# Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control
## 3 Phase Modulation in Graphene Metasurfaces
### Wavefront Shaping in Transmission
At a fixed frequency 0.65 THz, dynamic phase shift of 32\({}^{\circ}\) is observed by tuning the loss of graphene when V\({}_{g}\) is from 350 V to \(-\)500 V. Reproduced with permission from [28], Copyright Springer Nature, 2012. (**b**) Unit cell of the hybrid metasurface consisting of a split-ring resonator and double-layer graphene capacitor. (**c**) Transmission magnitude and phase spectra at various biasing voltages. The dynamic phase shift is due to the tunable material loss of graphene. Reproduced with permission from [45], Copyright The authors, 2018. (**d**) Phase coverage and scattered magnetic field of uniform graphene ribbons by tuning the Fermi level. The phase coverage is limited to 180\({}^{\circ}\). (**e**) Two parallel graphene ribbons are grouped in a unit cell to achieve nearly constant transmission intensity for different phase shifters. An array of such unit cells with individual biasing is simulated for anomalous refraction (top) and focusing with tunable focal length (bottom). Reproduced with permission from [46], Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2014.  
transmission amplitude of 0.4 at the optimum frequency. The phase profile for anomalous refraction is solely determined by the orientation of the graphene inclusions irrelevant to the conductivity. Therefore, highly efficient anomalous refraction is maintained over a wide bandwidth from 14.5 THz to 17 THz when the conductivity is dynamically adjusted, as shown in Figure 3b. The increased carrier density of graphene blue shifts the optimum frequency together with a dynamic scan of the beam direction. Although all the graphene elements experience the same voltage, the biasing is complicated due to the separate arrangement. The related study stops at the numerical validation. Until 2018, a similar idea was experimentally demonstrated by [PERSON] and [PERSON] [52] around 1.15 THz with a more feasible structure in Figure 3c. The geometric phase profile is provided by the metallic resonators with proper orientation, on top of which is a graphene monolayer biased at the periphery. For anomalous refraction and focusing, the phase profile does not change with gate voltage, while the intensity does (Figure 3d). Gate-induced increase in the carrier density of graphene results in a stronger absorption of THz waves through the intraband transitions. Therefore, the bending and focusing are most efficient at the CNP and experience an intensity decrease with further biasing (Figure 3e,f). Comparison of Figure 3a,c shows that graphene is a frequency-tunable resonator in the former and loss-tunable medium close to the metallic resonator in the latter, corresponding to the material properties of Figure 1a,b, respectively. Therefore, the optimum working frequency varies with the Fermi level in Figure 3b and stays the same in Figure 3d. Figure 3: Transmissive active metasurfaces for dynamic wavefront shaping based on the geometric phase. **(a)** Graphene nanocross metasurface with space-variant orientation for deflection of the circularly-polarized beam. **(b)** The transmitted circularly-polarized beam with the opposite handedness of the excitation gains the geometric phase as twice the rotation angle while keeping the transmission amplitude of 0.4 at the optimum frequency. **(c)** Deflection efficiency spectrum when the graphene nanocrosses have different Fermi levels. The large deflection efficiency is well maintained over a wide bandwidth and a large range of the Fermi level. Reproduced with permission from [51], Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2015. **(d)** Schematic of the active metasurface composed of a single layer of graphene deposited on a U-shaped metallic aperture where the spatial phase function is defined by the orientation of the U-shaped aperture. **(e)** Variation of the efficiency of anomalous refraction with biasing voltage and frequency. **(f)** Electric field distribution at two different gate voltages when the metasurface is designed for anomalous refraction.