# Plasmonic and Dielectric Metasurfaces: Design, Fabrication and Applications
## 2 Plasmonic Metasurfaces
### Graphene Split-Ring Metasurface-Assisted Terahertz Coherent Perfect Absorption [122]  
Design: We present a novel graphene split-ring metasurface displaying a strong plasmonic resonance in the terahertz regime. Figure 14 shows the 2D and 3D structures of the proposed split-ring graphene film for coherent perfect absorption (CPA). For split-ring graphene film with symmetric two side (air, air) conditions (Case 1), as illustrated in Figure 14a, the interference of two counter-propagating incident beams A and B (relative intensity \(I_{\mathrm{A}}/I_{\mathrm{B}}=1\)) on such a film is described by two special cases. When the phase difference \(\phi_{\mathrm{A}}-\phi_{\mathrm{B}}=0\), the CPA occurs. Thus, the graphene reaches the maximum absorption. When the phase difference \(\phi_{\mathrm{A}}-\phi_{\mathrm{B}}=\pi\), Beam A and Beam B pass through one another without mutual disturbance. For split-ring graphene film with asymmetric two side (air, SiO\({}_{2}\)) conditions (Case 2), gate-tunable CPA is illustrated in Figure 14b, which is based on the electro-absorption effect of graphene. By electrically tuning the Fermi level of the graphene sheet, corresponding to chemical potential \(\mu_{\mathrm{C1}}\), the absorption of split-ring graphene reaches the maximum limit \(\sim\)50% for single incident beam. In this situation, when two coherent beams with equal intensities and phases are incident on the graphene from opposite sides, they will interfere with each other, leading to coherent absorption. When the chemical potential of graphene is changed to \(\mu_{\mathrm{C2}}\), the absorption of split-ring graphene is tuned to be weak. Thus, Beams A and B pass through each other nearly without loss. Hence, gate-tunable CPA is achievable. We first study the CPA of split-ring graphene film with symmetric two side (air, air) conditions (Figure 14a). The CPA is enabled by 50% absorption of the single beam and equal intensities and phases of two counter-propagating coherent beams. The chemical potential (Fermi energy) \(\mu_{\mathrm{C}}=0.3\) eV and relaxation time \(\tau=0.5\) ps are initially considered. The transmission (T), reflection (R) and absorption (A) of a split-ring graphene patterned with a periodical array are plotted in Figure 15a. When a single beam is illuminated on the patterned split-ring graphene film at normal incidence, one can see an obvious resonance around 2.91 THz. The strong resonance behaviors are expected to be electric dipolar mode. The excitation of electric dipolar mode results in the enhancement of absorption in the graphene sheet with a maximum of A = 49.92%. While the other parts of the incident beam energy are reflected or  
Figure 14: (**a**) Schematic of the coherent perfect absorption (CPA) in a split-ring graphene film (Case 1); two coherent optical beams (A, B) impinge on the graphene film from opposite sides at normal incidence; (**b**) interaction of light with light on a split-ring graphene SiO\({}_{2}\) substrate (Case 2); (**c**) a unit cell of the split-ring graphene film with geometric parameters. Reproduced with permission from [122], Copyright The Optical Society, 2015.  
transmitted. As shown in Figure 15b, when two coherent beams with equal intensities and phases are incident on the graphene from opposite sides, they will interfere with each other, leading to coherent absorption of 99.69%. Figure 15c shows the normalized coherent absorption in the split-ring graphene as a function of the relative phase difference between two counter-propagating coherent beams. At the resonance frequency of 2.91 THz, the coherent absorption varies continuously from 99.7% to less than \(2.1\times 10^{-4}\)% as the phase difference changes from 0 to 0.969%, giving a modulation contrast of 56.7 dB. We then study the gate-tunable CPA of split-ring graphene film with asymmetric two side (air, SiO\({}_{2}\)) conditions (Figure 14b). The gate tunable operation relies on the electro-absorption effect of graphene.