# Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control
## 3 Phase Modulation in Graphene Metasurfaces
### In-Plane Plasmonic Wavefront Shaping and Coupling with Out-of-Plane Propagation
(**c**) Schematic representation of the graphene layer patterned with two types of organic molecules (TCNQ + TTF and F4 - TCNQ) to achieve an inhomogeneous conductivity profile through charge transfer. Reproduced with permission from [43], Copyright American Chemical Society, 2014. (**d**) Schematic of the spiral-shaped graphene vacancy for excitation and focusing of the SP wave. (**e**) Superfocusing using a spiral-shaped graphene vacancy together with a circularly-polarized incident beam. (**f**) Generation of plasmonic vortex beam with five segmented graphene vacancies. All the in-plane wavefront shaping is  
achieved in a notable subwavelength area and beyond the diffraction limit considering the strong localization of the graphene plasmon. Reproduced with permission from [68], Copyright Optical Society of America, 2014. On the other hand, the strong mismatch of the wave vectors in the plasmonic wave and free space wave causes a great obstacle in exciting and leaking the SP waves in graphene. Different mechanisms have been reported to excite the strongly-localized SP waves in graphene through diffraction gratings [69], sharp tips [70; 71], and vacancies [68]. Similarly, the coupling from the SP wave to the propagation wave is the reverse process, which can be done in the same structure. To further increase the flexibility, coupling the SP wave to the free space beam with steerable directions is a highly-desired feature in many applications including communications, remote sensing, and image scanning, which is not easily available especially in the THz region. In the design of Figure 7a, by densely distributing gate pads underneath the monolayer graphene, the surface reactance can be sinusoidally modulated with adequate biasing voltage to each pad [72]. The surface wave interacts with the sinusoidal modulation to produce the leaky wave radiation. Since the radiation direction is determined by the modulation periodicity, which can be dynamically varied by grouping different numbers of pads in one period, the radiation direction can be steered in real time at a fixed frequency, as calculated in Figure 7b. Alternatively, Figure 7c utilizes the periodic metal-dielectric-graphene plasmonic grating to achieve electrically-controllable THz beam scanning [73]. The graphene gratings are biased with the same voltage, which modulates the effective refractive index of the SP wave supported in graphene, leading to varied radiation directions based on the grating equation. Figure 7d shows the radiated near-field from \(13^{\circ}\) to \(-18^{\circ}\) when the biasing voltage is 256.5 mV (left) and 53.2 mV (right). The above leaky wave scanning is limited to one plane. Scanning in arbitrary directions in the full space is more difficult, as pixel-by-pixel biasing makes the configuration a huge challenge for device integration. Figure 7e is a simplified design to achieve such functionality. The dynamic bean scanning in both elevation and azimuth planes is achieved by applying two groups of one-dimensional biasing pads underneath the graphene sheet [74]. They are orthogonal and decoupled. One group offering monotonic impedance variation along the y direction mainly determines the radiation in the azimuthal plane, while the other provides sinusoidal impedance modulation along the x direction to decide the elevation angle of the radiation. Figure 7f shows examples of the two-dimensional radiation pattern towards different directions with the adequate choice of the voltages in the two groups of gating pads.