# Dynamic and Active THz Graphene Metamaterial Devices
## 3 Applications of Graphene Metamaterial
### THz Amplitude Modulation
\begin{table}
\begin{tabular}{c c c c c} \hline
**Work** & **Frequency** & **Mod. Speed** & **Depth Mod.** & **Ref.** \\ \hline [PERSON] et al. & 0.1–0.6 THz & 100 kHz & 47\% & 2012 [58] \\ [PERSON] et al. & 0.8–1.75 THz & - & 11.5\% & 2013 [59] \\ [PERSON] et al. & 2.2–3.1 THz & - & 18\% & 2014 [60] \\ [PERSON] et al. & 0.38–0.5 THz & - & 50\% & 2014 [61] \\ [PERSON] et al. & 3.5–5.5 THz & 40 MHz & 60\% & 2015 [62] \\ [PERSON] et al. & 0.1–2.5 THz & - & 93\% & 2015 [63] \\ [PERSON] et al. & 0.4–0.8 THz & - & 49.3\% & 2018 [64] \\ [PERSON] et al. & 1.5 THz & - & 92\% & 2018 [65] \\ [PERSON] et al. & 34.09–36.59 THz & 1 GHz & 90\% & 2018 [66] \\ [PERSON] et al. & 428 kHz & & 80\% & 2020 [67] \\ [PERSON] et al. & 2–0.26 THz & 2.79 ps & 40\% & 2019 [51] \\ [PERSON] et al. & 0.75–1.05 THz & 1.83 ps & 80\% & 2021 [68] \\ [PERSON] et al. & 1.6–1.74 THz & - & 70\% & 2022 [69] \\ [PERSON] et al. & 1.6–1.75 THz & - & 77\% & 2021 [70] \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of THz amplitude modulators. Compared with ionic liquids, solid-state ionic gels consisting of ionic liquids confined in copolymer blocks are more convenient to modify the carrier distribution of graphene at low voltages. [PERSON] et al. formed an electrical connection between the graphene ribbon and H-shaped units by placing a layer of ionic gel on the metal array [64]. Adjusting the gating voltage from 1 V to \(-3\) V, the maximum change of the transmitted wave reached 49.3%. In addition to amplitude, a maximum phase shift of 68.1\({}^{\circ}\) also occurred with the applied voltage. However, it is challenging to achieve amplitude or phase modulation independently. [PERSON] et al. proposed the concept of \"metamolecules\" to overcome the limitation [67]. As shown in Figure 3b, each \"metamolecule\" contains two independent subwavelength scatterers composed of the metal antenna and the graphene ribbon coupled with each other. The subwavelength noble metals improve radiative coupling to GPRs by reducing the mismatch between free photons and subwavelength scale graphene plasmons. Besides the metal plasmonic structure, metal reflectors are also incorporated to further  
Figure 3: Electronically controlled terahertz amplitude modulator based on graphene. (**a**) Sandwich structure of two-layer graphene and ionic liquid, holes, and electrons accumulate at the ionic-liquid/graphene interfaces when a voltage is applied, the transmission modulation from structures with different numbers of the graphene layer; (Reprinted with permission from ref. [63]. Copyright 2015, Wiley-VCH) (**b**) Plasmonic metamolecule composed of independently controlled graphene meta-atoms, the graphene Fermi levels applied to meta-atoms are defined by \(\mathrm{E_{F1}}\) and \(\mathrm{E_{F2}}\), a great amplitude modulation with the fixed phase of 0\({}^{\circ}\) and a 360\({}^{\circ}\) phase shift with the fixed amplitude of 0.5 can be realized by adjusting the \(\mathrm{E_{F1}}\) and \(\mathrm{E_{F2}}\) Reprinted with permission from ref. [67]. Copyright 2020, American Chemical Society; (**c**) Hybrid graphene metasurface for high-speed amplitude modulation where a-Si serves as part of the back gate electrode, the variation of reflection and modulation depth for \(\mathrm{V_{g}}=7\) V and \(-3\) V under different incident wavelengths, and spatial reflection patterns of “CNT” at \(\lambda=8.3\) μm by selectively applying different gate voltages. (Reprinted with permission from ref. [66]. Copyright 2015, Nature Publishing Group). enhance the light-matter interaction in graphene and electrostatically gate graphene. The general tuning mechanism is based on the modulation of a single resonance in the structure, which limits the degrees of freedom for independent control of amplitude and phase. For this metasurface, the GPRs are isolated from each other, and the graphene Fermi level of each scatterer can be adjusted separately, thereby providing two degrees of freedom to independently modulate the amplitude and the phase of the reflected light.