# Dynamic and Active THz Graphene Metamaterial Devices
## 3 Applications of Graphene Metamaterial
### THz Phase Modulation
The strong interactions between the composite coupling structure and the light enabled sufficient phase shifts at the resonant frequency range, achieving a maximum phase shift of 360\({}^{\circ}\) at 6.2 \(\upmu\)m and a phase shift of no less than 270\({}^{\circ}\) at 5.7 \(\upmu\)m to 6.1 \(\upmu\)m.  
[PERSON] et al. also realized a broadband phase modulator based on the graphene-metal hybrid structure [78]. The metal resonator is a disk with a gap in the middle, as shown in Figure 6b. It is well known that where the curvature of the conductor is large, the charge density becomes high. Therefore, the electric field is strongly localized at the edges  
Figure 6: The reflective tunable graphene terahertz phase modulator. (**a**) Graphene\(-\)metal hybrid modulator was composed of the silver split ring and nanorod with monolayer graphene as active material, the phase tunability of SRR and LC is smaller than that of the coupling structure; the phase modulation range and smoothness under four incident wavelengths, the maximum shift of nearly 360\({}^{\circ}\) can be achieved at 6.1 \(\upmu\)m; (Reprinted with permission from ref. [81] Copyright 2021, Elsevier) (**b**) Reflection unit consisted of a graphene sheet and a gold disk separated in the middle, comparison of phase difference for the bare graphene and the metal\(-\)graphene metasurface at 4.5 THz; the reflection phase distribution of \({}^{\circ}\)(\(E_{F}\) = 0.05 eV) and \({}^{\circ}\)(\(E_{F}\) = 0.4 eV) elements in coding metasurface, the phase difference was approximately 180\({}^{\circ}\) at frequency from 4 THz to 5 THz; (Reprinted with permission from ref. [78] Copyright 2021, Elsevier) (**c**) Tunable Brewster reflection phase modulator based on graphene\(/\)quartz surface with broad bandwidth and high modulation speed; diagram of the incident light from air to graphene\(/\)silica substrate, which was the operation principle for the Brewster modulator; the broadband phase modulation can be achieved under different gate voltages in the frequency range of 0.2\(-\)1.6 THz. (Reprinted with permission from ref. [79]. Copyright 2018, Nature Publishing Group). of the disk. When the Fermi level increases, the carrier density in graphene increases simultaneously; the free carriers are driven by the electric field of the metal disk and gather at the edge of the graphene ribbon. As a result, the strongly enhanced electric field in graphene induces nonlinear effects, causing the phase shift to change quadratically with the electric field. Therefore, the phase of the reflected wave can range from \(-150^{\circ}\) to \(145^{\circ}\) by tuning the Fermi level of graphene, and the maximum phase shift can approach \(350^{\circ}\). Furthermore, a coding metasurface with a disk radius of 18 \(\upmu\)m was proposed to modulate the far-field scattering of reflected waves. They defined the corresponding states of 0.05 eV and 0.4 eV Fermi levels as \"0\" and \"1\" codes, respectively. The phase difference between the two states was between \(140^{\circ}\) and \(-184.5^{\circ}\) in the 4.15-4.65 THz band, which can realize the regulation of reflected light in the broadband range. For the Pancharatnam-Berry phase above, it is also applicable in reflective modulators. [PERSON] et al. applied the PB phase for a reflector focusing lens by etching a rectangular aperture array on monolayer graphene [84]. The proposed lens comprised monolayer graphene, a metal reflector, and a dielectric layer. The continuous \(2\uppi\) phase shift and the high reflectivity enabled the lens to control the terahertz efficiently. The lens can achieve a high focusing efficiency of more than 60% and dynamically modify the focusing intensity and the focal length. Independent of resonant structure, [PERSON] et al. designed a graphene metasurface based on the tunable Brewster angle with a high modulation depth and a large bandwidth [79], as shown in Figure 6c.