Optical anisotropy of multilayer graphene probed by coupled plasmon- waveguide resonators

Optical anisotropy of multilayer graphene probed by coupled plasmon- waveguide resonators | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optical anisotropy of multilayer graphene probed by coupled plasmon- waveguide resonators Quaid Zaman, Giancarlo Margheri, André do Nascimento Barbosa, and 8 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6947590/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Aug, 2025 Read the published version in Plasmonics → Version 1 posted 9 You are reading this latest preprint version Abstract The characterization of the optical constants of single layer graphene has been subject of deep investigation in the last two decades and the optical anisotropy has been discovered to be an important parameter linked to the structural defects of the plane of the carbon atoms. Using graphene loaded coupled plasmon-waveguide resonator, which offer pure transverse electric or transverse magnetic electromagnetic modes, we demonstrate the possibility to characterize the optical anisotropy using evanescent electromagnetic fields in the visible and middle infrared range of a single, double and triple layer of graphene. On the assumption that a universal opacity of graphene holds for both in-plane and out-plane electronic displacement, we extract the anisotropic coefficient of the graphene layers with an accuracy of about 20%. The results are coherent with the literature and indicate that coupled plasmon-waveguide resonator spectroscopy is a valid low-cost and simple technique for the alternative optical characterization of uniaxial anisotropic bidimensional materials. Graphene Optical anisotropy Coupled plasmon-waveguide resonators Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction The optical conductivity of single layer graphene (SLG) is strongly influenced by the 2D nature of the atomic configuration, leading to unique characteristics such as a universal opacity and quantum conductance depending on the fine structure parameter [ 1 , 2 ] and an intrinsic optical anisotropy between the extraordinary (out-plane) and ordinary (in-plane) axis [ 3 ]. In most of the literature regarding the optical characterization of graphene by ellipsometric techniques [ 4 – 6 ] or by Surface Plasmon Resonance (SPR) Spectroscopy [ 7 – 9 ], poor attention has been devoted to anisotropy. Only a few works explicitly consider graphene as a uniaxial anisotropic material [ 3 ] [ 10 , 11 ], and traditional investigations with p-polarized SPR spectroscopy only give information about the out of-plane optical constant of the SLG. The anisotropy of SLG has been put to the attention of the scientific community about one decade ago, when Yu-Lun Liu et al. [ 11 ] discovered its significance in the evaluation of the structural quality of the carbon atoms plane, which might find application to other types of bidimensional materials. Although this scientific significance, still is missing in literature the report of evanescent field spectroscopy as an alternative technique to ellipsometry for the characterization of the anisotropy of large area graphene layers. Evanescent field spectroscopy in the Kretschmann configuration [ 12 , 13 ] has in fact the advantage to make use of pure transverse electric (TE, in-plane) or transverse magnetic (TM, out-plane) photonic modes in a simple experimental set-up, without the need of grazing incidence and complicated computational algorithm and protocols to probe the reflectivity of the samples and to calculate the optical constants of the material under study, such as in spectroscopic ellipsometry [ 11 , 14 ]. Moreover, thanks to the very high resolution in revealing interface changes, the evanescent field of the plasmon waveguide resonator is known to be from past studies an optimal probe for the detection and/or characterization of nanomaterials at metal-dielectric interfaces [ 13 , 15 , 16 ]. In this study we demonstrate the performances of coupled plasmon waveguide resonators (CPWRs), characterized by both TE and TM photonic modes, for the characterization of the optical anisotropy of large area multilayer graphene in the visible (633 nm) and near-infrared (783 nm) region. The presented research assumes that the dispersion relation obtained by fine structure dependent universal opacity of graphene [ 1 , 6 ] is valid independently for both TE and TM polarizations. The results are important for the characterization of the optical anisotropy of large area uniaxial low dimensional materials, which has several potential applications in photonics and optoelectronics [ 17 – 20 ]. Materials and methods Materials SiO 2 and Gold pellets were purchased from Kurt J. Lesker Company with purity better than 99%. Ethanol, acetone, trichloroethylene, tetrahydrofuran (THF), iron(III) chloride and 3-mercaptopropyltrimethoxysilane (MPTS) were purchased from Sigma-Aldrich. Polyurethane (PU) pellets were purchased from BASF, and copper foils of 25 µm thickness used for graphene synthesis were purchased from Alfa Cesar with 99.8% purity. Deionized water was obtained from a Milli-Q purification system, Millipore, USA. Fabrication of the CPWR loaded with SLGs SF4 glass substrates were ultrasonically cleaned in DI water, trichloroethylene, acetone and ethanol for 10 min in each step to remove any organic contaminant. Afterward, the substrates were dried with nitrogen and placed in an oven at 100o C for 10 min. The hydroxyl chemical groups (OH) were formed on the glass surface after placing the substrates into a plasma cleaner for 3 minutes. After these treatments, the substrates were immediately silanized to avoid potential to avoid potential contamination or oxidation of the silane groups. In the silanization process, the thiol-terminated surfaces were prepared by chemical treatment of the glasses with 2.5% of MPTS in ethanol for 2h at room temperature, followed by an ultrasonic bath in ethanol, and a curing at 100o C along 5 minutes. MPTS works as a molecular adhesion layer: its silane functional group [-Si(OCH 3 ) 3 ] can covalently bind to the hydroxyl group of glass surface with the elimination of CH 3 OH and H 2 O to form siloxane bonds (Si-O-Si), exposing to air the thiol groups [-SH] on top of the surface, that are thus suitable for an efficient grafting of the Au film. These layers were deposited immediately on the thiol-terminated SF4 surface by using an electron beam (e-beam) deposition system (model Univex 450) at a chamber pressure of about 3 × 10 − 6 Torr with a deposition rate 0.5 Å/sec. Finally, the fabrication of the CPWR is completed by the hydrolysis and condensation of a self-assembled monolayer of MPTS on the thin gold surface [ 15 ] and the subsequent deposition of a dielectric layer of SiO2 with the nominal thickness of 700 nm. This thickness was chosen since, as it will be shown in the manuscript, it allows the presence of independent modes for both polarizations (TM, TE) and wavelengths (633 nm, 783 nm). During evaporation, the nominal thin film thickness of both gold and SiO 2 thin films has been measured by placing the quartz crystal microbalance (QCM) close to the glass substrates. The SPR substrates were then kept in vacuum at room temperature before further use. Graphene layers were grown by chemical vapor deposition (CVD) on Cu foils (Alpha Aesar, 46986, 99.8% purity). The foils were cut into squares of about 2 cm² in area and were subsequently cleaned using acetone and isopropyl alcohol. The Cu foils were annealed at 1050°C under 50 sccm H 2 gas flow prior to growth to reorient the Cu foil crystalline structure to a preferential {111} direction [ 21 ], and to remove oxide species from the surface of the foils. The growth was carried out using 10 sccm CH 4 as carbon precursor at 1000°C under a partial pressure of 500 mTorr. The transfer process to Au substrates followed a similar protocol found in the author’s previous works elsewhere [ 22 , 23 ]. The graphene layers were transferred on top of the CPWR one by one, taking care to remove most of the PU sacrificial layer residues before the subsequent graphene film deposition was carried out. Between each graphene deposition, the samples were characterized by both Raman and reflectivity spectroscopy in the Kretschmann configuration [ 13 ]. Raman characterization of the layers of graphene Raman spectroscopy was carried out using a Micro-Raman spectrometer (NT-MDT, NTEGRA SPECTRA) equipped with a CCD detector and a solid-state laser (473 nm), and a 600l/mm diffraction grating, yielding a 4 cm − 1 spectral resolution. Its power ranges from 0.02 to 2 mW, controlled by a variable neutral density filter. Care was taken to avoid damage to the samples and multiple measurements were performed to rule out laser-induced heating effects in the acquired spectra. The measurements were carried out using a 100x objective lens, with a focal point of less than 1µm. SPR spectrometer The SPR spectrometer in the Kreschtmann configuration used for the experimental measurements is shown in Fig. 1 (a). The set-up is identical to the one described in detail [ 13 ], where a black box is used to keep the sample in dark conditions. The laser beam comes from linearly polarized sources at wavelengths of 633 nm (Thorlabs U.S.A, He-Ne, 5 mW) or 783 nm (Ondax U.S.A, model LM-783-PLR-75-1, 75 mW). The laser heads were rotated in order to have a linear polarization forming an angle of about 45 deg with the plane of incidence, in order to be used in both TE or TM polarization. The beam splitter deflects about 2% of the incident beam to a photodetector D R (Model DET36A) which measures the reference input intensity of the beam used to compensate for the possible long-term fluctuation of the laser power. Before the interaction with the sample, the TM or TE polarization of the laser is selected by a linear polarizer. The signal detector D s inside the black-box, used to measure the intensity variations while the angle is changed, is a photodiode sensor (Thorlabs U.S.A, 350–1100 nm), with a large18 mm x 18 mm sensor active area. The rotation base of Sigma-Koki (model SGSP-80, Japan) has an angular resolution of 0.005 0 . Figure 1 (b) illustrates the schematic structure of the coupled plasmon waveguide resonator. Characterization of the optical anisotropy of the layers of graphene The characterization of the optical anisotropy starts with the optical characterization of the gold and fused glass layers constituting the CPWRs, where the incidence and outer media are SF4 and deionized water, and the wavelengths of excitation are λ 1 = 783 nm and λ 2 = 633 nm. The refractive index values used to model the incidence and outer layers are n SF4 633 = 1.749, n SF4 783 =1.738, n water 633 = 1.331, n water 783 = 1.330 [ 24 ]. The thin films of gold have been characterized by SPR spectroscopy before the deposition of the SiO 2 guiding layer at both wavelengths. The initial trials values of thickness (t trial Au ) and complex dielectric constant (ε trial Au ) of the gold layer supporting the plasma wave were retrieved using Winspall 3.02 free software [ 25 ]. After the deposition of the SiO 2 layer on the gold, a full angular spectrum of the reflectivity curve of the resonator is recorded in both TM and TE polarizations. The code used to simulate the reflectivity curves of the resonators and for the determination of the parameters of the SiO 2 and graphene layers is based on the transfer-matrix method and developed using MatLab 9.0 software, as reported in [ 13 ]. Single layer graphene is modelled as an optical uniaxial crystal, with ordinary or extraordinary complex refractive index indicated as n o,e SLG + I κ o,e SLG , and corresponding to displacement of the electrons along the in-plane (n o ) or out-plane (n e ) direction, respectively. The experimental results are elaborated under the assumption that the dispersion relation obtained using the universal opacity of graphene can be applied independently for both TE or TM polarizations and is valid up to a few numbers of graphene layers. Under these assumptions, we derive the following polarization independent dispersion relation [ 6 ]: n λ1 κ λ1 / n λ2 κ λ2 = Im[ε SLG λ1 ]/Im[ε SLG λ2 ] = λ 1 /λ 2 = 1.237, (1) where Im[ε SLG λ ] is the imaginary part of the dielectric constant of single layer graphene at a particular wavelength λ, for both in-plane and out-plane polarizations (λ 1 = 783 nm; λ 2 = 633 nm). Considering that the absorption coefficient of the SLG is α = (4π/λ) κ, we define the optical anisotropy of a SLG as α o /α e = κ o /κ e , a parameter which is directly linked to the structural defects of the carbon plane [ 11 ]. Experimental results and discussion Raman characterization of the layers of graphene transferred on the CPWRs Raman spectroscopy was employed to probe the number of SLGs on the CPWRs. Figure 2 (a) shows the experimental Raman spectra after one (1L), two (2L), and three (3L) SLGs deposited on the SiO 2 thin films. The G band, located around 1590 cm − 1 , corresponds to the in-plane rocking vibrations of carbon atoms in the hexagonal rings. The D band, located around 1350 cm − 1 is associated with disorder effects in the graphene layer. It arises from vibrations in the hexagonal carbon rings adjacent to flake edges, impurities, and defects [ 22 , 26 , 27 ]. The 2D peak, situated around 2730 cm − 1 , is an overtone of the D peak, arising from two-phonon scattering process. It is known that the Raman spectra of graphene changes its characteristic depending on both the quality of the carbon atoms plane and the numbers of stacked SLGs. In particular, the FWHM of the 2D band is related to the degree of crystallinity of the bidimensional material [ 28 ], the I D /I G band ratio is related to general disorder effects in sp² carbon structures [ 29 ], while both the spectra position of the 2D band [ 27 ] and the I G /I 2D ratio serve as a reliable indicator of the number of stacked graphene layers [ 29 ]. To have a better picture of the evolution of the characteristics of the Raman spectra depending on the number of SLGs, we report the values of the parameters we described above in Table 1 and in Fig. 2 (b). Table 1 I G /I 2D , I D /I G , FWHM and spectral position of the 2D band for one, two and three SLGs deposited on the Au/SiO 2 resonator. Sample I D /I G ratio I G /I 2D ratio Position − 2D (cm − 1 ) FWHM − 2D (cm − 1 ) 1 SLG 4x10 − 2 4x10 − 1 2695 28 2 SLG 3x10 − 2 7x10 − 1 2703 36 3 SLG 3x10 − 1 1.3 2710 38 Herein, we observe a spectral shift of the 2D band of about 15 cm − 1 passing from one SLG (2695 cm − 1 ) to three SLGs (2710 cm − 1 ), while the ratio I G /I 2D varies from 0.4 to about 1.3. The observed behavior is very similar to the results reported in [ 8 ] and confirms the possibility to control the number of SLGs deposited on the Au/SiO 2 bilayer using our experimental protocol. Observing Fig. 2 (a), we highlight that the emergence of the D peak after the transfer of a third SLG is likely attributable to the accumulation of various impurities during the sequential transfer process the samples underwent, such as Fe 2 Cl 3 residues and leftover polymer remnants. It is noted that the sequential transfer of graphene layers hence changes the I D /I G ratio from values of the order of 10 − 2 to about 0.3 after the third SLG transfer. Additionally, the Raman spectra reveals that the FWHM of the 2D band varies, with the one SLG sample (1L) showing an FWHM of approximately 30 cm − 1 , and the three SLGs sample (3L) exhibiting a FWHM of about 38 cm − 1 . This variation indicates high crystallinity in the samples [ 28 ], despite the introduction of the small disorder expressed by the I D /I G ratio. Interestingly, as shown in other works in the literature [ 11 ], one may relate the I D /I G band ratios, associated with the structural quality of graphene, with the optical anisotropy of the material. Our high-quality graphene with values of I D /I G band of the order of 0.3 (or lower) should present an optical anisotropy α o /α e higher than 2.5. Optical characterization of the CPWRs The thin film of gold has been characterized by SPR spectroscopy before the deposition of the SiO 2 guiding layer, to fix the first trial values for both the thickness (t trial Au ) and dielectric constant (ε trial Au ) of the gold layer at both wavelengths. Subsequently, reflectivity measurements have been performed in water environment at both wavelengths and for both TM and TE polarization after the deposition of the SiO 2 layer. In Fig. 3 (a) is shown the reflectivity curve in both TE and TM polarization of the CPWRs at 783 nm in water environment, where is notable the presence of three modes, the surface plasmon resonance (SPR) at higher angle of incidence (or TM 0 ), the TM 1 and the TE 0 photonic modes at lower angles. The measurements and fit at the wavelength of 633 nm, represented in Fig. 3 (b) only reports the modes TM 1 and TE 0 , since the SPR mode is theoretically located at an incident angle above 65 0 degrees inside the SF4 prism, which cannot be probed in our experimental apparatus. With each experimental curve, is also reported as a line the fit on the reflectivity spectra. To obtain the optical parameters of the Au/SiO 2 bilayers for which we have an optimal fit of the reflectivity curves at both wavelengths and polarizations, we started by using the values t trial Au and ε trial Au measured on the bare gold samples to fit the SPR mode at 783 nm. Please note that for both wavelengths the SPR angle does not depend on the SiO 2 thickness, while the resonance position of the photonic TM 1 and TE 0 modes instead depends on both thickness and refractive index of the fused silica layer, coherently with the distribution of the evanescent field reported in Fig. 4 . Hence, the SPR mode is initially used for the determination of the first trial value of dielectric constant of the fused silica at 783 nm (ε SiO2 783 ). After, we look for a value of the SiO 2 thickness (t SiO2 ) which fits the angular positions of the TM 1 and TE 0 modes at 783 nm. In the case that we cannot find a good match for both the three modes (SPR, TM 1 , TE 0 ), we repeat the whole procedure by changing the value ε trial Au of a maximum of 5%, which takes in account the possible variations in the real part of the dielectric constant of the gold thin film produced by electron beam deposition, as reported in a previous work [ 30 ]. Once obtained the optical parameters of the waveguide at 783 nm, we impose that for fused silica it holds the relation ε SiO2 633 /ε SiO2 783 = 1.0047 [ 24 ], and repeat a fit procedure on the resonance angles for the TM 1 and TE 0 modes by letting as free parameter the dielectric constant of the gold layer at 633 nm, changing the value ε trial Au of a maximum of 5%. Using the reported computational strategy, we obtained an optimal fit for a thickness of the gold thin film of about 41 nm, with dielectric constants coherent in comparison to the literature of (-12.82 + I 1.34) and (-25.17 + I 1.57) at the wavelengths of 633 nm and 783 nm, respectively. We obtained a thickness of the SiO 2 layer of about 732 nm and dielectric constants of 2.12 and 2.13 for 783 nm and 633 nm, respectively. The results are reported in Table 2 . Table 2 Thickness and dielectric constant of Au and SiO 2 thin films composing the CPWRs at the wavelengths of 633 nm and 783 nm. Layer t (nm) ε r 633nm / 783nm ε i 633nm / 783nm Au 40.7 -12.82 / -25.17 1.34 / 1.57 SiO 2 732 2.13 / 2.12 0 It is worth noting that the theoretical full width half maximum (FWHM) of the SPR, TM 1 and TE 0 modes are about 2 o , 0.2 o and 0.02 o , respectively. This behaviour is associated to the different profile of the evanescent fields along the planar structures, with TE fields extending far away from the metal region with ohmic damping, as reported in Fig. 4 . Thus, TE modes are extremely sharp resonances, and their full shape cannot exactly be reproduced with our experimental system having a minimum experimental step of about 0.005 o . This explain why in TE polarization we can fit extremely well the experimental resonance angle, but we are not able to fit the experimental FWHM, which is artificially enlarged due to the angular limitations of our system. Measurement of the optical anisotropy of graphene layers Direct transfer of SLG on gold is known to lead to a redistribution of the electrons at the Au/SLG/water interface which can enhance the performances of SPR sensors [ 31 , 32 ], but is detrimental if the aim is to measure the optical constant of an ideal free standing SLG, since the charge transfer will control the value of the optical susceptivity and conductivity of the SLG interacting with gold [ 7 , 22 ]. The use of a dielectric spacer between the gold and the SLG has been properly used in past works [ 8 ], where to obtain unique results (two independent measurements for 3 parameters, the thickness t and optical constants n and κ) the authors assumed the approximation of a constant refractive index between 670 nm and 785 nm. In Figs. 5 (a-d), we reported the reflectivity spectra of the CPWRs with different layers of graphene, at both wavelengths and polarizations, where a layer of about 730 nm of SiO 2 is acting as spacer between the layers of graphene and the gold film. It is evident in panel (a) that the transfer of the SLGs on the Au/SiO 2 resonator does not influence the angular position of the plasmonic mode, which is fixed at 61.3 o , and will not be considered for the evaluation of the optical constant of the SLG. The reason for this behaviour can be understood by the near electromagnetic fields reported in Fig. 4 , where it is evident that the evanescent field associated to the SP mode does not reach the region of the SLG. As shown in Fig. 5 (e,f), he variation in the angle of resonance θ res of both TM and TE modes depending on the number of graphene transferred on the Au/SiO 2 bilayer, at both wavelengths. Herein we observe that, at least for the TM modes, the angle of resonance increases linearly with the number of SLGs, and we obtain an average angular shift per layer δθ SLG of 7.88 x 10 − 2 o /layer and 6.46 x 10 − 2 o /layer at 783 nm and 633 nm, respectively. These values are about five times smaller than reported in [ 8 ], due to the lowest sensitivity of the photonic modes with the respect to the SPR mode investigated in the work of Jussila et al., at least for thin samples such as graphene layers. It is interesting to note that, together with a progressive angular shift, also the FWHM of the reflectivity spectra increases with the number of graphene layers, coherently as reported for the SPR mode in [ 8 ]. The linearity of the angular shift depending on the number of graphene layers, allow us to assume that each graphene layer deposited subsequently on the CPWRs has the same thickness and the same refractive index. The characterization of the SLGs starts with the analysis of the TM curves at both wavelengths (Figs. 5 (a,c)), associated to the out-plane oscillation and extraordinary refractive index n e SLG + I κ e SLG . We remember here that the thickness t SLG and real part of the refractive index n e SLG of the SLG have a high influence on the position of the resonance angle, while the imaginary part κ e SLG does not influence significantly the resonant angle but the full width half maximum (FWHM) of the reflectivity curve. If the determination of κ e SLG is obtained without ambiguity through the experimental FWHM, exist infinite couples of values (t SLG , n e SLG ) which reproduce the observed experimental angular shift δθ SLG [ 30 , 22 ], so that we have an infinite set of solutions (t SLG , n e SLG , κ e SLG ) at each of the wavelengths. The behaviour of each set is that when the thickness gets higher, both n e SLG and κ e SLG decrease to match the experimental angular shift and FWHM. The unicity of the solution is obtained through Eq. 1, which is satisfied for a unique value of t SLG . As illustrated in Fig. 6 (a,b), we represented the theoretical fits of the experimental TM reflectivity curves for different number of SLGs. The shift of the reflectivity curves is well described by the fit, but not the minimum reflectivity, at least when more than one SLG is present. While the theoretical curves indicate a progressive lower value of the minimum reflectivity with the number of graphene layers, the experimental curves show an opposite trend. We believe that such a behaviour may be associated to the impurities inserted in the multi-layer structure after the transfer of the subsequent SLGs. In fact, also the Raman measurements reported in Fig. 2 indicate the presence of defects, probably polymeric residues sticking on the surface of the SLG after the transfer of the second graphene. We attribute this phenomenon to the kind of interrogation of the interfaces by evanescent modes which, differently from free electromagnetic waves techniques such as ellispsometry, is extremely sensitive to the presence of impurities and defects in the near field zone, which act as local fields ‘scatterers. Once obtained the values of the extraordinary optical constant and of t SLG using the TM modes, we pass to the analysis of the TE modes. As evident in Figs. 6 (c,d), the TE modes are rapidly quenched by the transfer of graphene layers, and the reflectivity damp disappears after the transfer of the third graphene layer. Although the rapid quenching, the depth of the modes is enough to guarantee a good fit at the wavelength of 633 nm, as reported in Fig. 6 (c), which fixes the optical constant n o SLG + I κ o SLG of the SLGs for in-plane oscillations at such a wavelength. Subsequently, a second fit is done on the TE reflectivity curve at 783 nm but taking in account only the matching of the resonance angle, which fixes the value of the real part n o SLG of the refractive index at the second wavelength. Finally, under the hypothesis that the dispersion relation obtained by fine structure dependent universal opacity of graphene [ 1 , 6 ] is valid independently for both TE (in-plane) and TM (out-plane) polarizations, we use Eq. 1 to retrieve the imaginary part of the refractive index κ o SLG for in-plane oscillations at 783 nm. In this last case, we can observe in Fig. 6 (c) that the FWHM of the fit is larger than the experimental one, which indicates a possible overestimation of κ o SLG . Before discussing our experimental results based on the existing literature, it is important to highlight that we also measured a second independent sample to check for the reproducibility of the results. The difference in the resonant angle between the two independent samples after the transfer of a unique SLG is less than 5 x 10 − 2 deg, similarly as reported in [ 8 ], showing the good reproducibility of both fabrication and measurement of the reflectivity. Repeating our computational approach on the independent sample with a unique SLG, we obtained a second independent evaluation of the thickness and optical constant of the single graphene layer. As result for both thickness and optical constants, we consider the average of the values (v 1 , v 2 ) obtained from the measurements on the two independent samples and take as absolute uncertainty the value of the standard deviation between the values [(v 1 -v 2 ) 2 /2] 0.5 . The results obtained for the optical characterization of the different graphene layers by CPWRs are reported in the last raw of Table 3 , together with the values reported in literature for both t SLG , n o,e SLG and κ o,e SLG at different wavelengths and using different experimental techniques. Based on these results, we evaluate an accuracy in the determination of thickness, real and imaginary part of the refractive index of the SLG of about 20%, 15% and 20%, respectively. It is difficult to compare these results with the ones reported in literature using SPR spectroscopy since, at the best of our knowledge, this point is not clearly addressed in none of the works [ 7 , 8 ]. The linearity of the angular shift shown in Fig. 5 (e,f) suggests that, in our case, the optical anisotropy α o /α e = κ o /κ e does not depend on the number of graphene layers. Based on our results (Table 3 ), we estimate the optical anisotropy to be 3.3 and 2.6 at the wavelengths of 633 nm and 783 nm, respectively. The results are coherent with what reported in the work of Yu-Lun Liu et al. [ 11 ], where they measured by ellipsometry an optical anisotropy between 2.7 and 3.7 at grazing incidence on a high-quality graphene at the wavelength of 633 nm. It is worth noting that the lowest value of the anisotropy at 783 nm is probably due to the overestimation of κ e that we observed in Fig. 6 (c). Table 3 Values of t SLG , n o,e SLG and κ o,e SLG reported in literature using different experimental techniques and substrates. In the last two columns are reported the approximations or constrains used for the determination of the parameters. In the columns n and κ the apex indicates, when possible, the polarization (o-ordinary axis, e-extraordinary axis) and the wavelength. Sample Technique Range (nm) n κ t(nm) Comments c-Si/SiO 2 /SLG (exfoliated) Spectroscopic ellipsometry 210–1000 2.7 (633) 2.8 (783) 1.4 (633) 1.5 (783) 0.34 Obtained by optimization No anisotropic investigation [ 4 ] SiO 2 /Graphite (Not Reported) Spectroscopic ellipsometry 300–1000 2.6 (o−633) 1.7 (e−633) 2.8 (o−783) 1.6 (e−783) 1.4 (o−633) 0 (e−633) 1.6 (o−783) 0 (e−783) 0.34 Obtained by optimization With anisotropic discrimination [ 10 ] SiO 2 /HOPG SiO 2 /SLG (CVD) Mueller Matrix Ellispometry 200–1200 2.6 (o−633) 1.4 (e−633) 2.7 (o−783) 1.4 (e−783) 2.8 (o−633) 2.8 (o−783) 1.2 (o−633) 0 (e−633) 1.4 (o−783) 0 (e−783) 1.4 (o−633) 1.6 (o−783) 0.34 Considered as standard With anisotropic discrimination only on highly oriented pyrolytic graphite (HOPG) [ 14 ] SiO 2 /SLG Up to five layers (CVD) Spectroscopic ellipsometry 300–1000 1.74 (633) 1.77 (783) 0.45 (633) 0.47 (783) 0.32 Optimized by depolarization No anisotropic investigation [ 5 ] Si/SiO 2 /SLG Up to 2 layers and graphite. (Exfoliation) Spectroscopic ellipsometry 400–2500 3.0 (633) 3.0 (783) 1.15 (633) 1.42 (783) 0.34 Considered as standard No anisotropic investigation. They use the relation κ = 5.446 µm − 1 λ/n, where n is constant [ 6 ] SiO 2 /PG Reflectivity measurements 250–620 2.74 (o−620) 1.53 (e−620) 1.40 (o−620) 0 (e−620) - With anisotropic discrimination on pyrolytic graphite (PG) [ 33 ] SiO 2 /Au/SLG and SiO 2 /SLG. Up to 5 layers. (CVD) Polarized reflectance and SPR spectroscopy 634 2.7 (e−634) 1.4 (e−634) 0.335 Considered as standard Charge transfer due to Au/SLG interface. Use of TM modes → n e (out of plane). Assume that Au/SLG interface is equal to SiO 2 /SLG interface. No anisotropic investigation [ 7 ] SiO 2 /Au/SLG SiO 2 /Au/Al 2 O 3 /SLG Up to 3 layers. (CVD) SPR spectroscopy 670/785 3.1 (e−670) 3.1 (e−785) 3.7 (e−670) 3.7 (e−785) 0.5 (e−670) 0.5 (e−785) 0.8 (e−670) 0.8 (e−785) First SLG on Au = 1.1 Second SLG = 0.31 First SLG on Al 2 O 3 = 0.8 Subsequent SLGs between 0.3 and 0.4 No anisotropic investigation. Use of TM modes → n e (out of plane). It is assumed that the values of n and κ are constants, without dispersion [ 8 ] SiO 2 /Au/SLG (CVD) SPR spectroscopy 783 2.3 (e−783) 0.3 (e−783) 1.9 Obtained by changing the external refractive index No anisotropic investigation. Use of TM modes → n e (out of plane). An Au/H 2 O/SLG/H 2 O effective layer was considered [ 22 ] SiO 2 /Au/SiO 2 /SLG Up to 3 layers. (CVD) Coupled Plasmon-Waveguide spectroscopy 633/783 2.5 ± 0.3 (o−633) 4.0 ± 0.5 (e−633) 3.3 ± 0.3 (o−783) 3.8 ± 0.6 (e−783) 1.3 ± 0.2 (o−633) 0.4 ± 0.1 (e−633) 1.3 ± 0.2 (o−783) 0.5 ± 0.1 (e−783) 1.1 ± 0.2 For all the SLGs This work : with anisotropic investigation. Use of the dispersion relation expressed by Eq. 1: n λ1 κ λ1 / n λ2 κ λ2 = Im[ε SLG λ1 ]/Im[ε SLG λ2 ] = λ 1 /λ 2 We also observe that the thickness of the SLG does not depend on the number of graphene layers, differently from the work of Jussila et al. [ 8 ] where a value of thickness of about 1 nm was observed only after the transfer of the first SLG on both Au or SiO 2 substrates, while values near to 0.3 nm were measured for the subsequent graphene layers. Interestingly, values of thickness of the order of 1 nm are only observed in literature using evanescent electromagnetic probes [ 7 , 8 ], while none of the works based on ellipsometry report this value. This is probably an indication that the evanescent waves can detect interface effects, comprising roughness and impurities effects, with a better sensitivity than techniques based on free electromagnetic waves. The roughness of the substrate over which the graphene layers are transferred is reported to have a deep effect on the accuracy in the determination of the optical constants [ 10 ] and is supposed to control the value of thickness of the SLG based on physical processes yet not fully understood [ 8 ]. In our case, the average root mean square surface roughness of the SiO 2 surface has been characterized to be around 3 nm in previous research [ 15 ], which is higher than the 1.8 nm reported by Jussila et al. that measured a thickness of the first SLG on Al 2 O 3 substrates of about 0.8 nm [ 8 ]. Our experimental value of 1.1 nm is also similar to the values of thickness measured by AFM in [ 11 ], although AFM is considered to overestimate the real thickness of the SLG [ 8 ]. Looking at Table 3 , we realize that few works report the anisotropy of the SLG or graphite by ellipsometry [ 10 , 14 ], and all of them consider that the imaginary part of the extraordinary refractive index (κ e ) is zero. This is not what is observed in all the investigations using evanescent waves probes with TM polarization, giving a value of κ e in the red visible region between 0.3 and 1.4 [ 7 , 8 , 22 ]. We believe that such a behaviour may be associated to the presence of polymeric residues from the SLG transfer process, which inevitably act as both scatterers of the evanescent wave and dispersive elements eventually leading to an overestimation of the value of both the real and imaginary parts of the refraction index [ 7 , 11 ]. In fact, while all of the ellipsometric studies report a refractive index value below or equal to 3, investigations by the use of evanescent interfacial fields report values of n e which range between 2.3 and 3.1 when the SLG is deposited over a gold surface [ 7 , 22 ], and that raise to about 4 when the SLG is transferred on a dielectric spacer [ 8 ], similarly to the present research. This observation suggests that the quality of the transfer process may depend not only on the roughness of the substrate, but also on its nature, which might influence the affinity of polymeric particle residues and the eventual condensation at the substrate-SLG interface during the cleaning step of the transfer process. If none of the works using evanescent waves reports a dispersion of the refractive index similarly to the ellipsometric studies, our approach is instead completely based on the validity of the dispersion relation expressed by Eq. 1, which inherently gives a dispersive character to our results. Interestingly, the trend of the dispersion for both TM and TE polarization are coherent with the results reported by Kravets et al. [ 10 ] for graphite. In fact, in that work n o and n e increases and decreases with the wavelength, respectively, similarly to our results. Furtherly, the values that we measured for n o and κ o for in-plane polarization are similar to the ones reported in literature by ellipsometry [ 10 , 14 , 33 ] while, to the best of our knowledge, there are no other reports on the investigation of the in-plane ordinary refractive index of the SLG by the use of evanescent fields. Conclusions Coupled plasmon-waveguide resonators spectroscopy has been applied to the characterization of the optical anisotropy of planar and large area multilayer graphene in the visible and near infrared regions. The experimental results were interpreted by assuming that the dispersion relation obtained from the universal opacity of graphene is valid for both in-plane and out-plane polarization. Although this assumption is found to lead to a possible overestimation of the imaginary part of the refractive index at one of the wavelengths, the values of the optical constants and of the anisotropy measured for a single layer graphene can be well explained in the frame of literature reports. The thickness and the real part of the extraordinary out-plane refractive index of the SLG are higher than reported in average for spectroscopic ellipsometry, but perfectly matching with other results reported in literature using SPR spectroscopy, probably suggesting that the near fields are highly sensitive to the particle residuals and interfacial effects which are less observable in spectroscopic ellipsometry. Using the TE modes of the CPWRs we also measured the optical constants of the SLGs along the ordinary axes using evanescent fields, obtaining an optical anisotropy between 2.6 and 3.3 in the NIR and visible regions, respectively. These values, together with the Raman spectroscopy results, indicates the presence of high quality SLGs, but with the presence of a detectable amount of defects after the transfer process. We evaluated the accuracy of the proposed method to be of the order of 20%, demonstrating that evanescent field spectroscopy by CPWRs can be considered as a valid low-cost alternative for the optical characterization of large area anisotropic uniaxial bidimensional materials. Declarations Funding This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)- Finance Code 001, and CNPq productivity grant. Funding from FAPERJ for processes E-26/211.540/2021, E-26/211.279/2021, E-26/010.002138/2019, E-26/010.000980/2019, E-26/200.810/2021, E-26/210.104/2020, and E-26/210.726/2021 are acknowledged. Author Contribution Q.Z and T.D.R. wrote the main manuscript text, A.N.B/N.S/M.E.H.M.C/F.L were responsible for the synthesis and Raman characterization of the graphenes; Tahir/R.K/S.F/K.Q.C/G.M participated in development of the numerical codes and in the data analysis; Q.Z/G.M fabricated and characterized the plasmon-waveguide resonators. All authors reviewed the manuscript. Acknowledgement This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES)- Finance Code 001, and CNPq productivity grant. Funding from FAPERJ for processes E-26/211.540/2021, E-26/211.279/2021, E-26/010.002138/2019, E-26/010.000980/2019, E-26/200.810/2021, E-26/210.104/2020, and E-26/210.726/2021 are acknowledged. References Nair, R. R., Blake, P., Grigorenko, A. N., Novoselov, K. S., Booth, T. J., Stauber, T., ... & Geim, A. K. (2008). Fine structure constant defines visual transparency of graphene. science, 320 (5881), 1308-1308. Kuzmenko, A. B., van Heumen, E., Carbone, F., & van der Marel, D. (2007). Universal dynamical conductance in graphite. arXiv preprint arXiv:0712.0835 . Liu J-M, Lin I-T. Optical Properties. In: Graphene Photonics. Cambridge University Press; 2018:66-106. Weber, J. W., Calado, V. E., & Van De Sanden, M. C. M. (2010). 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Del Rosso, T., Shtepliuk, I., Zaman, Q., Baldeón Huanqui, L. G., Tahir, Freire, F. L., ... & Margheri, G. (2024). On the Strong Binding Affinity of Gold-Graphene Heterostructures with Heavy Metal Ions in Water: A Theoretical and Experimental Investigation. Langmuir, 40(38), 20204-20218. Greenaway, D. L., Harbeke, G., Bassani, F., & Tosatti, E. (1969). Anisotropy of the optical constants and the band structure of graphite. Physical review , 178 (3), 1340. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6947590","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":477975786,"identity":"e725a27f-9ed4-4906-84ba-1cbfb5b34717","order_by":0,"name":"Quaid Zaman","email":"","orcid":"","institution":"Pontifical Catholic University of Rio de Janeiro","correspondingAuthor":false,"prefix":"","firstName":"Quaid","middleName":"","lastName":"Zaman","suffix":""},{"id":477975787,"identity":"698f0ec3-d4de-4fb7-9646-f39bddcfdc0d","order_by":1,"name":"Giancarlo Margheri","email":"","orcid":"","institution":"Istituto dei Sistemi Complessi Sezione di Sesto Fiorentino (I.S.C - 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(b) Scheme illustrating the individual layers of the CPWRs and the qualitative shape of the evanescent fields of both TM and TE modes.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/0827ed421e64a6f38ca1cd36.jpeg"},{"id":85729872,"identity":"fff06ef0-1b1c-4d9f-857e-b71e1bf28a58","added_by":"auto","created_at":"2025-07-01 07:13:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":149383,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) Raman spectra of one SLG (1L-red line), two SLGs (2L-blue line), and three SLGs (3L-pink line) deposited on the CPWRs. (b) Dependence of different parameters of the Raman spectra on the number of SLGs: I\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eD\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/I\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e ratio (grey circular points), I\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/I\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2D\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e ratio (grey triangular points), and spectral position of the 2D band (black circular points).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/35d32b6af983222780de6ea4.png"},{"id":85728928,"identity":"ac98f988-80cd-427a-879c-0479385d1c7f","added_by":"auto","created_at":"2025-07-01 07:05:49","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":508415,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental (exp) and theoretical (fit) reflectivity spectra at 783 nm (a) and 633 nm (b) of the CPWRs, at both TM and TE polarizations. The theoretical fit, obtained using the values reported in Table 1, are represented as a continuous line. The inset in (a) shows the details of the reflectivity of the TE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e mode.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/006b257ddc01606d232fa58a.jpeg"},{"id":85729873,"identity":"26517eae-c415-41dd-9a14-09f93705a60b","added_by":"auto","created_at":"2025-07-01 07:13:50","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":148264,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSquare of the electric or magnetic near field for TM (out-plane) or TE (in-plane) polarizations at 783 nm. \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ez\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e and \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e axis are perpendicular and parallel to the plane of the multilayers, respectively. (a) |H\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e|\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e – TM, SPR mode; (b) |H\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e|\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e – TM, TM\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e mode; (c) |E\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e|\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e – TE, TE\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e mode. In the panels is represented the geometry of the multi-layer structure composing the CPWRs. The values of the parameters of the Au/SiO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e bilayer are reported in Table 1.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/5dc3de9a9f00152a19aa1c13.jpeg"},{"id":85728933,"identity":"db338098-521f-4be7-9fa7-8e5d4b7ed2e5","added_by":"auto","created_at":"2025-07-01 07:05:50","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":507441,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental reflectivity spectra of the CPWRs at different wavelengths and polarization, and with different layers of graphene: (a) TM, 783 nm; (b) TE, 783 nm; (c) TM, 633 nm; (d) TE, 633 nm. The spectra are relative to the CPWRs without SLG (black lines), with one (red line), two (grey line), and three (pink lines) graphene layers. Angle of resonance (q\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003eres\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e) of the TE and TM modes at 783 nm (e) and 633 nm (f) depending on the number of graphene transferred on the CPWRs. As dashed lines are represented the linear fit on the experimental points.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/34e156cb316efef01223a3f0.jpeg"},{"id":85728934,"identity":"8df57e0e-1e0b-43fd-bab8-314697222a4f","added_by":"auto","created_at":"2025-07-01 07:05:50","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":122619,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental (points) and theoretical (lines) reflectivity spectra of the CPWRs at different wavelengths and polarization, and with different layers of graphene: (a) TM, 783 nm, 1-2-3 layers; (b) TM, 633 nm, 1-2-3 layers; (c) TE, 783 nm, 1-2 layers; (d) TE, 633 nm, 1-2 layers. The theoretical fits have been performed using the parameters reported in Table 2.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/01354733f43e7a038a1360a2.jpeg"},{"id":89847309,"identity":"0f66013e-4c0f-4599-9126-54f9b777e589","added_by":"auto","created_at":"2025-08-25 16:43:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3331429,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6947590/v1/c8b25fde-e09b-44f7-8eb6-314adbad88e8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optical anisotropy of multilayer graphene probed by coupled plasmon- waveguide resonators","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe optical conductivity of single layer graphene (SLG) is strongly influenced by the 2D nature of the atomic configuration, leading to unique characteristics such as a universal opacity and quantum conductance depending on the fine structure parameter [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] and an intrinsic optical anisotropy between the extraordinary (out-plane) and ordinary (in-plane) axis [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn most of the literature regarding the optical characterization of graphene by ellipsometric techniques [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] or by Surface Plasmon Resonance (SPR) Spectroscopy [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], poor attention has been devoted to anisotropy. Only a few works explicitly consider graphene as a uniaxial anisotropic material [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], and traditional investigations with p-polarized SPR spectroscopy only give information about the out of-plane optical constant of the SLG. The anisotropy of SLG has been put to the attention of the scientific community about one decade ago, when Yu-Lun Liu et al. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] discovered its significance in the evaluation of the structural quality of the carbon atoms plane, which might find application to other types of bidimensional materials. Although this scientific significance, still is missing in literature the report of evanescent field spectroscopy as an alternative technique to ellipsometry for the characterization of the anisotropy of large area graphene layers.\u003c/p\u003e \u003cp\u003eEvanescent field spectroscopy in the Kretschmann configuration [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] has in fact the advantage to make use of pure transverse electric (TE, in-plane) or transverse magnetic (TM, out-plane) photonic modes in a simple experimental set-up, without the need of grazing incidence and complicated computational algorithm and protocols to probe the reflectivity of the samples and to calculate the optical constants of the material under study, such as in spectroscopic ellipsometry [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Moreover, thanks to the very high resolution in revealing interface changes, the evanescent field of the plasmon waveguide resonator is known to be from past studies an optimal probe for the detection and/or characterization of nanomaterials at metal-dielectric interfaces [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this study we demonstrate the performances of coupled plasmon waveguide resonators (CPWRs), characterized by both TE and TM photonic modes, for the characterization of the optical anisotropy of large area multilayer graphene in the visible (633 nm) and near-infrared (783 nm) region. The presented research assumes that the dispersion relation obtained by fine structure dependent universal opacity of graphene [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] is valid independently for both TE and TM polarizations. The results are important for the characterization of the optical anisotropy of large area uniaxial low dimensional materials, which has several potential applications in photonics and optoelectronics [\u003cspan additionalcitationids=\"CR18 CR19\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eMaterials\u003c/h2\u003e\n \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e and Gold pellets were purchased from Kurt J. Lesker Company with purity better than 99%. Ethanol, acetone, trichloroethylene, tetrahydrofuran (THF), iron(III) chloride and 3-mercaptopropyltrimethoxysilane (MPTS) were purchased from Sigma-Aldrich. Polyurethane (PU) pellets were purchased from BASF, and copper foils of 25 \u0026micro;m thickness used for graphene synthesis were purchased from Alfa Cesar with 99.8% purity. Deionized water was obtained from a Milli-Q purification system, Millipore, USA.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eFabrication of the CPWR loaded with SLGs\u003c/h3\u003e\n\u003cp\u003eSF4 glass substrates were ultrasonically cleaned in DI water, trichloroethylene, acetone and ethanol for 10 min in each step to remove any organic contaminant. Afterward, the substrates were dried with nitrogen and placed in an oven at 100o C for 10 min. The hydroxyl chemical groups (OH) were formed on the glass surface after placing the substrates into a plasma cleaner for 3 minutes. After these treatments, the substrates were immediately silanized to avoid potential to avoid potential contamination or oxidation of the silane groups. In the silanization process, the thiol-terminated surfaces were prepared by chemical treatment of the glasses with 2.5% of MPTS in ethanol for 2h at room temperature, followed by an ultrasonic bath in ethanol, and a curing at 100o C along 5 minutes. MPTS works as a molecular adhesion layer: its silane functional group [-Si(OCH\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e] can covalently bind to the hydroxyl group of glass surface with the elimination of CH\u003csub\u003e3\u003c/sub\u003eOH and H\u003csub\u003e2\u003c/sub\u003eO to form siloxane bonds (Si-O-Si), exposing to air the thiol groups [-SH] on top of the surface, that are thus suitable for an efficient grafting of the Au film. These layers were deposited immediately on the thiol-terminated SF4 surface by using an electron beam (e-beam) deposition system (model Univex 450) at a chamber pressure of about 3 \u0026times; 10\u0026thinsp;\u0026minus;\u0026thinsp;6 Torr with a deposition rate 0.5 \u0026Aring;/sec.\u003c/p\u003e\n\u003cp\u003eFinally, the fabrication of the CPWR is completed by the hydrolysis and condensation of a self-assembled monolayer of MPTS on the thin gold surface [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e] and the subsequent deposition of a dielectric layer of SiO2 with the nominal thickness of 700 nm. This thickness was chosen since, as it will be shown in the manuscript, it allows the presence of independent modes for both polarizations (TM, TE) and wavelengths (633 nm, 783 nm). During evaporation, the nominal thin film thickness of both gold and SiO\u003csub\u003e2\u003c/sub\u003e thin films has been measured by placing the quartz crystal microbalance (QCM) close to the glass substrates. The SPR substrates were then kept in vacuum at room temperature before further use.\u003c/p\u003e\n\u003cp\u003eGraphene layers were grown by chemical vapor deposition (CVD) on Cu foils (Alpha Aesar, 46986, 99.8% purity). The foils were cut into squares of about 2 cm\u0026sup2; in area and were subsequently cleaned using acetone and isopropyl alcohol. The Cu foils were annealed at 1050\u0026deg;C under 50 sccm H\u003csub\u003e2\u003c/sub\u003e gas flow prior to growth to reorient the Cu foil crystalline structure to a preferential {111} direction [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e], and to remove oxide species from the surface of the foils. The growth was carried out using 10 sccm CH\u003csub\u003e4\u003c/sub\u003e as carbon precursor at 1000\u0026deg;C under a partial pressure of 500 mTorr.\u003c/p\u003e\n\u003cp\u003eThe transfer process to Au substrates followed a similar protocol found in the author\u0026rsquo;s previous works elsewhere [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. The graphene layers were transferred on top of the CPWR one by one, taking care to remove most of the PU sacrificial layer residues before the subsequent graphene film deposition was carried out. Between each graphene deposition, the samples were characterized by both Raman and reflectivity spectroscopy in the Kretschmann configuration [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eRaman characterization of the layers of graphene\u003c/h3\u003e\n\u003cp\u003eRaman spectroscopy was carried out using a Micro-Raman spectrometer (NT-MDT, NTEGRA SPECTRA) equipped with a CCD detector and a solid-state laser (473 nm), and a 600l/mm diffraction grating, yielding a 4 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e spectral resolution. Its power ranges from 0.02 to 2 mW, controlled by a variable neutral density filter. Care was taken to avoid damage to the samples and multiple measurements were performed to rule out laser-induced heating effects in the acquired spectra. The measurements were carried out using a 100x objective lens, with a focal point of less than 1\u0026micro;m.\u003c/p\u003e\n\u003ch3\u003eSPR spectrometer\u003c/h3\u003e\n\u003cp\u003eThe SPR spectrometer in the Kreschtmann configuration used for the experimental measurements is shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e(a). The set-up is identical to the one described in detail [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e], where a black box is used to keep the sample in dark conditions. The laser beam comes from linearly polarized sources at wavelengths of 633 nm (Thorlabs U.S.A, He-Ne, 5 mW) or 783 nm (Ondax U.S.A, model LM-783-PLR-75-1, 75 mW). The laser heads were rotated in order to have a linear polarization forming an angle of about 45 deg with the plane of incidence, in order to be used in both TE or TM polarization. The beam splitter deflects about 2% of the incident beam to a photodetector D\u003csub\u003eR\u003c/sub\u003e (Model DET36A) which measures the reference input intensity of the beam used to compensate for the possible long-term fluctuation of the laser power. Before the interaction with the sample, the TM or TE polarization of the laser is selected by a linear polarizer. The signal detector D\u003csub\u003es\u003c/sub\u003e inside the black-box, used to measure the intensity variations while the angle is changed, is a photodiode sensor (Thorlabs U.S.A, 350\u0026ndash;1100 nm), with a large18 mm x 18 mm sensor active area. The rotation base of Sigma-Koki (model SGSP-80, Japan) has an angular resolution of 0.005\u003csup\u003e0\u003c/sup\u003e. Figure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e(b) illustrates the schematic structure of the coupled plasmon waveguide resonator.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003ch3\u003eCharacterization of the optical anisotropy of the layers of graphene\u003c/h3\u003e\n\u003cp\u003eThe characterization of the optical anisotropy starts with the optical characterization of the gold and fused glass layers constituting the CPWRs, where the incidence and outer media are SF4 and deionized water, and the wavelengths of excitation are \u0026lambda;\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;783 nm and \u0026lambda;\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;633 nm. The refractive index values used to model the incidence and outer layers are n\u003csub\u003eSF4\u003c/sub\u003e\u003csup\u003e633\u003c/sup\u003e = 1.749, n\u003csub\u003eSF4\u003c/sub\u003e\u003csup\u003e783\u003c/sup\u003e =1.738, n\u003csub\u003ewater\u003c/sub\u003e\u003csup\u003e633\u003c/sup\u003e = 1.331, n\u003csub\u003ewater\u003c/sub\u003e\u003csup\u003e783\u003c/sup\u003e = 1.330 [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eThe thin films of gold have been characterized by SPR spectroscopy before the deposition of the SiO\u003csub\u003e2\u003c/sub\u003e guiding layer at both wavelengths. The initial trials values of thickness (t\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e) and complex dielectric constant (\u0026epsilon;\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e) of the gold layer supporting the plasma wave were retrieved using Winspall 3.02 free software [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. After the deposition of the SiO\u003csub\u003e2\u003c/sub\u003e layer on the gold, a full angular spectrum of the reflectivity curve of the resonator is recorded in both TM and TE polarizations.\u003c/p\u003e\n\u003cp\u003eThe code used to simulate the reflectivity curves of the resonators and for the determination of the parameters of the SiO\u003csub\u003e2\u003c/sub\u003e and graphene layers is based on the transfer-matrix method and developed using MatLab 9.0 software, as reported in [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eSingle layer graphene is modelled as an optical uniaxial crystal, with ordinary or extraordinary complex refractive index indicated as n\u003csup\u003eo,e\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e + I \u0026kappa;\u003csup\u003eo,e\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e, and corresponding to displacement of the electrons along the in-plane (n\u003csub\u003eo\u003c/sub\u003e) or out-plane (n\u003csub\u003ee\u003c/sub\u003e) direction, respectively.\u003c/p\u003e\n\u003cp\u003eThe experimental results are elaborated under the assumption that the dispersion relation obtained using the universal opacity of graphene can be applied independently for both TE or TM polarizations and is valid up to a few numbers of graphene layers. Under these assumptions, we derive the following polarization independent dispersion relation [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e]:\u003c/p\u003e\n\u003cp\u003en\u003csub\u003e\u0026nbsp;\u0026lambda;1\u003c/sub\u003e\u0026kappa;\u003csub\u003e\u0026lambda;1\u003c/sub\u003e / n\u003csub\u003e\u0026nbsp;\u0026lambda;2\u003c/sub\u003e\u0026kappa;\u003csub\u003e\u0026lambda;2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;Im[\u0026epsilon;\u003csup\u003eSLG\u003c/sup\u003e\u003csub\u003e\u0026nbsp;\u0026lambda;1\u003c/sub\u003e]/Im[\u0026epsilon;\u003csup\u003eSLG\u003c/sup\u003e\u003csub\u003e\u0026nbsp;\u0026lambda;2\u003c/sub\u003e] = \u0026lambda;\u003csub\u003e1\u003c/sub\u003e/\u0026lambda;\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.237, (1)\u003c/p\u003e\n\u003cp\u003ewhere Im[\u0026epsilon;\u003csup\u003eSLG\u003c/sup\u003e\u003csub\u003e\u0026nbsp;\u0026lambda;\u003c/sub\u003e] is the imaginary part of the dielectric constant of single layer graphene at a particular wavelength \u0026lambda;, for both in-plane and out-plane polarizations (\u0026lambda;\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;783 nm; \u0026lambda;\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;633 nm).\u003c/p\u003e\n\u003cp\u003eConsidering that the absorption coefficient of the SLG is \u0026alpha; = (4\u0026pi;/\u0026lambda;) \u0026kappa;, we define the optical anisotropy of a SLG as \u0026alpha;\u003csup\u003eo\u003c/sup\u003e/\u0026alpha;\u003csup\u003ee\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;\u0026kappa;\u003csup\u003eo\u003c/sup\u003e/\u0026kappa;\u003csup\u003ee\u003c/sup\u003e, a parameter which is directly linked to the structural defects of the carbon plane [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e"},{"header":"Experimental results and discussion","content":"\u003ch2\u003eRaman characterization of the layers of graphene transferred on the CPWRs\u003c/h2\u003e\u003cp\u003eRaman spectroscopy was employed to probe the number of SLGs on the CPWRs. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) shows the experimental Raman spectra after one (1L), two (2L), and three (3L) SLGs deposited on the SiO\u003csub\u003e2\u003c/sub\u003e thin films. The G band, located around 1590 cm\u003csup\u003e− 1\u003c/sup\u003e, corresponds to the in-plane rocking vibrations of carbon atoms in the hexagonal rings. The D band, located around 1350 cm\u003csup\u003e− 1\u003c/sup\u003e is associated with disorder effects in the graphene layer. It arises from vibrations in the hexagonal carbon rings adjacent to flake edges, impurities, and defects [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. The 2D peak, situated around 2730 cm\u003csup\u003e− 1\u003c/sup\u003e, is an overtone of the D peak, arising from two-phonon scattering process.\u003c/p\u003e\u003cp\u003eIt is known that the Raman spectra of graphene changes its characteristic depending on both the quality of the carbon atoms plane and the numbers of stacked SLGs. In particular, the FWHM of the 2D band is related to the degree of crystallinity of the bidimensional material [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], the I\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e band ratio is related to general disorder effects in sp² carbon structures [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], while both the spectra position of the 2D band [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and the I\u003csub\u003eG\u003c/sub\u003e/I\u003csub\u003e2D\u003c/sub\u003e ratio serve as a reliable indicator of the number of stacked graphene layers [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. To have a better picture of the evolution of the characteristics of the Raman spectra depending on the number of SLGs, we report the values of the parameters we described above in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eI\u003csub\u003eG\u003c/sub\u003e/I\u003csub\u003e2D\u003c/sub\u003e, I\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e, FWHM and spectral position of the 2D band for one, two and three SLGs deposited on the Au/SiO\u003csub\u003e2\u003c/sub\u003e resonator.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e ratio\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eI\u003csub\u003eG\u003c/sub\u003e/I\u003csub\u003e2D\u003c/sub\u003e ratio\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePosition − 2D (cm\u003csup\u003e− 1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFWHM − 2D (cm\u003csup\u003e− 1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1 SLG\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4x10\u003csup\u003e− 2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4x10\u003csup\u003e− 1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2695\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2 SLG\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3x10\u003csup\u003e− 2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7x10\u003csup\u003e− 1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2703\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3 SLG\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3x10\u003csup\u003e− 1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2710\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eHerein, we observe a spectral shift of the 2D band of about 15 cm\u003csup\u003e− 1\u003c/sup\u003e passing from one SLG (2695 cm\u003csup\u003e− 1\u003c/sup\u003e) to three SLGs (2710 cm\u003csup\u003e− 1\u003c/sup\u003e), while the ratio I\u003csub\u003eG\u003c/sub\u003e/I\u003csub\u003e2D\u003c/sub\u003e varies from 0.4 to about 1.3. The observed behavior is very similar to the results reported in [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] and confirms the possibility to control the number of SLGs deposited on the Au/SiO\u003csub\u003e2\u003c/sub\u003e bilayer using our experimental protocol.\u003c/p\u003e\u003cp\u003eObserving Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a), we highlight that the emergence of the D peak after the transfer of a third SLG is likely attributable to the accumulation of various impurities during the sequential transfer process the samples underwent, such as Fe\u003csub\u003e2\u003c/sub\u003eCl\u003csub\u003e3\u003c/sub\u003e residues and leftover polymer remnants. It is noted that the sequential transfer of graphene layers hence changes the I\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e ratio from values of the order of 10\u003csup\u003e− 2\u003c/sup\u003e to about 0.3 after the third SLG transfer. Additionally, the Raman spectra reveals that the FWHM of the 2D band varies, with the one SLG sample (1L) showing an FWHM of approximately 30 cm\u003csup\u003e− 1\u003c/sup\u003e, and the three SLGs sample (3L) exhibiting a FWHM of about 38 cm\u003csup\u003e− 1\u003c/sup\u003e. This variation indicates high crystallinity in the samples [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], despite the introduction of the small disorder expressed by the I\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e ratio.\u003c/p\u003e\u003cp\u003eInterestingly, as shown in other works in the literature [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], one may relate the I\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e band ratios, associated with the structural quality of graphene, with the optical anisotropy of the material. Our high-quality graphene with values of I\u003csub\u003eD\u003c/sub\u003e/I\u003csub\u003eG\u003c/sub\u003e band of the order of 0.3 (or lower) should present an optical anisotropy α\u003csup\u003eo\u003c/sup\u003e/α\u003csup\u003ee\u003c/sup\u003e higher than 2.5.\u003c/p\u003e\u003ch3\u003eOptical characterization of the CPWRs\u003c/h3\u003e\u003cp\u003eThe thin film of gold has been characterized by SPR spectroscopy before the deposition of the SiO\u003csub\u003e2\u003c/sub\u003e guiding layer, to fix the first trial values for both the thickness (t\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e) and dielectric constant (ε\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e) of the gold layer at both wavelengths. Subsequently, reflectivity measurements have been performed in water environment at both wavelengths and for both TM and TE polarization after the deposition of the SiO\u003csub\u003e2\u003c/sub\u003e layer.\u003c/p\u003e\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) is shown the reflectivity curve in both TE and TM polarization of the CPWRs at 783 nm in water environment, where is notable the presence of three modes, the surface plasmon resonance (SPR) at higher angle of incidence (or TM\u003csub\u003e0\u003c/sub\u003e), the TM\u003csub\u003e1\u003c/sub\u003e and the TE\u003csub\u003e0\u003c/sub\u003e photonic modes at lower angles. The measurements and fit at the wavelength of 633 nm, represented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b) only reports the modes TM\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e0\u003c/sub\u003e, since the SPR mode is theoretically located at an incident angle above 65\u003csup\u003e0\u003c/sup\u003e degrees inside the SF4 prism, which cannot be probed in our experimental apparatus. With each experimental curve, is also reported as a line the fit on the reflectivity spectra.\u003c/p\u003e\u003cp\u003eTo obtain the optical parameters of the Au/SiO\u003csub\u003e2\u003c/sub\u003e bilayers for which we have an optimal fit of the reflectivity curves at both wavelengths and polarizations, we started by using the values t\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e and ε\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e measured on the bare gold samples to fit the SPR mode at 783 nm. Please note that for both wavelengths the SPR angle does not depend on the SiO\u003csub\u003e2\u003c/sub\u003e thickness, while the resonance position of the photonic TM\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e0\u003c/sub\u003e modes instead depends on both thickness and refractive index of the fused silica layer, coherently with the distribution of the evanescent field reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Hence, the SPR mode is initially used for the determination of the first trial value of dielectric constant of the fused silica at 783 nm (ε \u003csup\u003eSiO2\u003c/sup\u003e\u003csub\u003e783\u003c/sub\u003e). After, we look for a value of the SiO\u003csub\u003e2\u003c/sub\u003e thickness (t\u003csub\u003eSiO2\u003c/sub\u003e) which fits the angular positions of the TM\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e0\u003c/sub\u003e modes at 783 nm.\u003c/p\u003e\u003cp\u003eIn the case that we cannot find a good match for both the three modes (SPR, TM\u003csub\u003e1\u003c/sub\u003e, TE\u003csub\u003e0\u003c/sub\u003e), we repeat the whole procedure by changing the value ε\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e of a maximum of 5%, which takes in account the possible variations in the real part of the dielectric constant of the gold thin film produced by electron beam deposition, as reported in a previous work [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eOnce obtained the optical parameters of the waveguide at 783 nm, we impose that for fused silica it holds the relation ε\u003csup\u003eSiO2\u003c/sup\u003e\u003csub\u003e633\u003c/sub\u003e/ε\u003csup\u003eSiO2\u003c/sup\u003e\u003csub\u003e783\u003c/sub\u003e = 1.0047 [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], and repeat a fit procedure on the resonance angles for the TM\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e0\u003c/sub\u003e modes by letting as free parameter the dielectric constant of the gold layer at 633 nm, changing the value ε\u003csup\u003etrial\u003c/sup\u003e\u003csub\u003eAu\u003c/sub\u003e of a maximum of 5%.\u003c/p\u003e\u003cp\u003eUsing the reported computational strategy, we obtained an optimal fit for a thickness of the gold thin film of about 41 nm, with dielectric constants coherent in comparison to the literature of (-12.82 + I 1.34) and (-25.17 + I 1.57) at the wavelengths of 633 nm and 783 nm, respectively. We obtained a thickness of the SiO\u003csub\u003e2\u003c/sub\u003e layer of about 732 nm and dielectric constants of 2.12 and 2.13 for 783 nm and 633 nm, respectively. The results are reported in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThickness and dielectric constant of Au and SiO\u003csub\u003e2\u003c/sub\u003e thin films composing the CPWRs at the wavelengths of 633 nm and 783 nm.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLayer\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003et (nm)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eε\u003csub\u003er\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e\u003csub\u003e633nm / 783nm\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eε\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e\u003csub\u003e633nm / 783nm\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAu\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-12.82 / -25.17\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.34 / 1.57\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e732\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.13 / 2.12\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eIt is worth noting that the theoretical full width half maximum (FWHM) of the SPR, TM\u003csub\u003e1\u003c/sub\u003e and TE\u003csub\u003e0\u003c/sub\u003e modes are about 2\u003csup\u003eo\u003c/sup\u003e, 0.2\u003csup\u003eo\u003c/sup\u003e and 0.02\u003csup\u003eo\u003c/sup\u003e, respectively. This behaviour is associated to the different profile of the evanescent fields along the planar structures, with TE fields extending far away from the metal region with ohmic damping, as reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThus, TE modes are extremely sharp resonances, and their full shape cannot exactly be reproduced with our experimental system having a minimum experimental step of about 0.005\u003csup\u003eo\u003c/sup\u003e. This explain why in TE polarization we can fit extremely well the experimental resonance angle, but we are not able to fit the experimental FWHM, which is artificially enlarged due to the angular limitations of our system.\u003c/p\u003e\u003ch2\u003eMeasurement of the optical anisotropy of graphene layers\u003c/h2\u003e\u003cp\u003eDirect transfer of SLG on gold is known to lead to a redistribution of the electrons at the Au/SLG/water interface which can enhance the performances of SPR sensors [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], but is detrimental if the aim is to measure the optical constant of an ideal free standing SLG, since the charge transfer will control the value of the optical susceptivity and conductivity of the SLG interacting with gold [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The use of a dielectric spacer between the gold and the SLG has been properly used in past works [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], where to obtain unique results (two independent measurements for 3 parameters, the thickness \u003cem\u003et\u003c/em\u003e and optical constants \u003cem\u003en\u003c/em\u003e and κ) the authors assumed the approximation of a constant refractive index between 670 nm and 785 nm.\u003c/p\u003e\u003cp\u003eIn Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a-d), we reported the reflectivity spectra of the CPWRs with different layers of graphene, at both wavelengths and polarizations, where a layer of about 730 nm of SiO\u003csub\u003e2\u003c/sub\u003e is acting as spacer between the layers of graphene and the gold film. It is evident in panel (a) that the transfer of the SLGs on the Au/SiO\u003csub\u003e2\u003c/sub\u003e resonator does not influence the angular position of the plasmonic mode, which is fixed at 61.3\u003csup\u003eo\u003c/sup\u003e, and will not be considered for the evaluation of the optical constant of the SLG. The reason for this behaviour can be understood by the near electromagnetic fields reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, where it is evident that the evanescent field associated to the SP mode does not reach the region of the SLG. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(e,f), he variation in the angle of resonance θ\u003csup\u003eres\u003c/sup\u003e of both TM and TE modes depending on the number of graphene transferred on the Au/SiO\u003csub\u003e2\u003c/sub\u003e bilayer, at both wavelengths. Herein we observe that, at least for the TM modes, the angle of resonance increases linearly with the number of SLGs, and we obtain an average angular shift per layer δθ\u003csub\u003eSLG\u003c/sub\u003e of 7.88 x 10\u003csup\u003e− 2 o\u003c/sup\u003e/layer and 6.46 x 10\u003csup\u003e− 2 o\u003c/sup\u003e/layer at 783 nm and 633 nm, respectively. These values are about five times smaller than reported in [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], due to the lowest sensitivity of the photonic modes with the respect to the SPR mode investigated in the work of Jussila et al., at least for thin samples such as graphene layers. It is interesting to note that, together with a progressive angular shift, also the FWHM of the reflectivity spectra increases with the number of graphene layers, coherently as reported for the SPR mode in [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The linearity of the angular shift depending on the number of graphene layers, allow us to assume that each graphene layer deposited subsequently on the CPWRs has the same thickness and the same refractive index.\u003c/p\u003e\u003cp\u003eThe characterization of the SLGs starts with the analysis of the TM curves at both wavelengths (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a,c)), associated to the out-plane oscillation and extraordinary refractive index n\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e + I κ\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e. We remember here that the thickness t\u003csub\u003eSLG\u003c/sub\u003e and real part of the refractive index n\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e of the SLG have a high influence on the position of the resonance angle, while the imaginary part κ\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e does not influence significantly the resonant angle but the full width half maximum (FWHM) of the reflectivity curve. If the determination of κ\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e is obtained without ambiguity through the experimental FWHM, exist infinite couples of values (t\u003csub\u003eSLG\u003c/sub\u003e, n\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e) which reproduce the observed experimental angular shift δθ\u003csub\u003eSLG\u003c/sub\u003e [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], so that we have an infinite set of solutions (t\u003csub\u003eSLG\u003c/sub\u003e, n\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e, κ\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e) at each of the wavelengths. The behaviour of each set is that when the thickness gets higher, both n\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e and κ\u003csup\u003ee\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e decrease to match the experimental angular shift and FWHM. The unicity of the solution is obtained through Eq.\u0026nbsp;1, which is satisfied for a unique value of t\u003csub\u003eSLG\u003c/sub\u003e. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a,b), we represented the theoretical fits of the experimental TM reflectivity curves for different number of SLGs. The shift of the reflectivity curves is well described by the fit, but not the minimum reflectivity, at least when more than one SLG is present. While the theoretical curves indicate a progressive lower value of the minimum reflectivity with the number of graphene layers, the experimental curves show an opposite trend. We believe that such a behaviour may be associated to the impurities inserted in the multi-layer structure after the transfer of the subsequent SLGs. In fact, also the Raman measurements reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e indicate the presence of defects, probably polymeric residues sticking on the surface of the SLG after the transfer of the second graphene. We attribute this phenomenon to the kind of interrogation of the interfaces by evanescent modes which, differently from free electromagnetic waves techniques such as ellispsometry, is extremely sensitive to the presence of impurities and defects in the near field zone, which act as local fields ‘scatterers.\u003c/p\u003e\u003cp\u003eOnce obtained the values of the extraordinary optical constant and of t\u003csub\u003eSLG\u003c/sub\u003e using the TM modes, we pass to the analysis of the TE modes. As evident in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c,d), the TE modes are rapidly quenched by the transfer of graphene layers, and the reflectivity damp disappears after the transfer of the third graphene layer. Although the rapid quenching, the depth of the modes is enough to guarantee a good fit at the wavelength of 633 nm, as reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c), which fixes the optical constant n\u003csup\u003eo\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e + I κ\u003csup\u003eo\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e of the SLGs for in-plane oscillations at such a wavelength. Subsequently, a second fit is done on the TE reflectivity curve at 783 nm but taking in account only the matching of the resonance angle, which fixes the value of the real part n\u003csup\u003eo\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e of the refractive index at the second wavelength. Finally, under the hypothesis that the dispersion relation obtained by fine structure dependent universal opacity of graphene [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] is valid independently for both TE (in-plane) and TM (out-plane) polarizations, we use Eq.\u0026nbsp;1 to retrieve the imaginary part of the refractive index κ\u003csup\u003eo\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e for in-plane oscillations at 783 nm. In this last case, we can observe in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c) that the FWHM of the fit is larger than the experimental one, which indicates a possible overestimation of κ\u003csup\u003eo\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e.\u003c/p\u003e\u003cp\u003eBefore discussing our experimental results based on the existing literature, it is important to highlight that we also measured a second independent sample to check for the reproducibility of the results. The difference in the resonant angle between the two independent samples after the transfer of a unique SLG is less than 5 x 10\u003csup\u003e− 2\u003c/sup\u003e deg, similarly as reported in [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], showing the good reproducibility of both fabrication and measurement of the reflectivity. Repeating our computational approach on the independent sample with a unique SLG, we obtained a second independent evaluation of the thickness and optical constant of the single graphene layer. As result for both thickness and optical constants, we consider the average of the values (v\u003csub\u003e1\u003c/sub\u003e, v\u003csub\u003e2\u003c/sub\u003e) obtained from the measurements on the two independent samples and take as absolute uncertainty the value of the standard deviation between the values [(v\u003csub\u003e1\u003c/sub\u003e-v\u003csub\u003e2\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e/2]\u003csup\u003e0.5\u003c/sup\u003e. The results obtained for the optical characterization of the different graphene layers by CPWRs are reported in the last raw of Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, together with the values reported in literature for both t\u003csub\u003eSLG\u003c/sub\u003e, n\u003csup\u003eo,e\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e and κ\u003csup\u003eo,e\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e at different wavelengths and using different experimental techniques.\u003c/p\u003e\u003cp\u003eBased on these results, we evaluate an accuracy in the determination of thickness, real and imaginary part of the refractive index of the SLG of about 20%, 15% and 20%, respectively. It is difficult to compare these results with the ones reported in literature using SPR spectroscopy since, at the best of our knowledge, this point is not clearly addressed in none of the works [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe linearity of the angular shift shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(e,f) suggests that, in our case, the optical anisotropy α\u003csup\u003eo\u003c/sup\u003e/α\u003csup\u003ee\u003c/sup\u003e = κ\u003csup\u003eo\u003c/sup\u003e/κ\u003csup\u003ee\u003c/sup\u003e does not depend on the number of graphene layers. Based on our results (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), we estimate the optical anisotropy to be 3.3 and 2.6 at the wavelengths of 633 nm and 783 nm, respectively. The results are coherent with what reported in the work of Yu-Lun Liu et al. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], where they measured by ellipsometry an optical anisotropy between 2.7 and 3.7 at grazing incidence on a high-quality graphene at the wavelength of 633 nm. It is worth noting that the lowest value of the anisotropy at 783 nm is probably due to the overestimation of κ\u003csup\u003ee\u003c/sup\u003e that we observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(c).\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues of t\u003csub\u003eSLG\u003c/sub\u003e, n\u003csup\u003eo,e\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e and κ\u003csup\u003eo,e\u003c/sup\u003e\u003csub\u003eSLG\u003c/sub\u003e reported in literature using different experimental techniques and substrates. In the last two columns are reported the approximations or constrains used for the determination of the parameters. In the columns \u003cem\u003en\u003c/em\u003e and \u003cem\u003eκ\u003c/em\u003e the apex indicates, when possible, the polarization (o-ordinary axis, e-extraordinary axis) and the wavelength.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTechnique\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRange (nm)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003en\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eκ\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003et(nm)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eComments\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ec-Si/SiO\u003csub\u003e2\u003c/sub\u003e/SLG\u003c/p\u003e \u003cp\u003e(exfoliated)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpectroscopic ellipsometry\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e210–1000\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.7 \u003csup\u003e(633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e2.8 \u003csup\u003e(783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.4\u003csup\u003e(633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.5\u003csup\u003e(783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003cp\u003eObtained by optimization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo anisotropic investigation [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Graphite\u003c/p\u003e \u003cp\u003e(Not Reported)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpectroscopic\u003c/p\u003e \u003cp\u003eellipsometry\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300–1000\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.6 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.7 \u003csup\u003e(e−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e2.8 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.6 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.4 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0 \u003csup\u003e(e−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.6 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003cp\u003eObtained by optimization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWith anisotropic discrimination [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/HOPG\u003c/p\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/SLG\u003c/p\u003e \u003cp\u003e(CVD)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMueller Matrix Ellispometry\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e200–1200\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.6 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.4 \u003csup\u003e(e−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e2.7 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.4 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e2.8 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e2.8 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.2 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0 \u003csup\u003e(e−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.4 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.4 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.6 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003cp\u003eConsidered as standard\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWith anisotropic discrimination only on highly oriented pyrolytic graphite (HOPG)\u003c/p\u003e \u003cp\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/SLG\u003c/p\u003e \u003cp\u003eUp to five layers\u003c/p\u003e \u003cp\u003e(CVD)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpectroscopic ellipsometry\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300–1000\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.74 \u003csup\u003e(633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.77 \u003csup\u003e(783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.45 \u003csup\u003e(633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0.47 \u003csup\u003e(783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.32 Optimized by depolarization\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo anisotropic investigation\u003c/p\u003e \u003cp\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSi/SiO\u003csub\u003e2\u003c/sub\u003e/SLG\u003c/p\u003e \u003cp\u003eUp to 2 layers and graphite.\u003c/p\u003e \u003cp\u003e(Exfoliation)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpectroscopic ellipsometry\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e400–2500\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.0 \u003csup\u003e(633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e3.0 \u003csup\u003e(783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.15 \u003csup\u003e(633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.42 \u003csup\u003e(783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003cp\u003eConsidered as standard\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo anisotropic investigation. They use the relation κ = 5.446 µm\u003csup\u003e− 1\u003c/sup\u003e λ/n, where n is constant [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/PG\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eReflectivity measurements\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e250–620\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.74 \u003csup\u003e(o−620)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.53 \u003csup\u003e(e−620)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.40 \u003csup\u003e(o−620)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0 \u003csup\u003e(e−620)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWith anisotropic discrimination on pyrolytic graphite (PG) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Au/SLG and\u003c/p\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/SLG. Up to 5 layers.\u003c/p\u003e \u003cp\u003e(CVD)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePolarized reflectance and SPR spectroscopy\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e634\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.7 \u003csup\u003e(e−634)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.4 \u003csup\u003e(e−634)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.335\u003c/p\u003e \u003cp\u003eConsidered as standard\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCharge transfer due to Au/SLG interface. Use of TM modes → n\u003csup\u003ee\u003c/sup\u003e (out of plane). Assume that Au/SLG interface is equal to SiO\u003csub\u003e2\u003c/sub\u003e/SLG interface.\u003c/p\u003e \u003cp\u003eNo anisotropic investigation [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Au/SLG\u003c/p\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Au/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/SLG\u003c/p\u003e \u003cp\u003eUp to 3 layers.\u003c/p\u003e \u003cp\u003e(CVD)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSPR spectroscopy\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e670/785\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.1 \u003csup\u003e(e−670)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e3.1 \u003csup\u003e(e−785)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e3.7 \u003csup\u003e(e−670)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e3.7 \u003csup\u003e(e−785)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5 \u003csup\u003e(e−670)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0.5 \u003csup\u003e(e−785)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0.8 \u003csup\u003e(e−670)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0.8 \u003csup\u003e(e−785)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFirst SLG on Au = 1.1 Second SLG = 0.31\u003c/p\u003e \u003cp\u003eFirst SLG on Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e = 0.8 Subsequent SLGs between 0.3 and 0.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo anisotropic investigation.\u003c/p\u003e \u003cp\u003eUse of TM modes → n\u003csup\u003ee\u003c/sup\u003e (out of plane).\u003c/p\u003e \u003cp\u003eIt is assumed that the values of n and κ are constants, without dispersion\u003c/p\u003e \u003cp\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Au/SLG\u003c/p\u003e \u003cp\u003e(CVD)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSPR spectroscopy\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e783\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.3 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.3 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.9\u003c/p\u003e \u003cp\u003eObtained by changing the external refractive index\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo anisotropic investigation.\u003c/p\u003e \u003cp\u003eUse of TM modes → n\u003csup\u003ee\u003c/sup\u003e (out of plane).\u003c/p\u003e \u003cp\u003eAn Au/H\u003csub\u003e2\u003c/sub\u003eO/SLG/H\u003csub\u003e2\u003c/sub\u003eO effective layer was considered [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e/Au/SiO\u003csub\u003e2\u003c/sub\u003e/SLG\u003c/p\u003e \u003cp\u003eUp to 3 layers.\u003c/p\u003e \u003cp\u003e(CVD)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCoupled Plasmon-Waveguide spectroscopy\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e633/783\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.5 ± 0.3 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e4.0 ± 0.5 \u003csup\u003e(e−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e3.3 ± 0.3 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e3.8 ± 0.6 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.3 ± 0.2 \u003csup\u003e(o−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0.4 ± 0.1 \u003csup\u003e(e−633)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e1.3 ± 0.2 \u003csup\u003e(o−783)\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e0.5 ± 0.1 \u003csup\u003e(e−783)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.1 ± 0.2\u003c/p\u003e \u003cp\u003eFor all the SLGs\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eThis work\u003c/b\u003e: with anisotropic investigation. Use of the dispersion relation expressed by Eq.\u0026nbsp;1:\u003c/p\u003e \u003cp\u003en\u003csub\u003e λ1\u003c/sub\u003eκ\u003csub\u003eλ1\u003c/sub\u003e / n\u003csub\u003e λ2\u003c/sub\u003eκ\u003csub\u003eλ2\u003c/sub\u003e = Im[ε\u003csup\u003eSLG\u003c/sup\u003e\u003csub\u003e λ1\u003c/sub\u003e]/Im[ε\u003csup\u003eSLG\u003c/sup\u003e\u003csub\u003e λ2\u003c/sub\u003e] = λ\u003csub\u003e1\u003c/sub\u003e/λ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eWe also observe that the thickness of the SLG does not depend on the number of graphene layers, differently from the work of Jussila et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] where a value of thickness of about 1 nm was observed only after the transfer of the first SLG on both Au or SiO\u003csub\u003e2\u003c/sub\u003e substrates, while values near to 0.3 nm were measured for the subsequent graphene layers. Interestingly, values of thickness of the order of 1 nm are only observed in literature using evanescent electromagnetic probes [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], while none of the works based on ellipsometry report this value. This is probably an indication that the evanescent waves can detect interface effects, comprising roughness and impurities effects, with a better sensitivity than techniques based on free electromagnetic waves. The roughness of the substrate over which the graphene layers are transferred is reported to have a deep effect on the accuracy in the determination of the optical constants [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] and is supposed to control the value of thickness of the SLG based on physical processes yet not fully understood [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In our case, the average root mean square surface roughness of the SiO\u003csub\u003e2\u003c/sub\u003e surface has been characterized to be around 3 nm in previous research [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], which is higher than the 1.8 nm reported by Jussila et al. that measured a thickness of the first SLG on Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e substrates of about 0.8 nm [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Our experimental value of 1.1 nm is also similar to the values of thickness measured by AFM in [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], although AFM is considered to overestimate the real thickness of the SLG [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eLooking at Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we realize that few works report the anisotropy of the SLG or graphite by ellipsometry [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], and all of them consider that the imaginary part of the extraordinary refractive index (κ\u003csup\u003ee\u003c/sup\u003e) is zero. This is not what is observed in all the investigations using evanescent waves probes with TM polarization, giving a value of κ\u003csup\u003ee\u003c/sup\u003e in the red visible region between 0.3 and 1.4 [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. We believe that such a behaviour may be associated to the presence of polymeric residues from the SLG transfer process, which inevitably act as both scatterers of the evanescent wave and dispersive elements eventually leading to an overestimation of the value of both the real and imaginary parts of the refraction index [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. In fact, while all of the ellipsometric studies report a refractive index value below or equal to 3, investigations by the use of evanescent interfacial fields report values of \u003cem\u003en\u003c/em\u003e\u003csup\u003ee\u003c/sup\u003e which range between 2.3 and 3.1 when the SLG is deposited over a gold surface [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], and that raise to about 4 when the SLG is transferred on a dielectric spacer [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], similarly to the present research. This observation suggests that the quality of the transfer process may depend not only on the roughness of the substrate, but also on its nature, which might influence the affinity of polymeric particle residues and the eventual condensation at the substrate-SLG interface during the cleaning step of the transfer process.\u003c/p\u003e\u003cp\u003eIf none of the works using evanescent waves reports a dispersion of the refractive index similarly to the ellipsometric studies, our approach is instead completely based on the validity of the dispersion relation expressed by Eq.\u0026nbsp;1, which inherently gives a dispersive character to our results. Interestingly, the trend of the dispersion for both TM and TE polarization are coherent with the results reported by Kravets et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] for graphite. In fact, in that work \u003cem\u003en\u003c/em\u003e\u003csup\u003eo\u003c/sup\u003e and \u003cem\u003en\u003c/em\u003e\u003csup\u003ee\u003c/sup\u003e increases and decreases with the wavelength, respectively, similarly to our results.\u003c/p\u003e\u003cp\u003eFurtherly, the values that we measured for \u003cem\u003en\u003c/em\u003e\u003csup\u003eo\u003c/sup\u003e and κ\u003csup\u003eo\u003c/sup\u003e for in-plane polarization are similar to the ones reported in literature by ellipsometry [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] while, to the best of our knowledge, there are no other reports on the investigation of the in-plane ordinary refractive index of the SLG by the use of evanescent fields.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eCoupled plasmon-waveguide resonators spectroscopy has been applied to the characterization of the optical anisotropy of planar and large area multilayer graphene in the visible and near infrared regions. The experimental results were interpreted by assuming that the dispersion relation obtained from the universal opacity of graphene is valid for both in-plane and out-plane polarization. Although this assumption is found to lead to a possible overestimation of the imaginary part of the refractive index at one of the wavelengths, the values of the optical constants and of the anisotropy measured for a single layer graphene can be well explained in the frame of literature reports. The thickness and the real part of the extraordinary out-plane refractive index of the SLG are higher than reported in average for spectroscopic ellipsometry, but perfectly matching with other results reported in literature using SPR spectroscopy, probably suggesting that the near fields are highly sensitive to the particle residuals and interfacial effects which are less observable in spectroscopic ellipsometry. Using the TE modes of the CPWRs we also measured the optical constants of the SLGs along the ordinary axes using evanescent fields, obtaining an optical anisotropy between 2.6 and 3.3 in the NIR and visible regions, respectively. These values, together with the Raman spectroscopy results, indicates the presence of high quality SLGs, but with the presence of a detectable amount of defects after the transfer process. We evaluated the accuracy of the proposed method to be of the order of 20%, demonstrating that evanescent field spectroscopy by CPWRs can be considered as a valid low-cost alternative for the optical characterization of large area anisotropic uniaxial bidimensional materials.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis study was financed in part by the Coordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior-Brasil (CAPES)- Finance Code 001, and CNPq productivity grant. Funding from FAPERJ for processes E-26/211.540/2021, E-26/211.279/2021, E-26/010.002138/2019, E-26/010.000980/2019, E-26/200.810/2021, E-26/210.104/2020, and E-26/210.726/2021 are acknowledged.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eQ.Z and T.D.R. wrote the main manuscript text, A.N.B/N.S/M.E.H.M.C/F.L were responsible for the synthesis and Raman characterization of the graphenes; Tahir/R.K/S.F/K.Q.C/G.M participated in development of the numerical codes and in the data analysis; Q.Z/G.M fabricated and characterized the plasmon-waveguide resonators. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de N\u0026iacute;vel Superior-Brasil (CAPES)- Finance Code 001, and CNPq productivity grant. Funding from FAPERJ for processes E-26/211.540/2021, E-26/211.279/2021, E-26/010.002138/2019, E-26/010.000980/2019, E-26/200.810/2021, E-26/210.104/2020, and E-26/210.726/2021 are acknowledged.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eNair, R. R., Blake, P., Grigorenko, A. N., Novoselov, K. S., Booth, T. J., Stauber, T., ... \u0026amp; Geim, A. K. (2008). Fine structure constant defines visual transparency of graphene. science, \u003cem\u003e320\u003c/em\u003e(5881), 1308-1308.\u003c/li\u003e\n \u003cli\u003eKuzmenko, A. B., van Heumen, E., Carbone, F., \u0026amp; van der Marel, D. (2007). Universal dynamical conductance in graphite. \u003cem\u003earXiv preprint arXiv:0712.0835\u003c/em\u003e.\u003c/li\u003e\n \u003cli\u003eLiu J-M, Lin I-T. Optical Properties. In:\u0026nbsp;Graphene Photonics. Cambridge University Press; 2018:66-106.\u003c/li\u003e\n \u003cli\u003eWeber, J. W., Calado, V. E., \u0026amp; Van De Sanden, M. C. M. (2010). 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Anisotropy of the optical constants and the band structure of graphite. \u003cem\u003ePhysical review\u003c/em\u003e, \u003cem\u003e178\u003c/em\u003e(3), 1340.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"plasmonics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"plas","sideBox":"Learn more about [Plasmonics](https://www.springer.com/journal/11468)","snPcode":"11468","submissionUrl":"https://submission.nature.com/new-submission/11468/3","title":"Plasmonics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Graphene, Optical anisotropy, Coupled plasmon-waveguide resonators","lastPublishedDoi":"10.21203/rs.3.rs-6947590/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6947590/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe characterization of the optical constants of single layer graphene has been subject of deep investigation in the last two decades and the optical anisotropy has been discovered to be an important parameter linked to the structural defects of the plane of the carbon atoms. Using graphene loaded coupled plasmon-waveguide resonator, which offer pure transverse electric or transverse magnetic electromagnetic modes, we demonstrate the possibility to characterize the optical anisotropy using evanescent electromagnetic fields in the visible and middle infrared range of a single, double and triple layer of graphene. On the assumption that a universal opacity of graphene holds for both in-plane and out-plane electronic displacement, we extract the anisotropic coefficient of the graphene layers with an accuracy of about 20%. The results are coherent with the literature and indicate that coupled plasmon-waveguide resonator spectroscopy is a valid low-cost and simple technique for the alternative optical characterization of uniaxial anisotropic bidimensional materials.\u003c/p\u003e","manuscriptTitle":"Optical anisotropy of multilayer graphene probed by coupled plasmon- waveguide resonators","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-01 07:05:45","doi":"10.21203/rs.3.rs-6947590/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-09T13:03:21+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-06T12:42:52+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-03T07:41:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"177401586393917944314541909503379151752","date":"2025-06-26T11:39:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"329230416029766671826046324150678365518","date":"2025-06-26T11:14:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-26T11:08:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-25T08:30:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-25T08:28:12+00:00","index":"","fulltext":""},{"type":"submitted","content":"Plasmonics","date":"2025-06-22T04:04:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"plasmonics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"plas","sideBox":"Learn more about [Plasmonics](https://www.springer.com/journal/11468)","snPcode":"11468","submissionUrl":"https://submission.nature.com/new-submission/11468/3","title":"Plasmonics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"add6c064-2d04-402c-973a-3f680cc5c7c1","owner":[],"postedDate":"July 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-08-25T16:36:14+00:00","versionOfRecord":{"articleIdentity":"rs-6947590","link":"https://doi.org/10.1007/s11468-025-03237-4","journal":{"identity":"plasmonics","isVorOnly":false,"title":"Plasmonics"},"publishedOn":"2025-08-19 16:29:32","publishedOnDateReadable":"August 19th, 2025"},"versionCreatedAt":"2025-07-01 07:05:45","video":"","vorDoi":"10.1007/s11468-025-03237-4","vorDoiUrl":"https://doi.org/10.1007/s11468-025-03237-4","workflowStages":[]},"version":"v1","identity":"rs-6947590","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6947590","identity":"rs-6947590","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}