# Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control
## 1 Introduction  
The electromagnetic response of an optical device, from basic lenses and mirrors to advanced metasurface alternatives, is governed by two factors: material and structure. Beam engineering in conventional optics relies on separate contributions from the material refractive index \(n\) and the interface profiles \(d(x,y)\), leading to bulky size and limited functionality. Driven by the continuous demand on minimization and the progress of nano-fabrication, metasurfaces offer a promising platform for beam transformation over a thin layer of meta-atoms [1; 2; 3]. Meta-atoms with deep subwavelength structures couple to the light with strong field localization such that the effective material property is modified locally as \(n_{eff}(x,y)\), which is quite different from that of the natural material. With such spatially-designable \(n_{eff}(x,y)\), beam molding is possible over an ultrathin layer of meta-atoms with fixed thickness \(d\). Metasurfaces significantly reduce the size of optical devices with comparable or even unavailable novel functionalities, such as a metalens with close-to-unity numerical aperture and a planar profile [4; 5; 6], polarization-multiplexed holography [7; 8; 9; 10], the synthesis of multiple functions [11; 12; 13], and coupling of spin-angular momentum [14; 15], to name a few. Actively-tunable or reconfigurable responses are highly desired in practical applications including dynamic wavefront shaping, adaptive optics, and single-pixel detection, which can be facilitated by including functional materials in the metasurfaces with dynamic modulation. Graphene, a single layer of carbon atoms arranged in a honey-comb lattice, is an outstanding candidate with extraordinary electrical and optical properties [16; 17], as its Fermi level and the corresponding charge carrier densitycan be drastically modified by DC gate biasing. In graphene metasurfaces, the material and structure promote each other such that the resonator strengthens the interaction of light with the atomic thin layer, and the tunable material property of graphene in turn modulates the response of meta-atoms. Therefore, the structured graphene or integration of graphene with passive metasurfaces is an effective solution to enhance the dynamic modulation of beam engineering. Compared to metasurfaces employing other active materials with different tuning mechanisms, such as electrically-tuned liquid crystals [18; 19], thermally-modulated phase change materials [20], and mechanically-deformed elastic materials [21; 22; 23], graphene metasurfaces have several advantages. Graphene as the thinnest active material is naturally compatible with planar metasurfaces and silicon photonics. The electrical tuning speed is very high, from MHz [24; 25] to GHz [26], with a large dynamic tuning range or tuning depth. More importantly, the material property of graphene can be electrically modulated in an extremely wide spectrum from sub-terahertz (sub-THz) to near-infrared (near-IR). Interestingly, the conductivity modulation in different sub-bands is quite different, with modulation focused on the real part at sub-THz and on the imaginary part at higher frequencies, leading to various adjustable properties in metadevices. The development of graphene metasurfaces starts from intensity modulation. In 2011, the intensity modulation of the THz wave in graphene micro-ribbon array was reported [27], followed by several designs as modulators and switches [24; 25; 28; 29; 30; 31], tunable metasurface absorbers [26; 32]. and spatial light modulators [33]. Besides intensity modulation, increasing attention has focused in recent years on the phase modulation for dynamic wavefront shaping and tunable polarization control, with plenty of theoretical designs and several experimental breakthroughs. This paper emphasizes recent development of graphene metasurfaces for active control of phase and polarization, which has not been systematically summarized in related review articles [3; 34; 35]. The paper is organized as follows.