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Philosophical transactions. Series A, Mathematical, physical, and engineering sciences logoLink to Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
. 2017 Mar 28;375(2090):20160061. doi: 10.1098/rsta.2016.0061

Electrical tuning of the polarization state of light using graphene-integrated anisotropic metasurfaces

Shourya Dutta-Gupta 1,5, Nima Dabidian 1, Iskandar Kholmanov 2,4, Mikhail A Belkin 3, Gennady Shvets 1,5,✉
PMCID: PMC5321826  PMID: 28219996

Abstract

Plasmonic metasurfaces have been employed for moulding the flow of transmitted and reflected light, thereby enabling numerous applications that benefit from their ultra-thin sub-wavelength format. Their appeal is further enhanced by the incorporation of active electro-optic elements, paving the way for dynamic control of light's properties. In this paper, we realize a dynamic polarization state generator using a graphene-integrated anisotropic metasurface (GIAM) that converts the linear polarization of the incident light into an elliptical one. This is accomplished by using an anisotropic metasurface with two principal polarization axes, one of which possesses a Fano-type resonance. A gate-controlled single-layer graphene integrated with the metasurface was employed as an electro-optic element controlling the phase and intensity of light polarized along the resonant axis of the GIAM. When the incident light is polarized at an angle to the resonant axis of the metasurface, the ellipticity of the reflected light can be dynamically controlled by the application of a gate voltage. Thus accomplished dynamic polarization control is experimentally demonstrated and characterized by measuring the Stokes polarization parameters. Large changes of the ellipticity and the tilt angle of the polarization ellipse are observed. Our measurements show that the tilt angle can be changed from positive values through zero to negative values while keeping the ellipticity constant, potentially paving the way to rapid ellipsometry and other characterization techniques requiring fast polarization shifting.

This article is part of the themed issue ‘New horizons for nanophotonics’.

Keywords: active metasurface, graphene, polarization

1. Introduction

Manipulation and control of light is of extreme importance for fundamental materials studies, as well as for the development of novel photonic devices [1]. Recently, plasmonic and dielectric metasurfaces (two-dimensional arrays of sub-wavelength structures) have been used for controlling light's properties, such as intensity, phase and polarization [2–7]. The choice of the unit cell as well as the lattice arrangement can be used for defining and controlling the functionality of the metasurface. In many cases, this flexibility, in addition to their small footprint and sub-micrometre thickness, makes metasurfaces either competitive with, or even superior to, conventional optical elements. One of the most appealing potential applications of metasurfaces is for polarization control and tuning. Polarization manipulation is instrumental to several crucial optical applications, such as ellipsometry, polarimetry [8], optical sensing [9] and polarization-division multiplexing [10], which have superior performance compared with conventional methods of material characterization [11] and telecommunication [12]. It has been shown that anisotropic metasurfaces can convert light polarization from linear to circular [13–18], rotate the polarization plane of a linearly polarized light [19–21] and induce asymmetric transmission [6,22,23]. However, most of the studies employed ‘passive’ metasurfaces: once fabricated, their properties cannot be tuned or controlled. To circumvent this problem, there is an increasing interest in ‘active’ devices whose optical properties can be dynamically tuned [5,24–32].

The most common approaches to active tuning have been based on mechanical [30,33] motions, thermal (e.g. using phase change materials) excitations [34,35] or electrical [36–39] gating. Among these, electrical control enables higher modulation speed and greater flexibility in device fabrication. Rapid electrical tuning requires incorporation of an electro-optic material that has a short-time response to electrical voltage. Depletion-type semiconductors have been used in the past for terahertz [36] and infrared [37] modulation. More recently, the simplicity of graphene's integration with various substrates and metasurfaces [40,41] is making it the material of choice for optical modulation [24,25,27–29]. While such graphene-integrated metasurfaces have been used primarily for modulating the intensity of the reflected light, recent experiments [29] show that the phase can also be modulated.

A number of exciting applications of phase modulation have been envisioned and demonstrated, such as interferometric motion detection [29] with sub-micrometre resolution and no moving parts. It was also suggested [29] that, by employing a graphene-integrated anisotropic metasurface (GIAM), it may be possible to dynamically control the polarization of light. In this work, using the rotating analyser Stokes polarimetry [6,42] technique, we directly measure the modification of light polarization produced by applying a gate voltage to a GIAM. Specifically, we demonstrate that a linearly polarized (LP) incident light is converted into an elliptically polarized (EP) one upon reflection from a GIAM that supports a Fano resonance for the light polarized along one of its two principal axes. The Stokes parameters of the reflected light are experimentally measured at multiple gate voltages.

The concept of active polarization control realized in this work is illustrated by figure 1, where a graphene-integrated metasurface converts the polarization state from LP (incident) to EP (reflected). The metasurface is fabricated on top of a single-layer graphene (SLG); see Material and methods (§4) for fabrication details. A gate voltage Vg is applied between a silicon back-gate and graphene to tune the ellipticity of the reflected wave via electrostatic doping of the SLG. The metasurface used in this work is essentially the same (i.e. the nominal geometric parameters defined in figure 2a are identical) as the one used in [29]. It consists of a two-dimensional array of infinite wires and C-shaped antennas as shown in figure 2a for a single unit cell. The anisotropic nature of the metasurface is apparent by observation: the electrically connected wires running parallel to the y-direction provide strong reflectivity of the y-polarized light, but hardly affect the x-polarized one. Moreover, due to mirror reflection symmetry with respect to the (x–z) plane passing through the middle of the C-shaped antenna, it follows from simple symmetry considerations that the polarization-conversion coefficients (from x- to y-polarized and vice versa) vanish: Rxy(λ) = Ryx(λ) = 0 for all wavelengths. Therefore, the x- and y-axes are the principal polarization axes of the metasurface. Furthermore, because the y-polarized light can excite the electric dipole resonance of the C-shaped antenna while the x-polarized light cannot, the respective Ryy(λ) and Rxx(λ) reflection spectra are qualitatively different: the Ryy(λ) exhibits a strong resonant dip around λ = λR ≈ 7.7 µm while the Rxx(λ) does not possess such a dip.

Figure 1.

Figure 1.

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Schematic of the electric control of the polarization state of light using graphene-integrated anisotropic metasurfaces. The incident light is linearly polarized at a finite angle to the principal axes of the metasurface. The reflected light acquires elliptical polarization that depends on the voltage Vg applied between the back-gate (Si) and graphene across an SiO2 insulating layer. Source and drain electrodes are used to measure graphene's conductivity as a function of Vg.

Figure 2.

Figure 2.

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(a) Schematic and geometry definitions of a GIAM that exhibits resonant behaviour for y-polarized light but not for x-polarized light. Numerical simulations of the current distribution 5 nm above the graphene plane (top right inset) and of the near-field enhancement Inline graphic at z = 0 (bottom right inset) illustrate the resonant excitation of the C-shaped plasmonic antenna. (b) Scanning electron microscope image of the fabricated metasurface. (c) Experimentally measured reflectivity for x-polarized light (dashed line) and y-polarized light (solid lines). Different colours correspond to different gate voltages Vg defined in the legend. (d) Numerical simulation results corresponding to (c). The Fermi energies EF correspond to the gate voltages in (c). Panels (a,b) are from [29]. The nominal dimensions of the structure defined in (a) are Px = Py = 2.1 µm, W = 250 nm, g = 120 nm, Ld = 1.8 µm, Lm = 600 nm.

The origin of the reflectivity dip in Ryy(λ) is the destructive Fano interference [43] between the broadband response of the wire and the C-shaped dipole [28,29]. Specifically, the current flows in the C-shaped antenna and in the wire are opposite to each other as shown in figure 2a, thereby nearly cancelling the overall polarizability of a unit cell of the metasurface. Therefore, only the y-polarization of light excites strong near fields at λ = λR. At the resonance frequency, the intensity of the in-plane electric field (which is responsible for the interaction between graphene and the metasurface) in the immediate proximity of the metasurface is enhanced by a large factor Inline graphic as shown in figure 2a. Both the current distributions and the in-plane field enhancements were calculated at λ = λR for a metasurface without graphene using the COMSOL Multiphysics commercial code.

Because only the y-polarized light, induces strong near-field enhancement of the in-plane electric field component that interacts with graphene's electrons, only the Ryy(λ) (but not the Rxx(λ)) spectrum is affected by field-effect doping of graphene. The effect of field-effect doping is to inject free carriers (electrons or holes, depending on the gating voltage Vg) into the SLG, thereby affecting its in-plane frequency-dependent conductivity σSLG(ω), where ω ≡ 2πc/λ. The standard expression for σSLG(ω), obtained under the random-phase approximation [44], is provided in the Material and methods section (§4). It relates σSLG to graphene's Fermi energy EF, which is itself related to the areal density n of the free carriers in graphene as Inline graphic, where vF = 1 × 108 cm s−1 is the Fermi velocity. As the Fermi energy increases, graphene behaves as an increasingly inductive [24,41] element that causes the blue-shifting of the resonance frequency as shown in figure 2d, where the simulated reflectivity Ryy for three different (colour-coded) Fermi energies are depicted as solid lines. Graphene does not affect Rxx(λ), so it is plotted as a single dashed line assuming that graphene is not present underneath the metasurface.

These theoretical results agree with the measured reflectivities from the metasurface for the y-polarized light, which is shown in figure 2c for the three different gate voltages Vg that approximately match the Fermi energies in figure 2d. The colour coding of Vg in figure 2c and their respective EF in figure 2d is the same. The connection between EF(n) and Vg is made using the expression n = CΔV/e, where C is the capacitance per unit area of the SiO2 spacer, and ΔV = Vg − VCNP, with VCNP the charge neutrality point (CNP), which is experimentally found by locating the resistance maximum between the source and the drain (figure 1) as a function of the applied back-gate voltage. For our sample, it was thus experimentally determined that VCNP = −200 V. The experimentally observed blue-shifting of the reflectivity dip from λ ≈ 7.8 µm (black solid line in figure 2c) at the CNP point to λ ≈ 7.6 µm (red solid line) at Vg = 250 V is around 2.6%. The physical reason for the blue-shift is the injection of holes into graphene [41]. Note that the amount of the blue-shift is in good agreement with theoretical predictions presented in figure 2d.

The measured and simulated Rxx spectra are also presented in figure 2c,d. These spectra are essentially featureless, thus confirming our earlier conjecture that the metasurface is non-resonant for x-polarized light for the wavelengths of our interest. The small feature that is experimentally observed at λ ≈ 8 µm in figure 2c is due to the epsilon-near-zero (ENZ) effect that originates from the longitudinal phonon polariton of SiO2 [45,46]. This effect is due to finite components of the incident electric field that are normal to the substrate (i.e. Ez), which are present in our experiment due to the large numerical aperture of our focusing objective (NA = 0.5). However, our simulation is performed for normal incidence. Therefore, the ENZ feature is not present in the simulated results as shown in figure 2d.

In our earlier work [29], we used an interferometric set-up to experimentally measure the voltage-dependent phase shift of the x- and y-polarized incident light. Based on those measurements, we conjectured the possibility of voltage-dependent polarization state control for the incident light polarized at an angle to the resonant principal axis of the metasurface. Below, we present a direct experimental evidence of such polarization control.

2. Experimental results

In order to measure the ellipticity of the reflected light, we must measures its Stokes parameters. This is accomplished using the rotating analyser set-up [6,42] shown in figure 3a. The set-up consists of a quantum cascade laser source of light, a polarizer, a CaF2 beam splitter, a graphene-integrated metasurface sample biased with a DC gate voltage, an analyser and a mercury cadmium telluride (MCT) detector. The polarization state of light after reflection from the metasurface can be described by

2. 2.1

where E0, θE and ϕ are the wavelength-dependent electric field amplitude, inverse tangent of amplitude ratio of Ey to Ex, and the phase difference between Ex and Ey, respectively. The time-averaged intensity of the analysed signal measured at the detector then can be expressed [6] as follows:

2. 2.2

where θA is the analyser angle.

Figure 3.

Figure 3.

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(a) The schematic for the Stokes polarimetry set-up consisting of an optical source, a beam splitter (BS), an infrared MCT detector and two linear polarizers, one after the source (polarizer) and one before the detector (analyser) of the polarization state. A graphene-integrated anisotropic metasurface controllably modulates the polarization state of the incident light when a varying gate voltage Vg is applied. (b) The reflectivity as a function of the wavelength for different analyser angles θA when the structure is illuminated with the laser light initially polarized at θP = 75°. The gate voltage is set at Vg = −200 V (the CNP point) for this measurement. The source is a quantum cascade laser (QCL).

In all our measurements, the polarizer angle θP (see figure 3a for a definition), which determines the ratio of the incident electric field components Inline graphic and Inline graphic, is set at θP = 75°. According to the reflectivity measurements shown in figure 2c, this angle results in approximately equal reflected intensities of the x- and y-polarized light at the resonance wavelength Inline graphic. We measured the reflection intensity as a function of the wavelength by changing the analyser angle from θA = 0° to θA = 90° in steps of 22.5° as shown in figure 3b. A subsequent least-squares fitting of equation (2.2) to the measured data of figure 3b at a given wavelength determines the fitting parameters E0, θE and ϕ as a function of λ. It is then straightforward to calculate the polarization state of the detected signal from equation (2.1).

The conventional representation of the polarization state of light is in terms of its Stokes parameters defined as follows: Inline graphic, Inline graphic, Inline graphic and Inline graphic. Here, Ix,y, I±45° and IRCP,LCP are the intensities of light that would pass through an analyser set parallel to x (y) axes, ±45° to the x-axis, and through a circular RCP/LCP analyser, respectively. Therefore, the qualitative physical meaning of the Stokes parameters is as follows: S0 represents the total light intensity, S1 represents the degrees of linear polarization with respect to the principal axes of the metasurface, S2 represents the degrees of linear polarization with respect to the axes tilted at 45° with respect to the principal axes, and S3 represents the degree of circular polarization. Of particular interest is the sign of the S2 coefficient because it indicates the orientation of the polarization ellipse. Specifically, S2 > 0 means that the polarization ellipse is elongated in the first and third polarization quadrants, whereas S2 < 0 means that the polarization ellipse is elongated in the second and fourth polarization quadrants. Note that the above calculation explicitly assumes that the reflected light is perfectly coherent, i.e. |S0|2 = |S1|2 + |S2|2 + |S3|2. This assumption is valid because the intensity of the reflected laser light is much higher than that of the infrared radiation thermally emitted by a heated metasurface.

A typical dependence of I(E0,θE,θA,ϕ) on θA is plotted in figure 3b for one specific value of Vg = −200 V (the CNP point). Note that the ellipticity of the reflected light depends on its wavelength. For example, the reflected polarization is nearly circular around λ ≈ 7.75 µm because the light intensity passing through the analyser is nearly independent of θA. On the other hand, a significant elongation of the polarization ellipse is expected at other wavelengths, e.g. at λ = 7.4 µm. We have repeated this polarimetric measurement for the same three gate voltages (Vg = −200, 0, 250 V) as in figure 2c and extracted the normalized values of the Stokes parameters, s1 = S1/S0, s2 = S2/S0 and s3 = S3/S0, by fitting the experimental results to equation (2.2). The values of θE(λ,Vg) and ϕ(λ,Vg) were then extracted for those gate voltages for a wide range of laser wavelengths (7.3 µm < λ < 8.3 µm). The normalized Stokes parameters were then calculated from θE(λ,Vg) and ϕ(λ,Vg) and plotted in figure 4a with dashed (s1), dotted (s2) and solid (s3) lines, respectively. The three values of the gate voltage are colour-coded using the same colour scheme as in figure 2c. The simulated values of the normalized Stokes parameters plotted in figure 4b show fairly accurate agreement with the experimental results.

Figure 4.

Figure 4.

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(a) Measured and (b) simulated normalized Stokes parameters of the reflected light as a function of the wavelength plotted for three different gate voltages. The curves are colour-coded based on the gate voltages and Fermi energies using the same convention as in figure 2c,d. (c,d) Polarization ellipses at λ1 = 7.76 µm and λ2 = 7.72 µm based on the measured Stokes parameters plotted in (a).

The non-zero values of S3 observed from figure 4a indicate that the linearly polarized incident light is converted to elliptic polarization upon reflection. This is the consequence of the different phase shifts acquired by the x- and y-polarized light. The ellipticity changes with gate voltage are observed to depend strongly on the wavelength of light. We consider two specific examples: λ1 = 7.76 µm (vertical magenta dashed line in figure 4a) and λ2 = 7.72 µm (vertical green dashed line in figure 4a). The normalized Stokes parameters at those wavelengths are obtained by reading off the values of si (i = 1,2,3) from the intersection of the si(λ,Vg) curves with the corresponding vertical lines. In addition, we have plotted the gate voltage-dependent polarization ellipses for λ = λ1 in figure 4c, and for λ = λ2 in figure 4d. The definitions of the semi-major and semi-minor axes a and b, respectively, and the tilt angle β are shown in the inset to figure 4b. The tilt angle β and the ellipticity Inline graphic are calculated from the following equations: tan 2β = s2/s1 and Inline graphic. Therefore, the ellipticity is controlled by a single parameter: |s3|. On the other hand, the tilt angle is mainly controlled by s2 and s1. These observations suggest the possibility of independent control of the tilt angle and ellipticity.

For λ = λ1, we observe that s3 = 1 for Vg = 0 V, which means the reflected light is circularly polarized Inline graphic. For the other two voltages, Vg = −200 V and Vg = −250 V, it acquires finite voltage-dependent ellipticity: Inline graphic for Vg = −200 V (figure 4c: black ellipse) and Inline graphic for Vg = −250 V (figure 4c: red ellipse). However, the sign of s2 ≤ 0 does not change with voltage. Therefore, the polarization ellipses shown in figure 4c remain in the second and fourth quadrants: β ≈ −16° for Vg = −200 V, and β ≈ −37° for Vg = 250 V. Note that for all three voltages s1 > 0, which implies that the tilt angle of the polarization ellipse is restricted by the following inequality: −45° < β < 45°.

The λ = λ2 example is particularly interesting because s3 remains the same for all three voltages: all three solid curves in figure 4a intersect the green vertical line at the same value of s3. However, the s2 parameter changes its sign from positive for Vg = 0 to negative for the other two voltages. Therefore, as the gate voltage shifts from Vg = 0 (figure 4d: blue ellipse) to Vg = 250 V (figure 4d: red ellipse), the tilt angle of the fixed shape polarization ellipse shifts from β ≈ 31° to β ≈ −41° as shown in figure 4d. Note that s1 > 0, so the tilt angle is restricted by the same condition as for the earlier case of λ = λ1. The independent modulation of the tilt angle for constant ellipticity can be useful in polarization encoding and multiplexing [47].

3. Conclusion and outlook

We provide the first experimental evidence of active modulation of the polarization state of mid-infrared light using a reflective GIAM. The rotating analyser approach is used to experimentally determine the Stokes parameters of the reflected light. Polarization ellipses were experimentally obtained at several representative wavelengths for different gate voltages. Our results show that we can controllably change the polarization state of light from linear to elliptical or circular. In general, it is shown that both the tilt angle and ellipticity can be changed by injecting carriers into graphene using field-effect doping. Furthermore, it is shown that the polarization ellipse can be rotated from the first to the fourth quadrant while keeping its ellipticity constant. This modulation of tilt angle, independent of the ellipticity, can be used for polarization encoding of light and could be instrumental for improving the telecommunication bandwidth. Various applications based on field-effect GIAMs that require fast (nanosecond-scale) polarization control, such as dynamic ellipsometry, can be envisioned, and will be explored in our future work.

4. Material and methods

(a). Optical simulations

We used a commercial finite-elements solver COMSOL Multiphysics v. 4.3b to simulate the reflectivity of the sample. To model the SLG, a surface current [41] JSLG = σSLGEt was defined, where Et is the tangential electric field on the SLG plane and σSLG = σinter + σintra is the optical conductivity of graphene that was calculated from random-phase approximation [44] as a sum of the interband and intraband contributions:

(a). 4.1

Here, kB is the Boltzmann constant, T = 300 K (room temperature), and the carrier scattering time of τ = 13 fs was assumed [29].

(b). Sample fabrication

SLG was grown on a polycrystalline Cu foil using a chemical vapour deposition (CVD) technique [48], then transferred [49] onto a commercially purchased Si/SiO2 substrate (University Wafer) with 1 µm oxide layer grown on lightly doped silicon. Electron-beam patterning followed by an oxygen plasma-cleaning step isolated the high-quality graphene regions. The anisotropic metasurface with a unit cell shown in figure 2a was fabricated by e-beam lithography on top of SLG in an area of 100 × 100 µm, followed by lift-off. The thickness of the metasurface was 30 nm (5 nm of Cr and 25 nm of Au). Source and drain contacts 100 nm thick (15 nm Cr + 85 nm Au) were deposited on top of graphene on the two sides of the metasurface samples. Finally, a metallic contact (15 nm Ni + 85 nm Au) was deposited on the back of the silicon sample for gating. Wirebonding of the contacts to a chip carrier concluded the fabrication.

(c). Reflection measurement

The set-up shown in figure 3a was used to measure the optical reflectivity of the sample. The source was a quantum cascade laser (Daylight Solution, MIRcat-1400) operated in the pulsed mode with the pulse repetitions rate of 250 kHz and the pulse duration of 100 ns. A ZnSe objective lens with high numerical aperture (NA = 0.5) was used to focus the laser light onto the metasurface. A liquid-nitrogen-cooled MCT detector measured the intensity of the signal. The measured signal was used for the measurements of signal intensity. A lock-in amplifier (Stanford Research Systems SR844) was used to amplify the measured signal with a 3 ms integration time.

Authors' contributions

S.D.-G. and G.S. conceived the experiments. N.D. performed the simulations and fabricated the sample. N.D. and S.D.-G. performed the optical measurements. S.D.-G. analysed the data. I.K. grew and transferred the CVD graphene. N.D., S.D.-G., M.A.B. and G.S. contributed to manuscript preparation. S.D.-G. and N.D. contributed equally to this project.

Competing interests

The authors declare no competing interests

Funding

This work was supported by the Office of Naval Research (ONR) Award N00014-13-1-0837 and by the National Science Foundation (NSF) Award DMR 1611379. M.A.B. acknowledges support from the Welch Foundation grant no. F-1705. We also acknowledge the assistance of Babak Fallahazad with electric characterization of the graphene sample.

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