# Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control
## 3 Phase Modulation in Graphene Metasurfaces
### Wavefront Shaping in Transmission  
In 2012, [PERSON]'s group experimentally demonstrated terahertz switching [28] by attaching graphene to a layer of hexagonal metallic meta-atoms with top and bottom electrodes for static biasing (inset of Figure 2a). Working in the low THz range similar to the case of Figure 1a, the graphene layer acts as the surrounding medium with tunable loss in close proximity to the meta-atoms. The charge carriers accumulated at the edges of the hexagon increasingly leak into the neighboring element through the graphene layer with increased conductivity. Therefore, the resonance becomes weaker and slightly shifted as the biasing voltage is applied from the charge neutral point (CNP). The measured phase response in Figure 2a based on the THz time-domain spectroscopy (THz-TDS) system shows a dynamic phase shift of 32\({}^{\circ}\) at 0.65 THz through 850-V voltage variation from the CNP. However, the limited phase coverage is not enough for wavefront shaping. In 2018, more than 90\({}^{\circ}\) phase modulation together with the 50-dB amplitude modulation was experimentally demonstrated [45] in a bilayer-graphene-loaded split ring resonator array, as shown in Figure 2b,c. Figure 1: \(\sigma\) (from Equations (2) and (3)), \(\epsilon_{r}\) (from Equation (4)), and \(n_{sp}\) (from Equation (5)) at sub-THz (**a**), THz to mid-IR (**b**), and near-IR frequencies (**c**). \(\mu=1\) m\({}^{2}\)/Vs, \(d=0.35\) nm, \(\epsilon_{ap}=1\). The thick lines are for \(E_{F}=0.2\) eV, and the thin lines are for \(E_{F}=0.25\) eV. The solid lines are the real parts, and the dash lines are the imaginary parts. The key material properties of graphene are summarized in (**d**) at different frequencies. When graphene itself is patterned as a phase shifter, such as a graphene ribbon or a graphene patch, it only provides a dynamic phase range of 180\({}^{\circ}\) around the plasmonic resonance by tuning the Fermi level or the dimension due to the intrinsic Lorentz-shape electric dipole resonance (Figure 2d). In fact, the effect of the material loss and the environment leads to an even smaller phase range [46; 47]. Additionally the transmission intensity is very small away from the resonance. To improve the efficiency of such a phase shifter, two graphene nanoribbons are combined in parallel in a unit cell [46]. By individually tuning the Fermi level of each nanoribbon, phase delay varies from 0 to 180\({}^{\circ}\) with comparable transmission intensity. Numerical simulations validate an anomalous deflector at IR composed of such elements with tunable beam direction and a flat lens with tunable focal length in Figure 2e. In order to cover the full 360\({}^{\circ}\) phase range, a stack of three graphene ribbons with proper dielectric separation was proposed as the metasurface unit cell for efficient beam focusing [48]. The phase shifters achieve a high transmission amplitude above 0.7 with full control over the phase of the transmitted wave when the outer and inner graphene ribbons are independently biased. However, separate gate biasing among elements in three layers is too complicated to implement at the studied mid-IR frequencies. Recently, the geometric phase has been utilized widely in metasurfaces for wavefront shaping by rotating the asymmetric inclusions [49; 50]. In Figure 3a, through an array of graphene nanocross resonators with different orientations [51], the transmitted circularly-polarized beam with the opposite handedness of the excitation gains the geometric phase as twice the rotation angle while keeping the  
Figure 2: Transmissive graphene phase shifters for dynamic wavefront shaping. (**a**) Transmission phase variation with biasing voltage and frequency in the hexagonal metallic metasurface integrated with graphene. The inset is a schematic of the structure. The dashed line at 350 V corresponds to the charge neutral point.