# Dynamic and Active THz Graphene Metamaterial Devices
## 3 Applications of Graphene Metamaterial
### THz Phase Modulation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Work** & **Frequency** & **Mod. Loss** & **Phase Mod.** & **Ref.** \\ \hline [PERSON] et al. & 0.5–0.75 THz & - & 32.2\({}^{\circ}\) & 2012 [58] \\ [PERSON] et al. & 0.1–0.8 THz & 18 dB & 57\({}^{\circ}\) & 2014 [61] \\ [PERSON] et al. & 11.82 GHz & 60 dB & 90\({}^{\circ}\) & 2018 [72] \\ [PERSON] et al. & 39 THz & 10 dB & 55\({}^{\circ}\) & 2016 [73] \\ [PERSON] et al. & 33.3–37.5 THz & - & 237\({}^{\circ}\) & 2017 [74] \\ [PERSON] et al. & 50.42 THz & 37 dB & 180\({}^{\circ}\) & 2017 [75] \\ [PERSON] et al. & 0.75 THz & 41.62 dB & 91.8\({}^{\circ}\) & 2018 [76] \\ [PERSON] et al. & 1.2 THz & 50 dB & 180\({}^{\circ}\) & 2018 [77] \\ [PERSON] et al. & 4.15–4.65 THz & 15.5 dB & 184.5\({}^{\circ}\) & 2018 [78] \\ [PERSON] et al. & 0.5–1.6 THz & 12 dB & 140\({}^{\circ}\) & 2018 [79] \\ [PERSON] et al. & 0.7–1.9 THz & 8 dB & 360\({}^{\circ}\) & 2019 [80] \\ [PERSON] et al. & 0.2–1.0 THz & - & 346\({}^{\circ}\) & 2021 [69] \\ [PERSON] et al. & 5.7–6.1 um & - & 330\({}^{\circ}\) & 2021 [81] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of THz phase modulators. Figure 5: The transmissive tunable graphene terahertz phase modulator. (**a**) Fabrication process of the photoelectric metasurface composed of graphene, polyimide, and perovskites, transmission phase difference of the perovskite\(-\)graphene metadevice under photo\(-\)electric excitation; (Reprinted with permission from ref. [69] Copyright 2022, American Chemical Society) (**b**) Phase shift and magnetic field amplitude of scatters by graphene plasmonic resonance for an infinitely long nanoribbon versus the Fermi level, where the magnetic field amplitude drops sharply from the resonance region; the magnetic field amplitude and phase shift are enhanced under two independent Fermi levels of two parallel nanoribbon; (Reprinted with permission from ref. [82] Copyright 2014, Wiley\(-\)VCH) (**c**) Monolayer graphene split-rings are transferred on the MgF2 with a layer of ion-gel on top for polarization modulation, the vertical view of split-ring with geometrical parameters; the eight units with different opening angles form one supercell, covering 360\({}^{\circ}\) phase response with an amplitude of nearly 0.4. (Reprinted with permission from ref. [80] Copyright 2019, Elsevier). Compared with the phase shift induced by resonance, the Pancharatnam-Berry (PB) phase comes from the rotation angle of the structure. [PERSON] et al. designed a metasurface based on the PB phase to modulate the phase of the cross-polarized transmitted wave [83]. The phase modulation of the structure is related to the polarization state of the transmitted wave. For the transmitted component with cross-polarization, the phase shift is equal to twice the rotating angle of the unit. Instead, there is no phase change for co-polarized waves, no matter how the unit rotates. [PERSON] et al. applied the PB phase to a tunable graphene focusing lens composed of the gold metasurface containing different rectangular apertures covered with monolayer graphene [76]. In order to realize the tunable focusing lens, the abrupt phase distribution of the lens needs to ensure that all transmitted light is in phase at the focal point, and as the Fermi level of graphene changes, the phase changes at different positions need to be different. For this lens, the total phase shift included the PB phase determined by the aperture rotation and the resonant phase determined by resonance. Therefore, apertures of different lengths were introduced because resonances from different lengths have diverse responses when changing the Fermi level of graphene. The lens' focal length can change from 10.46 mm to 12.24 mm when the applied gate voltage increases from 0 V to 2 V.  
Other patterned graphene structures, such as graphene nanoribbons and graphene split rings, have also been investigated to achieve phase modulation. [PERSON] et al. proposed the monolayer graphene as nanoribbons, exploring a significant phase modulation of graphene [82].