# Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control
## 3 Phase Modulation in Graphene Metasurfaces
### Wavefront Shaping in Reflection
Figure 5c shows that the smooth 360\({}^{\circ}\) phase variation is covered by tuning the Fermi level, and it is well maintained from 4 THz to 6 THz. Beyond this frequency range, the phase variation is either too sharp or too weak to use (Figure 5d). It leads to switching of the functionality by frequency, for example, from an anomalous reflector at 5 THz to a normal reflector at 3.5 THz. With the Fermi level of the graphene ribbon tuned spatially  
Figure 4: Reflective phase shifters with monolayer graphene for dynamic phase modulation. **(a)** Monolayer graphene is attached to the array of Al patches separated with the bottom Al film with an SU-8 spacer. **(b)** Gate-dependent reflection phase spectra of the combined structure when the Al patches have two sizes. Here, graphene as a lossy surrounding medium in sub-THz frequencies tunes the resonance intensity and phase. In each unit cell, the maximum phase change is 180\({}^{\circ}\) around the resonance frequency by tuning the biasing voltage. By utilizing two types of unit cells with different resonance frequencies and working in the shaded frequencies, a 360\({}^{\circ}\) phase change is accessible by tuning the biasing voltage. Reproduced with permission from [55], Copyright American Physical Society, 2015. **(c)** Graphene-tuned gold antenna array with back mirror. The zoom-in plot is the SEM image of the gold antennas with nanometer gaps. **(d,e)** Tunable absorption (d) and tunable reflection phase (e) for different graphene Fermi levels. The dielectric constant of graphene is sensitively modulated in the mid-IR, leading to a widely-tunable phase range of more than 200\({}^{\circ}\) from 8.5 \(\upmu\)m to 8.7 \(\upmu\)m. Reproduced with permission from [56], Copyright American Chemical Society, 2017.  
and temporally, a metalens of a large numerical aperture is numerically demonstrated with either a fixed or variable focal point over a wide bandwidth [58]. Completely different functionalities, such as cloaking, illusion, and focusing, can be implemented in one metasurface [60]. In such kinds of active designs, the efficiency is mainly governed by the mobility of graphene carriers. The study shows that the carrier relaxation time \(\tau\) seldom affects the reflection phase, but mainly controls the local reflectivity. \(\tau\) is around 1 ps in the designs of Figure 5, leading to an overall efficiency of around 60 to 70%. The efficiency can be improved to 90% if the relaxation time is increased to 5 ps [59]. Similar to the transmission cases, uniform biasing of either monolayer graphene or graphene ribbons is promising for fabrication, but limited to efficiency modulation or on-off switching of a specific function. In contrast, individual biasing of each ribbon is extremely difficult to implement in device integration, although at-will wavefront shaping is theoretically possible in real time with satisfactory efficiency. A compromise solution utilizes both the geometric phase and resonance phase with a similar configuration as Figure 3g, but working in the reflection side with a back mirror [61]. The geometric phase governs the general phase profile, and the resonance phase is tuned by the Fermi level to compensate minor phase variations needed for different focal lengths. However, in both transmission and reflection designs, the lens aperture is limited by the small tuning range of the resonance phase with the Fermi level, leading to an inaccurate focal point as compared to the design. In addition, the metasurface is endowed with increased power when more complicated graphene elements and the corresponding gate configuration are considered. For example, when two graphene patches are combined in a unit cell in-plane [62] or stacked on top of the substrate with individual gate control [63], the wavefront engineering has been studied with an increased bandwidth.