submicrometer-sized TiSi 2 powder.

MATERIALS AND EXPERIMENTAL PROCEDURES

A high purity micrometer-sized TiSi 2 powder (C-54 stable phase, 99.95% in purity, ~45µm, Neyco) is used. The raw powder is milled with a vibratory mixer mill (Retsch MM200) and with planetary ball mill (Retsch PM200). Nitriding process is carried out in a thermogravimetric analyser (Setaram TAG24) or in a furnace using alumina crucibles. This powder is heated under a flow of nitrogen gas (50mL/min) from 20°C to 1100°C at a heating rate of 10°C/min, during various durations (45min, 5h, 50h). The crystallographic structure is studied by XRD in Bragg-Brentano geometry, with a Bruker D8 Advance diffractometer, using a copper anode (CuK  ) and a one-dimensional position sensitive silicon strip detector (Bruker, Linxeye). XRD patterns are recorded using a step size of 0.01° for the 2θ range 10-90°, and a counting time of 0.3s per step. Sections of nitrided TiSi 2 grains are prepared using ion polishing system (Cross Polisher JEOL Ltd). These sections are observed with a FEI Quanta 400 FEG scanning electron microscope whereas the chemical composition is analyzed by EDX (EDAX Genesis XM4), operated at 5kV (interaction volume of roughly 150nm wide in this condition). Specific surface areas are determined by the BET method with an ASAP 2010 (Micromeritics); the samples are degassed by heating at 220°C during 4h immediately prior to measurements.

RESULTS AND DISCUSSION

Nitriding process of micrometer-sized TiSi 2 powder

Powder is analyzed by XRD. Pattern is analyzed using the Rietveld [2] whole profile fitting method with the software Fullprof [3]. Results indicate that the powder is composed of 4.2(±0.7)%wt of free silicon (ICDD-PDF 04-001-7247) and 95.8%wt of TiSi 2 compound (ICDD-PDF 04-007-1144).A low specific surface area of 0.33m²/g was measured by the BET method. According to the Ti-Si-N phase diagram , the partial nitridation of TiSi 2 is resumed by the equation 1 and respectively the complete nitridation of TiSi 2 by the equation 2. 2 TiSi 2 (s) + N 2 (g) → 2 TiN (s) + 4 Si (s) (W/W0 = 13.5 %) Eq. (1) 6 TiSi 2 (s) + 11 N 2 (g) → 6 TiN (s) + 4 Si 3 N 4 (s) (W/W0 = 49.4 %)

Eq. ( 2) The nitriding of powders are performed in a thermogravimetric analyser at three temperatures; 1100°C, and 1300°C. The variations of mass gain versus time are presented on figure 1.

XRD patterns (figure 2) and mass gains revealed different behaviours in the different conditions. At 1100°C partial nitriding reaction occurs with a mass gain less than 13.5% and the presence of residual TiSi 2 is revealed by XRD analysis. The Eq. 1 formulates this partial reaction with formation of TiN and Si. Above 1200°C a higher mass gain is observed, due to a total nitriding reaction of TiSi 2 (Eq. 1) and partial nitriding reaction of silicon (Eq. 2) leading to the formation of both nitrides TiN and Si 3 N 4 . The amount of Si 3 N 4 phase is probably too low to be revealed by the XRD pattern. This reaction is more efficient at 1300°C, with a higher conversion rate, peaks of Si 3 N 4 are clearly observed by XRD analysis (figure 2). These results show a two-step nitridation of TiSi 2 , as it was previously reported in literature [11][12].

Sections of nitrided TiSi 2 grains at 1100°C during 5h, are observed by SEM (figures 3a, b). EDX measurements also confirm the presence of TiN and Si. TiN is located at the extreme surface of the TiSi 2 powder. A thin discontinuous layer of around 60 nm is formed; it is composed of nanograins, of approximately 15 nm wide. TiN is also located along the porosity surface inside the grain. Free metallic silicon seems to precipitate at the grain periphery, between the TiSi 2 (observed by SEM in the center) and the TiN compounds. Free silicon embeds TiSi 2 and it is respectively covered by the TiN layer. Nevertheless, for smaller particules (diameter < 3m), TiSi 2 is completely transformed according to the reaction 1 (figure 3b). Some thermodynamic studies in the Ti-Si-N ternary system indicate that TiSi 2 can be nitrided into TiN and Si 3 N 4 at 1100°C [4][5][6][7][8][9][10]. This assertion is not confirmed by our first experiments, even after 5h of nitridation at 1100°C. So, it has been decided to mill the as received powders, with the intention of getting close to a submicronic scale. We expected that the total nitriding reaction of milled powders can occur at lower temperatures in order to get Si 3 N 4 .

Milling study

The TiSi 2 commercially powders are milled with a vibratory ball mill or a planetary ball mill in order to get sub-micronic particles. Results are shown in Table 1.

Thermogravimetric analyses were then performed on these milled powders at 1100°C (figure 4). The milling improved significantly the nitridation rate, with a weight gain of 8.6% after 5h at 1100°C. Nitridation of planetary milled powder starts at a clearly lower temperature of 650°C, with a much steeper slope during the heating stage. Furthermore after planetary milling the weight gain of TiSi 2 nitriding reaction reached the value of 29.5% (5h at 1100°C). This indicated the formation of Si 3 N 4 . XRD analyses of the powders were performed on the powders treated within the thermogravimetric device (Figure 5). XRD patterns of all nitrided products indicate the presence of TiN and Si. The XRD pattern of the TiSi 2 powder nitrided after planetary milling also exhibits small peaks corresponding to the -Si 3 N 4 and β-Si 3 N 4 phases.

CONCLUSION

Our experiments confirm that the complete nitridation of TiSi 2 at 1100°C is discribed by two steps: the precipitations of free silicon and TiN followed by the nitridation of the free silicon. It was observed that decreasing the grain size allows to lower the nitriding temperature to form Si 3 N 4 . For instance in the case of raw powders, the formation of Si 3 N 4 starts above 1200°C while for planetary milled powder the reaction begins at 1100°C after five hours of treatment.

List of figure and table captions

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Thermogravimetric curves of TiSi 2 commecialy powder heated at various temperatures within N 2 atmosphere

Figure 4 .Figure 5 .

 45 Figure 4. Thermogravimetric curves of TiSi 2 milled and raw powders heated to 1100°C into N 2 atmosphere Figure 5. XRD patterns after TGA experiments at 1100°C in N 2 on raw and milled powders. (•)TiSi 2 ; (∆)Si; (■)TiN; (▲) and β-Si 3 N 4

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4 Figure 5

 45 Figure 4

Table 1 .

 1 Specific surface area and granulometry of raw powders and milled powders.

Table 1

 1

		commercial powders	vibratory ball milling powders	planetary ball milling powders
	Specific area S (m²/g)	0.3	2.0	41
	Mean size d 50	45 µm	2 µm	550 nm