O Mitrofanov
email: o.mitrofanov@ucl.ac.uk

W Yu

R J Thompson

Y Jiang

Z J Greenberg

J Palmer

I Brener

W Pan

C Berger

W A De Heer

Z Jiang

Terahertz near-field imaging of surface plasmon waves in graphene structures

Keywords: E. THz near-field microscopy, D. Surface plasmons, A. Epitaxial graphene

We introduce a near-field scanning probe terahertz (THz) microscopy technique for probing surface plasmon waves on graphene. Based on THz time-domain spectroscopy method, this near-field imaging approach is well suited for studying the excitation and evolution of THz plasmon waves on graphene as well as for mapping of graphene properties at THz frequencies on the sub-wavelength scale.

Introduction

Graphene plasmons, the collective oscillations of Dirac fermions enabling strong enhancement of lightmatter interaction, have recently attracted a great deal of attention (for a recent review, see Ref. [1]). It has been shown that surface plasmons can be confined in graphene nanostructures with a characteristic dimension more than 100 times smaller than the wavelength of incident light [2,3]. Graphene plasmons are highly tunable; the plasmon frequency depends on the carrier density and doping [4][5][6], the characteristic dimension (for graphene structures) [4,5,7], the number of stacked layers [5], the packing density of graphene structures [8], the substrate phonon modes [9,10], and the applied magnetic field [3,7,11]. Graphene plasmons can be excited and probed locally using a scattering-type scanning near-field optical microscope with a focused infrared beam [12,13]. Such a high-resolution near-field technique has created great excitement in the field. The spectral range of these studies (600-2500 cm -1 ) was however limited by the mid-infrared light source [14].

In the terahertz (THz) spectral range (10-100 cm -1 ) graphene also exhibits rich physics and great application potential [15][16][17]. THz spectroscopy and imaging techniques have been used to study the THz conductivity of graphene [18][19][20], enabling non-contact characterization of graphene and providing direct information about its doping level and uniformity. These far-field methods however provide only limited information about plasmon excitations, which are localized at the surface. In this Communication, we will introduce a near-field scanning probe THz microscopy technique for probing graphene plasmons at THz frequencies. Based on time-domain analysis, this technique is particularly suited for studies of excitation and propagation of surface waves [21].

Material and methods

Epitaxial graphene on silicon carbide

The epitaxial graphene studied in this work was grown on silicon carbide (SiC) substrate using a diffusion-limited confinement controlled sublimation method [22]. Generally speaking, there are two principally different types of epitaxial graphene forming on the Si-or C-terminated face of SiC, respectively. The growth on the Si-terminated face has a better layer control and the material consists of mono-and bi-layers of graphene but with a relatively high carrier concentration due to the charge transfer from SiC [23]. The graphene grown on the C-terminated face however are usually multilayers. Although the first few layers of graphene close to the interface with SiC are still highly doped (as that on the Siterminated face), the subsequent top layers are practically charge neutral and electrically decoupled from each other behaving like monolayer graphene [24,25]. The Fermi energy of such quasi-neutral top layers of graphene is typically E F < 20 meV [3,25], while E F > 200 meV for the highly doped layers close to the interface [23].

The epitaxial graphene samples were patterned into mesas and ribbon arrays via standard electronbeam lithography, followed by oxygen plasma etching and high vacuum annealing. The vacuum annealing process is crucial for removing the chemical residue left on graphene surface after lithography.

The annealing was conducted in high vacuum ( < 5×10 -5 mTorr ) at 600 ℃ for 2 hours. Cyclotron resonance measurements reveal that the vacuum annealed top graphene layers grown on the Cterminated face recover their low density and high mobility, E F ≈ 17 meV and μ > 50,000 cm 2 V -1 s -1 [3], similar to the values observed in as-grown samples.

THz near-field microscopy and its application on metallic surfaces

Graphene ribbon arrays allow excitation of confined plasmon modes by a plane wave incident at normal incidence [4,9], similar to periodic metallic structures (arrays of ribbons or corrugations). Even a continuous graphene mesa can in principle support surface plasmon waves. In the latter case, the surface wave can be excited at the mesa edges, similar to the excitation of surface waves at the edges of metallic patterns [START_REF] Mitrofanov | Selected Topics in Quantum Electronics[END_REF]27]. Unlike the metallic films however, graphene is highly transparent to the incident electromagnetic wave. The transmission coefficient for a graphene layer at THz frequencies can be reduced only to the level of 60-70%, even for the highest achievable carrier densities [18][19][20][21]. This presents a challenge for observation and investigations of surface plasmon waves in graphene structures: the incident THz wave is typically dominant in the region where the confined plasmon modes and surface plasmon waves are excited.

Studies of surface plasmons in graphene therefore require both local (near-field) probing at the surface and method for differentiating surface plasmon waves from the incident wave. In this work, we will address the questions of excitation and detection of THz surface plasmon waves on patterned graphene structures illuminated by a plane incident wave. In our analysis of THz surface waves, we take advantage of the temporal resolution provided by the THz time-domain spectroscopy technique. Combined with near-field scanning probe THz microscopy [27], this method allows detecting temporal evolution of the electric field distribution over the surface, in which surface wave signatures become apparent.

The near-field probe employed in this study is an integrated sub-wavelength aperture probe. It detects THz waves through a 10 μm input aperture [28]. For excitation, we use short THz pulses (~2 ps) with the spectrum covering the frequency range from 0.5 to 2.5 THz. Before discussing THz surface plasmon waves on graphene, we briefly examine THz surface plasmon signatures on metallic surfaces.

Consider a metallic pattern, for example a bow-tie antenna, on a dielectric substrate illuminated by a plane wave at normal incidence from the substrate side. Such an experimental configuration is illustrated in Fig. 1(a). We use a large diameter THz waveguide with a well-defined beam profile for illumination of the antenna. The waveguide also ensures that the incident wave is described by a narrow distribution of wave-vectors ( k x < 0.1 k z ) centered around k x = 0.

The incident THz wave induces charges at the edges of the bow-tie antenna. The electric field distribution near the antenna as a result has regions of field concentration near the edges, where the field component perpendicular to the surface, E z is created in addition to the E x -component of the incident field (Fig. 1(b)). The E z -component starts propagating away from the edge as a surface wave [27,29].

To understand how the incident THz wave with k x = 0 couples into the surface wave, it is useful to consider the angular spectrum representation of the induced E z -component near the edge. This field is localized at the edge and thus it contains a broad distribution of wave-vectors k x (as illustrated in the upper panel of Fig. 1(b)). For any frequency of the incident wave ω 0 , there is a component in the angular spectrum of E z that matches the transverse component k x required for launching a surface wave (lower panel of Fig. 1(b)). Therefore, the illumination of a metallic pattern by a plane wave at normal incidence causes excitation of surface waves at the pattern edges.

The process of excitation and propagation of THz surface waves at the edges of a metallic bow-tie antenna was studied in details by Mueckstein et al. [27]. Figure 1(c) shows an example of spatial distribution of the electric field on the antenna surface. The antenna surface becomes a resonator for the surface waves that move from one side of the antenna to the other. It is important to note that this THz image shows the electric field distribution on an opaque metallic surface illuminated from the substrate side. Therefore, only the surface waves contribute to the detected field over the antenna area [29].

The surface wave nature of the detected field is verified in its evolution displayed as a space-time map in Fig. 1(d). It shows that the field over the antenna area originates from the edges (marked by the dashed lines). The incident plane wave and the surface waves exhibit distinctive patterns in the spacetime map. The phase of the incident plane wave is constant for any position x, thus it is represented by horizontal 'fringes' in the map (outside the region between the dashed lines). The phase of the surface wave on the other hand changes with x according to the phase velocity relationship and it forms tilted 'fringes' in the map (in the region between the dashed lines).

The space-time map also illustrates that the field pattern on the antenna surface changes over time. At the beginning of excitation, the field is present only near the edges of the antenna. As time elapses the surface waves spread over the entire area of the antenna and a standing wave pattern forms. After the incident pulse passes, the surface waves remain on the antenna surface for several picoseconds, decreasing in amplitude over time and eventually disappearing.

Results and discussion

3.1. THz near-field imaging of graphene bow-tie A bow-tie antenna made of monolayer epitaxial graphene grown on the Si-terminated face of SiC is studied using the same THz near-field microscopy technique (Fig. 1(a)). The multilayer graphene, simultaneously grown on the C-terminated face, is removed by oxygen plasma etching, and the monolayer graphene on the Si-terminated face is identified by Raman spectroscopy and confirmed by transport measurements on samples grown in the same condition. The right-hand side of the bow-tie structure is shown in the optical image in Fig. 2(a). The bow-tie geometry and dimensions are chosen to be the same as for the metallic bow-tie in Fig. 1(c). As in the experimental schematic shown in Fig. 1(a), the bow-tie is illuminated by the THz pulse (Fig. 2(b)) incident from the substrate side. Two THz images acquired at two moments, t 1 and t 2 , are shown in Figs. 2(c) and 2(d). In Fig. 2(c), the antenna pattern makes only small impact on the uniform distribution of the electric field. Attenuation of the THz wave by graphene is barely noticeable. The image however shows variation of the field amplitude over the antenna area, similarly to the surface wave interference pattern in Fig. 1(c). This pattern becomes more pronounced in Fig. 2(d) at t 2 = t 1 + T, where T is approximately the period of the THz wave, indicating that more energy is converted from the incident plane wave into the surface wave.

The surface wave pattern observed on the graphene bow-tie remarkably replicates the pattern formed on the metallic bow-tie, despite the fact that the metallic layer is opaque for the incident THz wave, whereas the graphene layer is transparent. We note that in the case of graphene, the pattern is superimposed over the incident wave field, which is practically uniform in the xy-plane, while in the metallic bow-tie case, the pattern is formed in the 'shadow' area of the antenna, where the incident wave field is zero.

THz near-field imaging of graphene ribbons

The similarity between the patterns observed on the metallic and graphene bow-ties indicates that the corresponding surface waves are weakly confined as in the case of metallic surfaces [28]. Ribbon arrays on the other hand are predicted to support strongly confined plasmon modes, with the wave-vector several times larger than the free-space wave-vector. To investigate confined plasmon modes we now consider samples with periodic structures on the sub-wavelength scale.

Figure 3 shows a sample, which contains arrays of graphene ribbons oriented parallel and perpendicular to the electric field vector of the incident wave and two areas of continuous graphene, arranged as four quadrants. In this experiment, we use multilayer epitaxial graphene grown on the Cterminated face of SiC. Ellipsometry measurements show that the sample consists of 10 graphene layers. The ribbons in both arrays are W = 4 μm in width and the spacing between the adjacent ribbons is 4 μm. The frequency of the confined plasmon mode in ribbons is given by [3]

ℏω pl = e 2 E F 2ϵ 0 ϵW , ( 1
)
where ℏ is the reduced Planck's constant, e is the electron charge, ϵ 0 is the vacuum permittivity, and ϵ = (ϵ SiC +1)/2 ≈ 5 is the relative permittivity of epitaxial graphene. Taking E F = 215 meV [23] for the highly doped graphene layers near the interface with SiC, we expect ω pl ≈ 2.4 THz, while ω pl ≈ 0.67 THz for the quasi-neutral top layers where E F = 17 meV [3]. These frequencies fall in the spectral range of our measurement (0.5-2.5 THz).

In our experiment, we find that the detected THz field is noticeably reduced in the areas of all four quadrants. The continuous mesas show lower transmission compared with the arrays, consistent with the reduced graphene area in the array. It is unlikely that the confined plasmons are excited in these arrays as their response to the incident THz pulse does not show a significant difference for both orientations of the ribbons. Arrays of 200nm-wide graphene ribbons also exhibit no effect of the ribbon orientation in our previous work [21]. A possible explanation for not being able to observe the confined plasmon mode in Fig. 3 is the charge inhomogeneity of the sample, particularly in the highly doped graphene layers close to the interface with SiC. While the near-field probe with a 10 μm aperture does not resolve individual ribbons in Fig. 3, it shows that the transmission coefficient varies considerably within each 100 μm × 100 μm quadrant. A similar variation of the local transmission properties has also been observed in other multilayer epitaxial graphene samples on SiC [21]. One can attribute this variation to the non-uniform electron density in graphene, caused potentially by the substrate. The electron density affects the dispersion relationship of surface plasmons and thus the non-uniformity is likely to scatter surface plasmon waves.

Arrays of 1μm -wide graphene ribbons however exhibit a noticeable change in the transmission properties for the two orientations, parallel and perpendicular to the electric field vector. The ribbon arrays were fabricated from multilayer (10-layer) epitaxial graphene grown on the C-terminated face of SiC. The ribbons are 200 μm in length and 1 μm in width, and the spacing between the adjacent ribbons is 1.2 μm. Figure 4 illustrates the orientation dependence by comparing THz space-time maps for three patterns fabricated on the same substrate. The left and right columns display experimental results for the ribbon arrays oriented parallel (left) and perpendicular (right) to the electric field, while the middle column shows the map of continuous graphene ( 200 μm × 200 μm square). Although the detected field, E(x,t) , is dominated by the incident plane wave (middle row of Fig. 4), there are noticeable changes in the field amplitude in the ribbon regions. To display the changes, we subtract the incident wave from the space-time maps in the bottom row of Fig. 4. For the ribbons parallel to the field, the incident field is scaled by a factor of 0.73 and removed from the detected field, E(x,t) -0.73E inc (t). The subtraction illustrates that the transmission through the horizontal ribbons is reduced by ~27% compared to the bare SiC substrate. For the ribbons oriented perpendicular to the field, E(x,t) -E inc (t) is plotted. In this case, we find surprisingly that more transmission occurs through the ribbon area (shown as fringe patterns) after subtracting the waveform of the incident THz pulse through the substrate. Quantitative analysis shows that the transmission is increased by ~50% compared to the bare SiC substrate.

In addition, we notice that the subtracted maps in the left and right columns of Fig. 4 show no surface wave patterns in the ribbon array region. Similar background subtraction conducted for the space-time map measured over the graphene mesa (middle column) however reveals the signature of surface waves: the phase of the wave present in the mesa area changes with x, indicating that the surface waves are originated from the edges. The lack of surface waves in graphene ribbon arrays can be caused by several factors: the excitation of surface wave at the end of the ribbon is likely to be less efficient compared to the large-area mesa; the (rough) ribbon edges can also provide additional absorption or scattering for a wave propagating along the ribbon.

The increase in transmission coefficient for the area with ribbons oriented perpendicular to the electric field compared to the bare SiC substrate requires a more detailed consideration. One possible interpretation is that it is due to the impedance matching provided by the graphene ribbon array. The THz wave incident on the SiC-air interface experiences significant partial reflection because of the large refractive index contrast (n SiC ≈ 3.0). The reflection coefficient can be reduced if graphene acts as an impedance matching layer. For example, it was reported recently that a continuous graphene layer can exhibit complete elimination of reflection from the quartz-air and silicon-air interfaces [30]. In the case of the ribbon array, the impedance matching can occur if the reflected waves from the SiC-air (between adjacent ribbons) and SiC-graphene-air interface have opposite polarities, producing a destructive interference and therefore minimizing the reflected wave amplitude. This effect should not be frequency selective, but dependent on the filling ratio of the array and the Fermi energy. The latter affects the conductivity of graphene. The impedance matching explanation is consistent with the lack of the surface waves originating from the ribbon array edges. Further finite-element simulations are needed to explain why the orientation dependent effect is absent in the 4μm-wide and 200nm-wide ribbon arrays with a similar graphene filling ratio (~50%).

An alternative interpretation for the enhanced transmission through the ribbons oriented perpendicular to the electric field is the excitation of the confined surface plasmons in the ribbon array. In this case, oscillating and possibly enhanced field is expected near the surface. Our experiment however shows no phase shift in the detected field and no induced oscillations following the incident pulse. The response of the ribbons is expected to be dominated by the highly doped layers of graphene close to the interface with SiC and ω pl ≈ 4.8 THz from Eq. (1), beyond the spectral range of our technique (0.5-2.5 THz). It is worth mentioning that ω pl ≈ 1.3 THz for the high-mobility quasi-neutral top layers of graphene in our samples, and it is centered in our spectral range. Further experimental work is needed to understand the effect of the confined plasmons in the quasi-neutral graphene top layers.

Conclusions

We have performed THz near-field microscopy study of epitaxial graphene structures (bow-ties, mesas, and ribbons) and observed surface plasmon waves excited at the edges of graphene structures (similar to metallic edges). Near-field images show that the THz absorption of graphene varies on a scale smaller than the wavelength and the Fresnel reflection at the SiC substrate surface is modified by the presence of graphene ribbons, leading to either reduced or enhanced transmission of THz waves depending on the orientation of the ribbons with respect to the electric filed and the ribbon width. The observations illustrate intriguing properties of graphene, which hold promise for new applications in THz spectroscopy, sensing, imaging, and communications. They also illustrate complexity of graphene plasmonic responses.

Fig. 1 .

 1 Fig. 1. Near-field microscopy system for probing THz surface plasmon waves. (a) Schematic diagram displaying a hollow THz waveguide, a sample with a metallic pattern placed at the waveguide center, and the integrated THz near-field probe. (b) Mechanism of surface wave excitation at the edges of a metallic pattern. The upper panel shows the spatial distribution and its angular spectrum for the E z -component induced at the edge. The lower panel shows the dispersion relation for the surface wave (blue line) in a similar k x range as for the angular spectrum E z (k x ) in the upper panel. The horizontal dashed line indicates the plane wave dispersion for reference. (c) THz electric field distribution on a metallic bow-tie antenna deposited on a GaAs substrate. The snapshot corresponds to t = 1.16 ps. (d) A space-time map of the electric field near the antenna surface during the excitation of the antenna by a THz pulse. Dashed lines mark the location of the bow-tie edges.

Fig. 2 .

 2 Fig. 2. Graphene bow-tie antenna patterned on SiC substrate. (a) Optical image of the right-hand side of the bow-tie. (b) Waveform of the incident THz pulse, E inc (t). (c,d) THz near-field images of the bow-tie area in (a) captured at t 1 = 0.67 ps (c) and t 2 = 1.13 ps (d). The color scales are normalized to the field values E inc (t 1 ) and E inc (t 2 ), respectively.

Fig. 3 .

 3 Fig. 3. THz near-field image of multilayer graphene (10-layer) mesas and ribbon arrays: (a) optical image and (b) THz transmission image of the same sample area. The size of the mesas is 100 μm × 100 μm; the ribbons are 100 μm in length and 4 μm in width, and the spacing between the adjacent ribbons is 4 μm.

Fig. 4 .

 4 Fig. 4. Near-field THz space-time maps measured for a 200 μm × 200 μm graphene mesa (middle) and arrays of 1μmwide graphene ribbons oriented parallel (left) and perpendicular (right) to the electric field polarization. The space-time maps were obtained within several microns from the sample surface. The top row shows the optical images of the samples; the middle row shows the detected THz field E(x,t); and the bottom row shows E(x,t)-α × E inc (t), to emphasize the difference in electric field between the graphene pattern and the bare substrate. Here, α = 0.73 for horizontal ribbons (left), α = 0.8 for graphene mesa (middle), α = 1 for vertical ribbons (right), and E inc (t) is a waveform of the reference THz pulse taken on bare SiC substrate without graphene.

Acknowledgments

This work was supported by the Royal Society [Grant No. UF080745] and performed at UCL and at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by SNL [Contract No. DE-AC04-94AL85000]. Epitaxial graphene growth and device fabrication are carried out at GaTech, supported by the NSF [DMR-0820382] and the DOE Office of Basic Energy Sciences through a contract with SNL. The work at SNL was supported by a Laboratory Directed Research and Development project. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.


Ryan J Suess
email: ryan.suess@gmail.com

Stephan Winnerl

Harald Schneider

Manfred Helm

Claire Berger

Walter A De Heer

Thomas E Murphy

Martin Mittendorff

Role of Transient Reflection in Graphene Nonlinear Infrared Optics

Understanding the optical response of graphene at terahertz frequencies is of critical importance for designing graphene-based devices that operate in this frequency range. Here we present a terahertz pump-probe measurement that simultaneously measures both the transmitted and reflected probe radiation from multilayer epitaxial graphene, allowing for an unambiguous determination of the pump-induced absorption change in the graphene layers. The photon energy in the experiment (30 meV) is on the order of the doping level in the graphene which enables the exploration of the transition from interband to intraband processes, depending on the amount of pump-induced heating. Our findings establish the presence of a large, photoinduced reflection that contributes to the change in sign of the relative transmitted terahertz radiation, which can be purely positive or predominantly negative depending on the pump fluence, while the change in absorption is found negative at all fluences. We develop a straightforward theory that confirms the sign reversible nature of the relative transmitted terahertz radiation through the graphene multilayer and determine that this behavior originates from either an absorption-bleached or reflection-dominated regime.

The theoretical results are incorporated into a model utilizing an energy balance equation that reproduces the measured pump-probe data. These findings, which extend to mid-and far infrared frequencies, illuminate the importance of considering reflection in graphene-light interactions and have implications for the design of future terahertz photonic components.

POPULAR SUMMARY

Despite being technologically underdeveloped compared to optical and radio frequency domains, there remains substantial interest in utilizing terahertz frequencies for applications ranging from astronomy and security to communications systems. Though there has been progress through the development of terahertz emitters and detectors, this range still lacks materials that allow for fabrication of efficient optoelectronic devices that can sense, control, and modify terahertz radiation. Owing to its unique electrical properties and a strong interaction with light, graphene exhibits great potential for the future development of such devices. A thorough understanding of the underlying light-matter interaction in this material is therefore of critical importance for building the next generation of devices that operate at terahertz frequencies. In this work we present a comprehensive experimental study complemented by theoretical work that explores the interaction of high intensity terahertz light with graphene.

The optical properties of graphene are investigated with photons having energies comparable to the chemical potential using terahertz pump-probe spectroscopy. Probing the graphene at intermediate photon energies enables the investigation of the nonlinear optical properties in the graphene as its electron system is heated by the intense pump pulse.

By simultaneously measuring the reflected and transmitted terahertz light, a precise determination of the pump-induced change in absorption can be made. We observe that as the intensity of the terahertz radiation is increased, the optical properties of the graphene change from interband, semiconductor-like absorption, to a more metallic behavior with increased intraband processes. This transition reveals itself in our measurements as an increase in the terahertz transmission through the graphene at low fluence, followed by a decrease in transmission and the onset of a large, photoinduced reflection as fluence is increased. Our study further demonstrates the important role that reflection plays in the mid-and far-infrared range -noting that the absorption saturation intensity can be underestimated if only the transmitted light is considered. These findings will contribute to the development of new optoelectronic devices designed to operate in the mid-and far-infrared frequency range.

I. INTRODUCTION

Graphene has attracted tremendous attention as a material suitable for a variety of applications due to its linear and gapless band structure and high carrier mobility. These properties make graphene particularly suitable for applications in the terahertz region, where there are notoriously few materials that interact strongly with electromagnetic radiation of this frequency [START_REF] Otsuji | Graphene-based devices in terahertz science and technology[END_REF][START_REF] Bonaccorso | Graphene photonics and optoelectronics[END_REF][START_REF] Tredicucci | Device concepts for graphene-based terahertz photonics[END_REF]. Significant attention has been given to developing graphene-based terahertz photonic components including devices such as saturable absorbers which are often employed as materials for passive mode-locking [START_REF] Sun | Graphene mode-locked ultrafast laser[END_REF][START_REF] Bao | Atomiclayer graphene as a saturable absorber for ultrafast pulsed lasers[END_REF], terahertz filters [START_REF] Jadidi | Tunable terahertz hybrid metal-graphene plasmons[END_REF][START_REF] Ju | Graphene plasmonics for tunable terahertz metamaterials[END_REF], and broadband detectors [START_REF] Mittendorff | Universal ultrafast detector for short optical pulses based on graphene[END_REF][START_REF] Bianco | Terahertz detection by epitaxial-graphene field-effecttransistors on silicon carbide[END_REF]. A detailed understanding of the terahertz-graphene interaction is required to take full advantage of the material, and there have accordingly been many recent studies investigating the heating and cooling characteristics of graphene in the terahertz region [START_REF] Dawlaty | Measurement of ultrafast carrier dynamics in epitaxial graphene[END_REF][START_REF] George | Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene[END_REF][START_REF] Choi | Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene[END_REF][START_REF] Tielrooij | Photoexcitation cascade and multiple hotcarrier generation in graphene[END_REF][START_REF] Mics | Thermodynamic picture of ultrafast charge transport in graphene[END_REF][START_REF] Winnerl | Carrier Relaxation in Epitaxial Graphene Photoexcited Near the Dirac Point[END_REF], though many have been carried out using a transmission geometry exclusively. Taking into account the pump induced change in reflectivity can reveal new information; for example, the first clear experimental demonstration of carrier multiplication in graphene utilized both reflected and transmitted light [START_REF] Plötzing | Experimental verification of carrier multiplication in graphene[END_REF]. Studies involving terahertz time-domain transmission spectroscopy enable one to extract the complex dynamic conductivity [START_REF] Horng | Drude conductivity of dirac fermions in graphene[END_REF][START_REF] Frenzel | Semiconducting-to-Metallic Photoconductivity Crossover and Temperature-Dependent Drude Weight in Graphene[END_REF][START_REF] Hwang | Nonlinear THz Conductivity Dynamics in P-Type CVD-Grown Graphene[END_REF][START_REF] Jnawali | Observation of a Transient Decrease in Terahertz Conductivity of Single-Layer Graphene Induced by Ultrafast Optical Excitation[END_REF][START_REF] Hafez | Intense terahertz field effects on photoexcited carrier dynamics in gated graphene[END_REF] but often employ photon energies of a few meV, and are therefore limited to probing intraband absorption only. In this work, we explore a regime of intermediate photon energies, where interband processes also contribute to the optical properties. Here we present a far-infrared pump-probe study that measures both the transmitted and reflected light that enables a comprehensive accounting of the radiation. The data from this experiment reveals the presence of a prominent nonlinear reflection, that saturable absorption is present at all fluences, and a transmission that changes sign with fluence. By employing straightforward theory to determine the graphene optical properties, we show that it is possible, at sufficiently strong intensity, to switch from a primarily interband absorption dominated regime, to one exhibiting significant intraband processes. Together, the measurement and theory give a full picture of the interaction of intense terahertz radiation with low-doped multilayer graphene and provides insight for the design of photonic components that operate in this frequency range. This effect is general in nature and will persist at other wavelengths since it depends primarily on the chemical potential relative to the photon energy.

In this work we investigate multilayer epitaxial graphene (MEG) produced by thermal decomposition of the carbon terminated face of (0001)-oriented silicon carbide. This growth process yields individual layers that are rotated with respect to one another, thus producing multiple decoupled graphene layers [START_REF] Hass | Why multilayer graphene on 4h-SiC(0001) behaves like a single sheet of graphene[END_REF]. The graphene properties were verified using angular resolved photoemission spectroscopy to ensure linear dispersion [START_REF] Sprinkle | First direct observation of a nearly ideal graphene band structure[END_REF] while the thickness was measured using ellipsometry, which indicated that the sample consists of approximately 50 layers. Investigation using magneto-spectroscopic measurements reveal long momentum relaxation times that can be attributed to low defect densities (scattering time: τ s = 300 fs) [START_REF] Orlita | Approaching the dirac point in high-mobility multilayer epitaxial graphene[END_REF] and extremely low doping for the majority of the layers (in the range of 8-15 meV) [START_REF] Orlita | Approaching the dirac point in high-mobility multilayer epitaxial graphene[END_REF][START_REF] Winnerl | Time-resolved spectroscopy on epitaxial graphene in the infrared spectral range: relaxation dynamics and saturation behavior[END_REF].

It should be noted that the layers near the SiC-graphene interface can have larger doping levels (≈ 300 meV) due to interfacial charge redistribution from the SiC substrate. The doping levels decrease rapidly within the first few layers away from the substrate, leaving a mostly intrinsic graphene multilayer [START_REF] Winnerl | Time-resolved spectroscopy on epitaxial graphene in the infrared spectral range: relaxation dynamics and saturation behavior[END_REF][START_REF] Sun | Ultrafast relaxation of excited dirac fermions in epitaxial graphene using optical differential transmission spectroscopy[END_REF][START_REF] Sun | Spectroscopic measurement of interlayer screening in multilayer epitaxial graphene[END_REF].

To carry out a pump-probe study in which both reflected and transmitted light are collected, an off-axis parabolic mirror (OAP) is used (cf. Fig. 1). This approach allows spatial separation of the pump and probe pulses in both the transmitted and reflected directions and produces a focussed spot size of 500 µm. The beam path begins with high fluence pulses generated from a free-electron laser (FEL) [START_REF] Michel | First lasing of the elbe mid-ir fel[END_REF] being directed through a beam splitter which separates the beam in to pump and probe paths. The pulses from the FEL have a center wavelength of 42 µm (30 meV) or equivalently a center frequency of ≈7 THz, pulsewidth of 7.5 ps FWHM, and a repetition rate of 13 MHz. The pump and probe beam paths are independently attenuated and are linearly cross-polarized. The pump was chopped using a mechanical chopper and a pump-to-probe power ratio of around 25 was maintained for all measurements reported in the study. As shown in Fig. 1, the probe beam is delayed with respect to the pump pulse using a delay stage that allows for delays of up to 250 ps to be scanned.

Pump-probe measurements are carried out on a MEG sample for a variety of pump fluences spanning over two orders in magnitude (25 nJ•cm -2 to 8.6 µJ•cm -2 ) at a temperature of 10 K. The pump-induced modulation on the reflected and transmitted probe pulse is measured using lock-in detection; producing the values ∆T and ∆R respectively. The changes in transmission and reflection can be specified as a percentage by dividing ∆T and ∆R by the signal obtained by chopping the probe directly and measuring the transmitted and reflected signals when no pump is present. This gives, respectively, the relative change in transmission and reflection ∆T /T and ∆R/R. The pump-induced change in absorption is calculated from the transmission and reflection measurements using the relation ∆A = -(∆T + ∆R). Since an accurate measurement of the absorbed probe is difficult, ∆A cannot be easily normalized to a relative value, as was done for the transmitted and reflected signals, and is therefore given in arbitrary units. which is entirely negative, verifying that the MEG behaves as a saturable absorber over the entire range of pump fluences investigated. As a result of the strong pump-induced reflection, determination of the absorption saturation fluence using only the transmission data can lead to a significant underestimation of its actual value. In the present work, the absorption saturation fluence was estimated [START_REF] Garmire | Resonant optical nonlinearities in semiconductors[END_REF] from the positive portion of the transmission data to be 8 mW, seven times smaller than the value determined by including both transmitted and reflected light in the estimation (56 mW). An accurate accounting of the saturation fluence and the presence of a large, photoinduced reflection are important considerations for graphene-based saturable absorbers employed in laser mode-locking applications [START_REF] Tolstik | Graphene mode-locked cr:zns laser with 41 fs pulse duration[END_REF]. This also creates the possibility of using graphene as a broadband saturable absorbing mirror, a device that traditionally relies on semiconductor materials to achieve an enhanced reflectivity as pulse fluence is increased [START_REF] Keller | Semiconductor saturable absorber mirrors (sesam's) for femtosecond to nanosecond pulse generation in solid-state lasers[END_REF].

III. THEORY

To understand the transient changes in the optical properties, we first consider the temperature dependent conductivity of graphene. We assume that thermalized distribution is achieved in the material during the pump excitation which is well justified by noting that the carrier-carrier scattering processes through which the electron population is heated is much faster than the temporal resolution of our experiment. We can calculate the temperature dependent terahertz conductivity using [START_REF] Falkovsky | Optical far-infrared properties of a graphene monolayer and multilayer[END_REF]:

σ(ω, T ) = e 2 (hω) iπh +∞ -∞ dE |E| (hω) 2 ∂f (E, T ) ∂E - +∞ 0 dE f (-E, T ) -f (E, T ) (hω) 2 -4E 2 . (1)
In the above expression E is the energy, e is the electron charge, ω is the frequency of the illumination, h is the reduced Planck's constant, and

f (E, T ) = (exp [(E -µ(T ))/k B T ] + 1) -1
is the Fermi function, where µ(T ) is the temperature dependent chemical potential, k B is the Boltzmann constant, and T is the electron temperature. The first and second terms in Eqn. 1 describe the intraband and interband conductivity respectively. The intraband portion can be evaluated to give:

2ie 2 πh k B T h(ω+iτ -1 s ) ln 2 cosh(µ(T ) 2k B T
, where τ s is the electron scattering time, while the interband portion is evaluated numerically [START_REF] Falkovsky | Optical far-infrared properties of a graphene monolayer and multilayer[END_REF]. The number of charge carriers is conserved in our calculations (n = +∞ -∞ D(E)f (E)dE where D(E) is the graphene density of states), and defines an implicit relationship between the chemical potential and temperature [START_REF] Falkovsky | Optical far-infrared properties of a graphene monolayer and multilayer[END_REF][START_REF] Jensen | Competing ultrafast energy relaxation pathways in photoexcited graphene[END_REF]. In the following analysis, we attribute the optical response of the MEG to be entirely from the low-doped layers [START_REF] George | Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene[END_REF] which comprise the majority of our multilayer graphene sample.

The media surrounding the graphene impacts the optical properties expected from the combined superstrate-graphene-substrate interface [START_REF] Holovský | Effect of the thin-film limit on the measurable optical properties of graphene[END_REF]. The temperature dependent conductivity is calculated and then used to find the temperature dependent optical parameters (∆T /T , ∆R/R, and ∆A/A) for the well known case of a lossy film of thickness, d, separating two materials with permittivities a and b [START_REF] Born | Principles of Optics[END_REF]. In this calculation we use a thickness corresponding to 50 graphene layers and a super-/substrate permittivity of 1 (vacuum)/12.3 (SiC). Charge impurities in the substrate material as well as surface topography and defects can further influence the properties of the graphene through the formation of spatial charge puddle inhomogeneities which modify the transport properties in low-doped graphene [START_REF] Li | Disorder-induced temperature-dependent transport in graphene: Puddles, impurities, activation, and diffusion[END_REF][START_REF] Hwang | Carrier transport in two-dimensional graphene layers[END_REF][START_REF] Zhang | Origin of spatial charge inhomogeneity in graphene[END_REF][START_REF] Waldmann | Bottom-gated epitaxial graphene[END_REF]. In the present work, the far-infrared beam samples a large area of the multilayer graphene containing a spatially inhomogeneous distribution of chemical potential patches (length scale for potential patches have been reported to be of order 10 2 nm [START_REF] Martin | Observation of electron-hole puddles in graphene using a scanning single-electron transistor[END_REF]). The beam averages over these patches and effectively samples a broadened Fermi distribution edge.

The puddle potential distribution has been measured experimentally [START_REF] Zhang | Origin of spatial charge inhomogeneity in graphene[END_REF][START_REF] Martin | Observation of electron-hole puddles in graphene using a scanning single-electron transistor[END_REF] and considered theoretically using Gaussian statistics [START_REF] Li | Disorder-induced temperature-dependent transport in graphene: Puddles, impurities, activation, and diffusion[END_REF]. Optical parameters consistent with the experimental data are produced by convolving the Fermi distributions used in our calculations with a charge puddle distribution having a standard deviation (fluctuation strength) of approximately 20 meV [START_REF] Li | Disorder-induced temperature-dependent transport in graphene: Puddles, impurities, activation, and diffusion[END_REF].

Figure 3 shows the change in optical coefficients as a function of change in temperature at a lattice temperature of T = 10 K. The reflection and absorption curves are seen to be entirely monotonically increasing and decreasing functions of change in temperature respectively, while the relative change in transmission changes sign, becoming negative for temperature changes higher than 140 K. The absorption and reflection curves illustrate that this behavior emerges when the influence of the pump-induced reflectivity surpasses that of the interband absorption bleaching. This bleaching appears as a negative change in the absorption in Fig. 3 and is the result of Pauli-blocking. This effect is dominant over the pump-induced reflection for small changes in temperature and leads to a net positive ∆T /T .

It will appear at other frequencies in the infrared where the doping and photon energy are of similar scale and changes in temperature from the absorbed radiation will sufficiently broaden the Fermi distribution.

Having established the role of the pump-induced reflection in the optical transmission in graphene, we next demonstrate that the derived temperature dependent optical parameters will lead directly to pump-probe signals with identical characteristics to those measured experimentally. An energy balance equation is used to form a relationship between the incident power and the pump-induced change in temperature in the graphene. For the sake of clarity, a model consisting of only the essential heating and cooling terms, similar to those used by others studying monolayer graphene [START_REF] Graham | Photocurrent measurements of supercollision cooling in graphene[END_REF][START_REF] Betz | Supercollision cooling in undoped graphene[END_REF][START_REF] Mckitterick | Electron-phonon cooling in large monolayer graphene devices[END_REF], are used to describe the thermodynamics of the multilayer graphene in our pump-probe experiment. The resulting nonlinear differential equation contains terms for the electronic heat capacity, cooling, and a self-consistent absorption/heating term:

C el (T ) dT dt = A(T )ηP (t) -g 1 (T -T l ). ( 2
)
The terms in the energy balance equation are given as follows: C el denotes the electronic specific heat capacity, where C el (T ) = 18ζ(3)

πh 2 v 2 F
T 2 for our low-doped graphene [START_REF] Lui | Ultrafast photoluminescence from graphene[END_REF][START_REF] Shi | Controlling graphene ultrafast hot carrier response from metal-like to semiconductor-like by electrostatic gating[END_REF][START_REF] Mihnev | Electronic cooling via interlayer Coulomb coupling in multilayer epitaxial graphene[END_REF] where v F denotes the Fermi velocity and ζ is the Riemann zeta function. The term A(T ) is the temperature dependent absorption as determined from our previous analysis of a lossy film separating two dielectrics. A phenomenological heating efficiency term [START_REF] Jensen | Competing ultrafast energy relaxation pathways in photoexcited graphene[END_REF], η ≈ 0.03, was introduced into Eqn. 2 to achieve similar fluence scaling between the thermodynamic model and the data by scaling the incident power. The efficiency factor accounts for all of the unknown parameters in the energy balance equation with a single term. The incident laser pulse heating the graphene is described by a Gaussian envelope, P (t). The parameter

g 1 = T 4 7π 3 k 5 B D 2 30ρh 5 v 6 F
is the cooling power coefficient in the clean limit when the temperature is above the Bloch-Gruneisen temperature [START_REF] Mckitterick | Electron-phonon cooling in large monolayer graphene devices[END_REF] (T BG <10 K for the low-doped layers), D ≈ 2 eV is the deformation potential, v s = 2 × 10 4 m/s is the sound velocity in graphene, and ρ = 7.6 × 10 -7 kg/m 2 is the mass density of graphene. Equation 2 is solved self-consistently to give the change in temperature as a function of time and used to calculate the delaydependent optical parameters in the weak probe limit (i.e., the temperature change results solely from the pump pulse). The left panel of Fig. 4 shows the optical parameters produced by the measurement at selected pump fluences defined in Fig. 1 while the right panel of Fig. 4 shows the corresponding curves determined by the model.

IV. DISCUSSION

As can be seen from Fig. 4(a), the model and data show relative transmission curves that are strictly positive at low fluence (< 0.6µJ•cm -2 ) and mostly negative at higher fluences (> 3µJ•cm -2 ). The relative change in reflection from the model and data are presented in Fig. 4(b). These curves display a relative reflection that rapidly increases with pump fluence. The change in absorption curves decrease with pump fluence as seen in Fig. 4(c).

The transmission curves change sign as a function of fluence when the increasing reflection becomes larger than the steadily decreasing absorption; marking a change from a fluence regime exhibiting primarily saturable absorption, to one exhibiting primarly pump-induced reflection. This changeover in phenomenology takes place when heating reduces the amount of interband absorption due to a decreased difference in carrier occupation at ±hω/2 and a simultaneous increase in intraband conductivity, which scales with temperature, that pro-duces a change in reflectivity. Figure 5(a) plots the Fermi function for a range of temperature changes and shows the degree of the temperature dependent change in chemical potential and edge broadening with respect to the incident photon energy. The effect of disorder can be observed as a broadened width of the Fermi function at low temperatures.

The real and imaginary components of the graphene conductivity as determined by Eqn. 1 are plotted in Fig. 5 (b) and (c) respectively. Here the conductivity resulting from interband and intraband processes are plotted independently (dash-dotted and dashed lines respectively) and together add up to the total conductivity (solid trace). As shown in the figure, the heating modifies the conductivity of the graphene and results in inter-and intraband processes playing a diminished and increased role respectively (an estimated peak change in temperature of around 200 K was reached in our experiments). Furthermore, since absorption in the graphene is proportional to the real part of the conductivity, the decrease shown in Fig. 5(b) confirms that the graphene behaves as a saturable absorber for all fluences in our experiment and that the sign change in the transmitted signal results exclusively from an increase in the reflectivity.

The observed sign change in transmission was previously shown to originate from a temperature dependent change in inter-and intraband conductivity. To generalize this result, we consider the temperature at which the real component of the conductivity from interband and intraband processes are equal for a range of photon energies and carrier concentrations (plotted in Fig. 6 as solid colored lines). Though the temperature at which the conductivity contributions from interband and intraband processes achieve parity was not reached in our experiment, this temperature identifies a general point of comparison for the optical properties studied in this work. Analogous energy scales to the ones used in our experiment are represented for the case where the incident photon energy is in the vicinity of the chemical potential (shown as dashed colored lines in Fig. 6) where, with increasing temperature, the conductivity transitions from being interband to intraband dominant as in Fig. 5(b). For photon energies well below the chemical potential, the crossover temperature represents the crossover from intraband to interband processes. Above the chemical potential, all curves asymptotically approach the high temperature limit (k B T µ(T ), black dashed line) which is independent of the graphene doping. In the high temperature limit, the crossover temperature increases with photon energy which means that at higher photon energies, the electrons must be heated by a greater amount in order for the intraband processes to compete with the interband ones. At low temperature and doping, the disorder-broadened Fermi function limits the solution to finite valued photon energies. The conductivity crossover temperatures in Fig. 6 are well within the range of experimentally observed values [START_REF] George | Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene[END_REF][START_REF] Jnawali | Observation of a Transient Decrease in Terahertz Conductivity of Single-Layer Graphene Induced by Ultrafast Optical Excitation[END_REF][START_REF] Jensen | Competing ultrafast energy relaxation pathways in photoexcited graphene[END_REF] and indicate that the same phenomena will be observed for a range of wavelengths spanning the midand far-infrared frequency range.

V. CONCLUSION

We have investigated the terahertz response of low-doped multilayer epitaxial graphene using pump-probe spectroscopy that measures both the reflected and transmitted farinfrared radiation. This radiometrically comprehensive measurement allows for clear determination of the absorption in the material which was shown to be negative, and monotonic with fluence; verifying that the graphene behaves as a saturable absorber. Additionally, the relative change in the terahertz transmission was observed to change sign depending on the magnitude of the pump fluence as the result of a large, photoinduced reflection. This effect was clearly explained by a straightforward theory that identified two distinct physical mechanisms for the terahertz optical properties: one at low fluence where the properties are dominated by interband absorption of the incident terahertz photons, and a metallic regime that is characterized by increased intraband processes resulting from a heated electron system with significant carrier populations above the incident photon energy. These results demonstrate that it is possible to observe a self-induced modification of the absorption mechanism and underscores the importance of considering reflection graphene optics. These findings apply to a range of mid-and far-infrared frequencies and will be important for the design of next generation graphene-based terahertz devices.

Variable Delay

To Detector

Re ected Light

Figure 2

 2 Figure 2 shows the measured change in transmission, reflection, and absorption as a function of probe delay and pump fluence. In Fig.2(a) the relative change in tranmission exhibits a fluence dependent sign change apparent as red and blue regions in the colormap. At pump fluences below 0.6 µJ•cm -2 the transmitted signal is positive suggesting that saturable absorption is dominant in the terahertz transmission for low pump fluences. When the pump fluence increases beyond 3 µJ•cm -2 the sign of the terahertz transmission becomes predominantly negative; indicating either a pump-induced absorption effect or reflection is responsible for the decrease in transmission. The relative change in reflection is displayed in Fig. 2(b) and exhibits a strictly positive signal that increases monotonically with pump fluence. The positive nature of this signal strongly indicates that the negative relative transmission at high pump fluences is at least partially caused by an increase in the graphene reflectivity. A similar monotonic trend is seen for the change in absorption, (cf. Fig. 2(c))

FIG. 1 . 2 FIG. 2 .FIG. 3 . 10 FIG. 4 .

 1223104 FIG. 1. Diagram showing beam paths for pump and probe beams. The transmitted and reflected portions of the probe beam were measured as a function of the pump-probe delay.

FIG. 5 .FIG. 6 .

 56 FIG. 5. (a) Contour plot of the occupation probability for different changes in temperature. The ordinate axis is scaled by the photon half energy (hω/2 = 15 meV); horizontal dashed lines at -1, 0, and 1 are plotted for visual reference. Real (b) and imaginary (c) conductivity curves showing intra-and interband contributions versus change in temperature for the photon energy used in the experiment (hω = 30 meV).

ACKNOWLEDGEMENTS

This work was sponsored by the US ONR (N000141310865) and the US NSF (ECCS 1309750). We are grateful to P. Michel and the FELBE team for their dedicated support.


Some Housekeeping…

• As a participant you will be muted and not be seen throughout the webinar. • For questions and remarks please use the chat. For questions, please use the word question. • Your questions are going to be answered by the trainers during / after the presentation. • aim: create a crowd-sourced digital collection of letters written around the Easter Rising (Ireland) • participants transcribe (edit and tag) letters and also add letters to the collection • huge public engagement factor, educational aspects • data collection, analysis Screenshot of: http://letters1916.maynoothuniversity.ie/

•

  PARTHENOS stands for: Pooling Activities, Resources and Tools for Heritage eResearch Networking, Optimization and Synergies • PARTHENOS is a Horizon 2020 project with the aim to strengthen the cohesion of Heritage related E-research • Running time: 1 May 2015 -30 April 2019 • PARTHENOS has 16 partners from 9 European countries Povlsen https://www.clarin.eu/showcase/gesta-danorum • frequent use of elements from the Christian register of words indicates that the topic described has to do with Christianity in this case the transition from heathen to the Christian period in the Gesta Danorum The Cultural Heritage Data Reuse Charter • aim: Opening up Cultural Heritage data where possible and improve the interplay between scientific research and CHIs • prerequisite: a non-restrictive, easy to understand and applicable general framework that provides incentives and best practices to all stakeholders about access, use, and reuse • the Cultural Heritage Data Reuse Charter as a common online environment is currently under development with several supra-national infrastructures and projects involved (including CLARIN, DARIAH, PARTHENOS etc.) The Cultural Heritage Data Reuse Charter: Vision • go to the Charter mission statement • read more in the PARTHENOS Training Suite about Managing Cultural Heritage Assets and the Cultural Heritage Reuse Charter Talk of Europe (2014-2015) Source: http://www.talkofeurope.eu/2014/01/about/ • Erasmus University Rotterdam, University Amsterdam, DANS, Netherlands Institute for Sound and Vision • goal: facilitate richer research of the European Parliament by turning the EP proceedings into Linked Open Data and organizing creative camps to spark collaborative development on the new database • Linked Open Data • semantic: Give me politicians who held a speech on 23 March 2011. • linked: Give me politicians from the Committee on Foreign Affairs who held a speech on 23 March 2011. • open: Give me politicians from the Committee on Foreign Affairs who held a speech on the topic of human rights 23 March 2011.

Picture from slides by Laurent Romary 'Access to Cultural Heritage Data: A Challenge for Digital Humanities', 09.04.2018, https://www.ifla.org/files/assets/academic-and-research-libraries/conferences/laurent_romary_data_reuse_charter.pdf

(Picture CC0 https://pixabay.com/photo-2999583/)

• "Digital Transformation" (Web 2.0, new technologies, new philosophy of sharing) provides huge potential for Citizen Science • many successful Citizen Science projects take place in the digital world (VREs) • digital solutions mobilize individual and collective engagement for co-creation

Clavs Povlsen https://www.clarin.eu/showcase

Venice Time Machine Open Innovation Strategy for Austria 2016

• aim: develop a semantic search engine for digitised works of art wuttke@fh-potsdam.de Twitter: @UWuttke www.parthenosproject.eu www.fh-potsdam.de