Polarimetry Using Graphene-integrated Anisotropic Metasurfaces

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Polarimetry Using Graphene-integrated Anisotropic Metasurfaces Minwoo Jung, Shourya Dutta Gupta, Nima Dabidian, Igal Brener, Maxim R. Shcherbakov, and Gennady Shvets ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01216 • Publication Date (Web): 31 Oct 2018 Downloaded from http://pubs.acs.org on November 2, 2018

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Polarimetry Using Graphene-integrated Anisotropic Metasurfaces Minwoo Jung,∗,† Shourya Dutta-Gupta,‡ Nima Dabidian,¶ Igal Brener,§ Maxim Shcherbakov,k and Gennady Shvets∗,k †Department of Physics, Cornell University, Ithaca, New York, 14853, USA ‡Department of Materials Science and Metallurgical Engineering, Indian Instiute of Technology Hyderabad, Sangareddy, Telangana, 502285, India ¶Department of Physics and Center for Nano and Molecular Science and Technology, The University of Texas at Austin, Austin, Texas 78712, USA §Sandia National Laboratories, Albuquerque, New Mexico, 87185, USA kSchool of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA E-mail: [email protected]; [email protected] Abstract Polarization is one of the important properties of light, and its detection is of significant interest for various fundamental and practical applications. We demonstrate a mid-infrared polarimetry device using a gate-tunable graphene-integrated anisotropic metasurface. The Stokes parameters of the incident light are extracted by sweeping the gate voltage applied to the device and subsequent fitting of the measured reflected intensities. Considering sub-picosecond carrier relaxation times in graphene, the polarization measurement rate of our device is governed only by the speed of the gate voltage sweep. Thus, our work serves as a proof-of-principle demonstration for highspeed microscale polarimetric devices.

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Keywords Plasmonic metasurfaces, Polarimetry, Graphene, Fano resonance Plasmonic metasurfaces, the periodic arrangement of sub-wavelength metallic structures, have been exploited for sensing, holography, realization of ultra-thin optical components and non-linear signal generation. 1–16 In particular, integration of plasmonic structures with 2D materials like single-layer graphene (SLG) opens new pathways for active control over the properties of plasmonic metasurfaces. 4,10,13,17–22 The primary advantage of graphene over other active materials (e.g. liquid crystals, 23 temperature-controlled vanadium dioxide 24 and semiconductors with tunable charge depletion 25 or carrier densities 26 ) is the higher operational speeds 17,27 and the absence of an absorption lines in the mid-infrared (mid-IR) spectral region. Most switching operations in graphene-integrated metasurfaces are performed by changing the carrier density in the SLG by applying a gate voltage, which in turn controls the Fermi level and the optical conductivity of SLG. 13,17,19 Using this approach, modulators of intensity, phase and polarization have been demonstrated. 13,17,19,27 Yao et al. showed that graphene-integrated metasurfaces could have a wavelength tuning of almost 1.5 µm in the mid-IR with switching times of a few nanoseconds. 27 Semiconductor modulators based on voltage-controlled charge depletion have also achieved megahertz-rate switching speed, but only for terahertz waves. 28,29 In addition to modulating the fundamental properties of light, it is possible to exploit such active devices for practical applications. Dabidian et al. exploited the active control over the phase for developing an accurate non-moving motion detector with sub-50 nm error. 19 Even though polarization state generation has been demonstrated using graphene-integrated metasurfaces, 19,20 they have not yet been applied for polarization detection. Note that conventional polarization measurements, such as rotating analyzer polarimetry, 30 requires multiple measurements of the light intensities by placing a polarizer and a quarter-wave plate at different angles. The Stokes parameters can be then extracted from the measured intensities. Even though high accuracy can be achieved using more advanced modulators, 2


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e.g., based on liquid-crystals 31 or photoelastic materials, 32 their speed is limited below a megahertz due to the relatively slow time response of such materials. This prevents the application of conventional polarimeters from those situations where the polarization state of the analyzed light changes rapidly with time. Recently, a different concept for division of amplitude polarimeters (DoAmPs) operating on the principle of wavefront separation has been demonstrated. 33–37 Such novel DoAMPs rely on judiciously designed metasurfaces splitting different polarization components of the incoming light into separate plane waves which are independently detected. Metasurface-based DoAMPs are fast, less bulky than their conventional predecessors, 38 and have already been used for detecting the polarization state of light propagating through an optical fiber. 35 Some of the limitations of metasurfacebased DoAMPs include the complexity of the polarization-splitting metasurfaces, the need for multiple detectors (of focal plane arrays, if imaging capability is desired), and the loss of intensity due to the separation of different polarization components. In this paper, we propose a method for measuring the polarization state of an incident beam using graphene-integrated anisotropic metasurfaces (GIAMs). We fabricate an electrically-actuated device that supports a gate-tunable spectral shift of a plasmonic resonance of the metasurface excited by the polarization component directed along one of the principal axes, while maintaining a broadband and voltage-independent response along the other principal axis. A straightforward calibration of the voltage-controlled GIAM, which needs to be performed only once, consists of extracting a diagonal Jones matrix of the GIAM JGIAM (Vg ) (see Eq. 1) as a function of the gate voltage Vg . The Stokes parameters experimentally measured with the GIAM are found to be in excellent agreement with those measured using the conventional rotating analyzer method, paving the way to a number of promising fast and ultra-compact polarimetry devices. Those include active polarimetric devices, such as polarimetric lidars that can benefit the most from the resonant nature of plasmonic metasurfaces. 39 Unlike the majority of polarimetric devices that typically measure three out of four Stokes parameters, 33 a GIAM-based polarimeter can extract all four Stokes parameters,

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including differentiating between right- and left-hand circularly polarized light. To understand the principle of action of a GIAM-based polarimeter, consider an arbi~ in which is normally trarily polarized light wave with a two-dimensional polarization vector E impinging onto a GIAM in the z -direction as shown in Figs. 1(a) and (b). The GIAM used in this work consists of a periodic array of unit cells shown in Fig. 1(a) (a unit cell’s sketch with geometry definitions) and Fig. 1(a) (an SEM image of the fabricated structure). The polarization state of light changes upon the reflection from a GIAM according to ~ out = JGIAM · E ~ in , where E ~ out is the polarization vector of the reflected light, and the Jones E matrix is given by the following expression: 



0  rxx (Vg ) JGIAM (Vg ) =  . 0 ryy (Vg )

(1)

Note that JGIAM is diagonal due to the mirror reflection symmetry of the GIAM’s with respect to xz−plane passing through the middle of the unit cell of the metasurface, see Fig. 1(a). When the incident light with intensity S0 and polarization vector cos θ; sin θeiφ reflects off the GIAM and passes through a polarizer oriented at an angle θp with respect to the x-axis, the intensity of light at the photodetector is given by I(Vg ; [θ, φ] , θp )/I0 = X(Vg )2 [cos2 θ cos2 θp + ρ(Vg )2 sin2 θ sin2 θp (2) + 0.5ρ(Vg ) sin(2θ) sin(2θp ) cos(φ − ∆φ(Vg ))], where I0 = S0 |rxx (Vg = 0V)|2 , X(Vg ) = |rxx (Vg )/rxx (Vg = 0V)|, ρ(Vg ) = |ryy (Vg )/rxx (Vg )|, and ∆φ(Vg ) = arg(rxx (Vg )) − arg(ryy (Vg )). Therefore, given the full information on the GIAM’s characteristic functions ∆φ(Vg ), ρ(Vg ), and X(Vg ) as functions of Vg , it is possible to extract the complex-valued polarization vector of the incident light (characterized by θ (i)

and φ) by fitting to Equation (2)the intensity data I (i) (Vg ) measured for a large set of (i)

voltages Vg . Because of the inevitable noise sources (e.g., in the detector), the larger is the

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(i)

number of data points Vg

that are used for the best fit, the more accurate is the extracted

polarization vector. For the experimental realization of a GIAM-based polarimeter (GIAMP), schematically illustrated in Fig. 1(d), a quantum-cascade laser (QCL) was used as source of polarized midIR radiation. A polarizer and a quarter-wave plate are placed after the QCL to generate various incident polarization states to be measured with the GIAMP. Different polarization states were obtained by rotating the polarizer with respect to the axes of the quarter-wave plate. The incident light is directed to the GIAM after reflection off a beam-splitter in order to ensure normal incidence onto a metasurface. Upon reflection from the metasurface, the beam is directed to a liquid-nitrogen cooled mercury-cadmium-telluride (MCT) detector through the beam-splitter and a polarizer.

Figure 1: (a) Geometry of a unit cell of the anisotropic metasurface periodically arranged with Px = Py = 2.1 µm periods: Lx = 0.6 µm, Ly = 1.4 µm, w = 0.25 µm, and g = 0.12 µm. (b) SEM image of the fabricated device. (c) Reflectivity spectra (Rxx(yy) = |rxx(yy) |2 ) for the incident light polarized along the y−axis (circles) at three values of Vg (color-coded), and along the x−axis (squares) at Vg = 0 V. Vertical dotted line: wavelength of operation λ0 = 6.7µm. (d) Schematic of the GIAM-based polarimeter. If the difference in the phase responses along x− and y−axes is constant over the range of Vg that we sweep (i.e. ∆φ(Vg ) = ∆φ0 ), φ cannot be uniquely determined by fitting to

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Equation (2) because the same value of the cosine function corresponds to two arguments: cos(φ − ∆φ0 ) = cos(α) ⇒ φ = ∆φ0 ± α, where α > 0 is a number determined from the fitting. Thus, for unique and precise determination of φ from the fitting, we need to determine the ± sign in front of the α > 0 coefficient, a voltage-dependent anisotropic response of the metasurface, i.e. ∆φ(Vg ) 6= const, is needed. Then the correct ± sign is determined by the sign of d∆φ/dVg . The anisotropy of the metasurface is created by the combination of a continuous nanowire and a c-shaped dipole antenna. The GIAM shown in Fig.!1 possesses two principal polarization axes: the y−axis (along the continuous nanowire) and the x−axis (perpendicular to the nanowire). For the y−polarized light, Fano interference between the broadband reflectivity from the wire and the resonant (at λR (Vg )) reflectivity from the antenna produces a sharp reflectivity dip at λ = λR that can be classified as electromagnetically-induced transparency (EIT). 19 Therefore, both the amplitude and phase of the reflected y−polarized light is dependent on the optical properties of graphene, which are determined by the gate voltage Vg . On the other hand, the x−polarized light does not exhibit any sharp spectral features in the vicinity of λ = λR . Therefore, the optical response of the GIAM to x−polarized light is not sensitive to Vg . The anisotropic metasurface was fabricated (see Methods for complete details) on top of a single layer graphene (SLG). A scanning electron microscopy (SEM) image of the fabricated device is shown in Fig. 1(b). The gate-tunable resonant reflection dips of the y−polarized light are shown in Figure 1(c) for three values of Vg . The charge-neutral point (CNP) of graphene was confirmed to be VCNP < −200 V, but the exact value could not be determined because it would have exceeded the breakdown gradient of the spacer material (SiO2 ). However, the operating principle of the GIAM polarimeter does not rely on operating near the CNP of the underlying SLG. The only criterion for operating a GIAM polarizer is that the variations of at least some of the GIAM’s characteristic functions (amplitudes and phases of the two reflectivities, rxx and rxx ) are large enough to enable numerical best fitting of Eq.1 to the polarization parameters, θ and φ. The operating wavelength λ0 is selected as

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λ0 = 6.70 µm because the variations of in ∆φ(Vg ) and ρ(Vg ) with Vg are sufficiently large at that wavelength. We have found that the operating wavelength can be varied within ∼ 100 nm around the resonant wavelength, see the Supporting Information for additional GIAM polarimetry data at λ = 6.8 µm. Prior to performing GIAM polarimetry, we first experimentally measure the components of GIAM’s Jones’ matrix at λ0 by following the procedures described below. (1) At each value of Vg , we vary the polarizer angle θp to collect a set of intensity data I(Vg ; [θ, φ] , θp ) at the detector using the light source with the known polarization state (i.e., known θ and φ); (2) the intensity data I is then fitted to Equation (2) as a function of θp , yielding the values of ∆φ(Vg ) and ρ(Vg ) as the fit parameters; (3) X(Vg ) is obtained by directly measuring the reflectivity of x−polarized light while varying Vg . More detailed discussions in the calibration process (e.g. an issue with anisotropic responses out of the beam-splitter in our experimental setup, and the calibration dataset) are provided in the Supporting Information. The measured GIAM’s characteristic functions measured at λ = λ0 are plotted in Fig. 2. As expected, X(Vg ) is almost a constant function due to the broadband response of the metasurface to the electric field polarized along the x−axis. We conclude that the modulation in ρ(Vg ) is primarily originating from the inductive shift of the resonant reflection dip for the y−polarized light. As the gating voltage Vg increases, the plasmonic resonance wavelength approaches the operating wavelength λ0 gets closer to the Fano-resonance from the longwavelength side as shown in Fig. 1(c). Accordingly, ∆φ(Vg ) decreases from ∼ 176◦ to ∼ 161◦ as Vg increases, see Fig. 2. Figures 3 and 4 provide the results of the GIAM polarimety for four different input polarization states: (1) almost right-circularly polarized (RCP), (2) almost left-circularly polarized (LCP), (3) almost x−polarized, and (4) elliptically polarized light with significant eccentricity of the polarization ellipse. Next, we compared the results of GIAM-based polarimetry with the reference data obtained using the conventional rotating analyzer technique. 30 The signs of φ in the reference measurement was chosen according to the rotation

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Figure 2: The GIAM characteristic functions—X(Vg ), ρ(Vg ), and ∆φ(Vg )—measured at λ0 = 6.7µm. The measurements were taken from Vg = −200V to 200V in increments of 5V, and the data was linearly interpolated. direction of the quarter-wave plate placed before the beam-splitter for generating various polarization states. We provide additional GIAM polarimetry results for other choices of input polarization states in the Supporting Information. In GIAM-based polarimetry, we fix the angle θp ≈ 45◦ of the analyzer in front of the detector. The choice of θp is made with the purpose of maximizing |∂φ I(Vg ; [θ, φ], θp )|, thereby improving the accuracy of determining the unknown value of φ from fitting I(Vg ; [θ, φ], θp ) to Eq. (2). Figure 3(a) shows examples of GIAM polarimetry fittings with θp = 44◦ . The gate voltage Vg was varied from −200V to 200V in increments of 5V. The polarization ellipses measured from the GIAM polarimetry are then compared to those drawn from the reference data in Fig. 3(b)-(e). In addition, since a polarization ellipse does not carry information regarding the handedness of the light, we provide the normalized Stokes parameters—s1 = cos(2θ), s2 = sin(2θ) cos φ, and s3 = sin(2θ) sin φ—marked on the surface of a Poincare sphere, see Fig. 4. The shot-to-shot variation of a polarization state measured by the GIAM polarimetry is mainly due to the statistical fluctuation in the detector readouts. As seen in Fig. 4, the shot-to-shot variation of a polarization state measured by the GIAM polarimetry is relatively much smaller than the deviation of the GIAM polarimetry results from the reference measurement. Thus, we know that the deviation is

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Figure 3: (a) Colored circles: measured intensities of the reflected light at the detector measured for the four incident polarization states. Green: near-RCP, blue: near-LCP, magenta: near-x−polarized, red: elliptical polarization with high eccentricity. Black solid lines: fits to Equation (2) using the characteristic functions plotted in Fig. 2. (b)-(e) Comparison between the polarization ellipses obtained from the GIAM polarimetry (dashed lines color-coded as in (a)) and those obtained from the rotating analyzer polarimetry (solid black lines).

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due to systematic errors rather than statistical errors. Possible candidates for the source of systematic errors are (i) depolarization from the GIAM device and (ii) non-zero off-diagonal elements of the Jones matrix in Equation (1). Both (i) and (ii) would originate from imperfection in the device fabrication, but their difference is that (i) is an incoherent effect whereas (ii) is a coherent contribution.

Figure 4: The normalized Stokes parameters si ≡ Si /S0 , visualized on the Poincare spheres. Solid stars: rotating analyzer polarimetry; solid circles: GIAM-based polarimetry (colorcoded based on incident light polarization, same as in Fig. 3). For each input polarization, 10 data points from the GIAM polarimetry (10 tightly overlapping solid circles for each color) are shown. Low spread of the measurement results demonstrates low statistical uncertainty of GIAM-based polarimetry. To exclude the effect of nondiagonal components of the GIAM in Jones matrix, we confirmed that Rxy = (1.04 ± 0.04) × 10−3 , Ryx = (2.09 ± 0.19) × 10−3 , at Vg = 0V, are much smaller than the direct reflectivities; Rxx and Ryy are around 0.1, see Fig. 1(c). We made sure, by minimizing those cross reflectivities, that the x− and y−axes of the GIAM device coincide with the principal axes of the polarizer. Both Rxy and Ryx almost linearly decrease as a function of Vg : Rxy = (1.25 ± 0.05) × 10−3 , Ryx = (2.55 ± 0.20) × 10−3 at Vg = −200V and Rxy = (0.87 ± 0.05) × 10−3 , Ryx = (1.87 ± 0.18) × 10−3 at Vg = +200V, and at all times stay much smaller than the diagonal terms (full data is provided in the Supporting Information). Therefore, we conclude that the differences between the measured and anticipated polarization states are due to sample imperfections that result in a slight spatial 10


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depolarization. Nevertheless, the results provided in Fig. 3 and 4 show that the GIAM polarimetry successfully distinguishes between all major input polarization states, and that the Stokes parameters measured from the GIAM-based polarimetry are in good agreement with the reference data. Further improvement of the device performance may take different directions, such as introducing ultrathin high-κ dielectrics as insulating spacers to reduce the sweep range of the gating voltage. Note that, whereas the majority of polarimetric devices based on mechanical rotation of polarizers/retarders or photoelastic modulators operate at sub-MHz speeds, this approach has a potential to operate at speeds of up to tens of MHz. 17,27 So far, all the analyses are done for perfectly polarized light sources, since we didn’t have a light source with controllable degree of polarization. In principle, however, our GIAM device is capable of doing polarimetry also for partially polarized light sources. The Jones matrix given in Equation (1) and the Jones matrix for a polarizer needs to be converted into a Mueller matrix for the analysis of partially polarized light. Then, the final intensity at the detector is calculated in the Mueller calculus to be:

I(Vg ; S, θp ) = S0 M00 (Vg ; θp ) + S1 M01 (Vg ; θp ) + S2 M02 (Vg ; θp ) + S3 M03 (Vg ; θp ),

(3)

where S = [S0 ; S1 ; S2 ; S3 ] is the Stokes vector of the incident light, and Mµν is the total Mueller matrix taking both the GIAM and the polarizer into account; e.g. M00 = (|rxx |2 cos2 θp +|ryy |2 sin2 θp )/2, M01 = (|rxx |2 cos2 θp −|ryy |2 sin2 θp )/2, M02 = |rxx ||ryy | sin(2θp ) cos(∆φ)/2, and M03 = |rxx ||ryy | sin(2θp ) sin(∆φ)/2. The polarimetry fit shall be done with a p constraint S12 + S22 + S32 ≤ S0 . If we use the spherical parametrization—S1 = S0 r cos(2θ), S2 = S0 r sin(2θ) cos φ, and S3 = S0 r sin(2θ) sin φ, where r is the degree of polarization—for simpler treatment of the constraint (r ≤ 1), we get: I(Vg ; [r, θ, φ] , θp )/I0 =(1 − r)X(Vg )2 [cos2 θp + ρ(Vg )2 sin2 θp ] +rX(Vg )2 [cos2 θ cos2 θp + ρ(Vg )2 sin2 θ sin2 θp + 0.5ρ(Vg ) sin(2θ) sin(2θp ) cos(φ − ∆φ(Vg ))]. (4) 11


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Note that, for r = 1, Equation (4) reduces back to Equation (2). In general, the fitting is more efficient when the Hessian matrix, Hµν = ∂Sµ ∂Sν C, of the cost function, P (i) C(S) ≡ i (I(Vg ; S, θp ) − I (i) )2 , has overall greater eigenvalues or, in other words, greater P (i) (i) determinant. 41 In our specific case, we get Hµν = i M0µ (Vg )M0ν (Vg ), and it is easily seen that its determinant vanishes when M0µ (Vg )’s are linearly dependent. Thus, we expect that the GIAM polarimetry fit to Equation (3) or Equation (4) will be more accurate if M0µ (Vg ; θp )’s, as functions of Vg , have more distinct (linearly independent) curve shapes. In conclusion, we have experimentally demonstrated an electrically actuated grapheneintegrated anisotropic metasurface that performs polarimetry of mid-infrared radiation. The device supports a gate-tunable blue shift of a plasmonic Fano-resonance along one of its principal axis, which enables unique determination of all normalized Stokes parameters of the incident light through fitting to a simple model that utilizes the a priori measured components of the GIAM’s Jones matrix at multiple values of the gate voltage. The Stokes parameters measured using GIAM-based polarimetry agrees well with the values obtained from the conventional rotating analyzer method. Our findings are a promising step toward high-speed, ultrathin electro-optic polarimetric devices that could find use in metrology, imaging, and polarization multiplexing.

Methods Sample Fabrication The single-layer graphene was grown on polycrystalline Cu foil using a chemical vapor deposition 40 and transferred from the Cu foil onto 1µm thick SiO2 layer that was grown on a lightly doped silicon substrate 19 using wet thermal oxidation. Next, a 105µm by 105µm metasurface sample (50 by 50 unit cells) was fabricated on top of the SLG with unit cell dimensions given in Fig. 1(a) caption, using electron beam lithography (EBL). The thickness of the metasurface was 30nm (5nm Cr + 25nm Au). An additional step of EBL was used 12


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to deposit the source and drain contact pads (10nm Cr + 90nm Au). An SEM image of a segment of the fabricated sample is shown in Fig. 1(b). The gate voltage was applied between the lightly doped Si substrate and either of the source or drain pads for active control of graphene carrier density.

Reflectivity Measurements The experimental setup shown in the table of contents graphic was used to measure the optical reflectivity of the sample and the intensity of reflected light out of the sample as a function of the gating voltage. The laser source was a quantum cascade laser (Daylight solution, MIRcat-1400) operated in the pulsed mode with the pulse repetition rate of 50 kHz and the pulse duration of 40 ns. A high numerical aperture aspheric GeSbSe lens (NA = 0.56) was utilized as an objective to focus the light onto the metasurface. A liquid nitrogencooled MCT detector was used for the intensity measurement. The signal from the MCT detector was amplified and measured by a lock-in amplifier (Signal Recovery 7225) with a integration time of 3 ms. In the measurement of the metasurface reflectivity shown in Fig. 1(c), the reflected intensity out of the metasurface was normalized with respect to the reflected intensity out of a contact pad.

Acknowledgment This work was supported by the Office of Naval Research under a Grant No. N00014-171-2161, by the National Science Foundation under a Grant No. DMR-1741788, and by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multi-mission laboratory managed and operated by National Technology and Engineering Solutions wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. M.J. was also supported in part by Cornell Fellowship and in part by the Kwanjeong Fellowship

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from Kwanjeong Educational Foundation. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

References (1) Holloway, C. L.; Kuester, E. F.; Gordon, J. A.; O’Hara, J.; Booth, J.; Smith, D. R. An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials. IEEE Antennas Propag. Mag. 2012, 54, 10–35. (2) Minovich, A. E.; Miroshnichenko, A. E.; Bykov, A. Y.; Murzina, T. V.; Neshev, D. N.; Kivshar, Y. S. Functional and nonlinear optical metasurfaces. Laser Photonics Rev. 2015, 9, 195–213. (3) Wu, C.; Khanikaev, A. B.; Adato, R.; Arju, N.; Yanik, A. A.; Altug, H.; Shvets, G. Fanoresonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers. Nat. Mater. 2012, 11, 69–75. (4) Mousavi, S. H.; Kholmanov, I.; Alici, K. B.; Purtseladze, D.; Arju, N.; Tatar, K.; Fozdar, D. Y.; Suk, J. W.; Hao, Y.; Khanikaev, A. B.; Ruoff, R. S.; Shvets, G. Inductive Tuning of Fano-Resonant Metasurfaces Using Plasmonic Response of Graphene in the Mid-Infrared. Nano Lett. 2013, 13, 1111–1117. (5) Yu, N.; Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 2014, 13, 139–150. (6) Lee, J.; Tymchenko, M.; Argyropoulos, C.; Chen, P.-Y.; Lu, F.; Demmerle, F.; Boehm, G.; Amann, M.-C.; Al, A.; Belkin, M. A. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature (London) 2014, 511, 65–69. 14


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Graphical TOC Entry

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(a) Geometry of a unit cell of the anisotropic metasurface periodically arranged with $P_x=P_y=2.1{\rm~\mu m}$ periods: $L_x=0.6{\rm~\mu m}$, $L_y=1.4{\rm~\mu m}$, $w=0.25{\rm~\mu m}$, and $g=0.12{\rm~\mu m}$. (b) SEM image of the fabricated device. (c) Reflectivity spectra ($R_{xx(yy)}=|r_{xx(yy)}|^2$) for the incident light polarized along the $y-$axis (circles) at three values of $V_g$ (color-coded), and along the $x-$axis (squares) at $V_g=0~$V. Vertical dotted line: wavelength of operation $\lambda_0 = 6.7 \mu m$. (d) Schematic of the GIAM-based polarimeter.


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The GIAM characteristic functions---$X(V_g)$, $\rho(V_g)$, and $\Delta\phi(V_g)$---measured at $\lambda_0=6.7 {\rm \mu m}$. The measurements were taken from $V_g=-200$V to $200$V in increments of $5$V, and the data was linearly interpolated.


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(a) Colored circles: measured intensities of the reflected light at the detector measured for the four incident polarization states. Green: near-RCP, blue: near-LCP, magenta: near-$x-$polarized, red: elliptical polarization with high eccentricity. Black solid lines: fits to Equation~(\ref{eq.2.}) using the characteristic functions plotted in Fig.~\ref{fig.2.}. (b)-(e) Comparison between the polarization ellipses obtained from the GIAM polarimetry (dashed lines color-coded as in (a)) and those obtained from the rotating analyzer polarimetry (solid black lines).


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The normalized Stokes parameters $s_i \equiv S_i/S_0$, visualized on the Poincare spheres. Solid stars: rotating analyzer polarimetry; solid circles: GIAM-based polarimetry (color-coded based on incident light polarization, same as in Fig.~\ref{fig.3.}). For each input polarization, $10$ data points from the GIAM polarimetry ($10$ solid circles for each color) are shown. Low spread of the measurement results demonstrates low statistical uncertainty of GIAM-based polarimetry.


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Table of Contents/Abstract Graphic


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Polarimetry Using Graphene-integrated Anisotropic Metasurfaces

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