# Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control
## 4 Polarization Modulation in Graphene Metasurfaces
### General Polarization Control in Graphene Metasurfaces  
In general, the output beam through graphene metasurfaces may exhibit elliptical polarization, where the tilt angle and/or the ellipticity can be actively engineered with the variation of the graphene Fermi level. Multiple polarization states are flexibly switchable with proper biasing voltage at high modulation speed in a single structure, which is highly demanding for polarization encoding and multiplexing. In 2017, [PERSON] group experimentally demonstrated an active graphene metasurface that converts a linear polarization into an elliptical one with controllable tilt angle and ellipticity [100]. The configuration is a C-bar-shaped anisotropic metallic metasurface integrated with a graphene layer (Figure 10a), which induces a strong Fano resonance only when the polarization is along the bar direction (y direction). Therefore, the reflection spectra of the y-polarized beam were well controlled by the voltage due to the intense interaction of the in-plane electric field with graphene, while the x polarization is unaffected, as shown by the measurement results in Figure 10b. At a specific wavelength of 7.72 \(\upmu\)m, the tilt angle can be modulated with constant ellipticity when the biasing voltages are \(-200\) V, 0 V, and 250 V in Figure 10c. Figure 9: Graphene metasurfaces as active polarizers. (**a**) Rectangular slots in the graphene layer with artificial birefringence and its biasing configuration. (**b**) Different lengths along the x and y directions lead to different resonance frequencies. At the frequency of 12.7 THz, x polarization is on resonance and strongly reflected, while y polarization is off resonance and weakly reflected. The x polarization is filtered upon reflection. Reproduced with permission from [95], Copyright American Physical Society, 2012. (**c**) Two layers of orthogonally-orientated graphene strips sandwiching an L-shaped metallic resonator. The asymmetric L resonator couples to the orthogonal graphene strips, leading the LCP and RCP beams to different resonance frequencies, such that one polarization is blocked by strong resonances and the other goes through with small insertion loss. (**d**) Variation of the LCP transmission with the graphene Fermi level leads to a frequency-tunable polarizer. Reproduced with permission from [96], Copyright Optical Society of America, 2015. (**e**) Graphene as a loss-tunable material attached to the bilayer of a conjugated double-Z chiral metamaterial for active control of the radiation loss. (**f**) Measured transmission spectra for LCP and RCP waves with different gate voltages. The RCP wave experiences underdamped to overdamped phase transition, while the off-resonance LCP wave experiences negligible modulation. The isolation depth is 45 dB at the critical coupling condition and can be actively controlled via biasing. Reproduced with permission from [99], Copyright The authors, 2017. Similarly, by utilizing another anisotropic metasurface, namely the rectangle slot array in Figure 10d, the polarization conversion comes from strong resonance along the short edge and weak interaction along the long edge [101]. The voltage variation shifts the resonance frequency, as well as the phase difference between the orthogonal LP modes. Figure 10e shows that the phase differences of 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\) are obtained at 7.1 \(\mu\)m with the corresponding voltage applied, which are used to convert an LP mode into LCP, cross-LP, and RCP, respectively (Figure 10f). The three polarization states can be used for encoding binary data and polarization multiplexing with any desired time-domain  
Figure 10: Continuous or multi-state active polarization engineering. (**a**) Graphene integrated with an anisotropic metasurface for linear to elliptical polarization conversion upon reflection. (**b**) Reflection spectra of x- and y-polarized beams with different gate biasing voltages.