# Dynamic and Active THz Graphene Metamaterial Devices
## 3 Applications of Graphene Metamaterial
### THz Phase Modulation
The surface plasmon resonance of nanoribbon allows a significant phase shift, and both the Fermi level and the width of nanoribbon can affect the phase shift. However, the single nanoribbon cannot provide enough scattered amplitude for wave front control, as shown in Figure 5b. Researchers have attempted to combine the two nanoribbons as a unit cell to increase the intensity of the magnetic field. The unit cell's normalized scattered wave amplitude is maintained at approximately 0.5. At the same time, the phase shift range of nearly 180\({}^{\circ}\) is sufficient for the modulation requirements, which can be used to build new ultra-thin graphene metasurface. [PERSON] et al. arranged graphene split rings on a dielectric substrate to form tunable lenses for tunable polarization conversion and wave front control [80], as shown in Figure 5c. The collective oscillation of electrons was excited by incident light in graphene split rings, corresponding to efficient surface plasmons. Due to the structural properties of the graphene split rings, the mode of the surface plasmon transformed, resulting in a strong polarization conversion. For the efficient manipulation of the cross-polarized components, a linear variation of the phase shift (360\({}^{\circ}\)) along the metasurface must be achieved. The 360\({}^{\circ}\) phase modulation can be reached by adjusting the geometric parameters of split rings in 0.7-1.9 THz, while maintaining a high transmission amplitude. The overall modulation of the eight rings provides additional momentum for the cross-polarized transmitted light to deviate the wavefront from the normal metasurface. It is demonstrated that the deflection of the transmitted light decreases with increasing frequency, and the efficiency of the beam splitter can be dynamically tuned by tuning the graphene chemical potential. In contrast to the transmissive modulator, a metallic mirror is added below the dielectric substrate in the reflector phase modulator. Therefore, the incident wave propagates in a multi-path between the top and the bottom layers, resulting in resonance on the top metasurface and the bottom reflector for a large phase modulation range. [PERSON] et al. placed the monolayer graphene on the metal plate, which operates as a back reflector and gate electrode [77]. The gate voltage can adjust the surface plasma, altering the terahertz transmission in the dielectric layer and the excitation in the reflection surface, resulting in experimental phase modulation. Experiments show that a maximum of a 180\({}^{\circ}\) phase shift can be achieved at the resonant frequency of 1.2 THz. However, phase modulation at a single frequency cannot fully meet its application. [PERSON] et al. combined graphene with a gold antenna array to increase the modulation bandwidth. The unit cells are arranged together with a small gap size to enhance the in-plane component of the electric field, increasing the sensitivity to graphene optical response. Therefore, by exploiting the tunable optical permittivity of graphene, this gate-tunable device is able to continuously shift the resonance peak from 8.24 \(\upmu\)m to 8.81 \(\upmu\)m. In the tuning range, the scattering phase is significantly modulated due to the effect of changing resonant states. The metasurface achieved dynamic phase modulation in the 8-9 \(\upmu\)m band, gaining a modulation depth of more than 200\({}^{\circ}\) in the 8.5-8.75 \(\upmu\)m band [74]. [PERSON] et al. proposed another graphene coupling structure composed of multiple resonance modes to attain a more extensive depth, including dipole resonance, LC resonance, and SRR resonance [81], as shown in Figure 6a. These resonant modes are coupled with each other at a similar resonant wavelength, improving the sensitivity to the change of the surface plasmon; thus, the tunability of the composite structure is more robust than that of a single resonator with the same Fermi level variation range.