# Design of Tunable Broadband Graphene-Based Metasurface with Amplitude-Phase Modulation
## 3 Unit Design of Proposed Graphene-Based Metasurface  
As shown in Figure 1, the unit of graphene-based metasurface consisted of two graphene layers, two substrate layers, two layers of polyvinyl chloride (PVC), a spacer and a ground layer. The dimensions of the graphene layer and the substrate were \(a\) and \(b\), respectively. The relative permittivity for the PVC was 3.5 and the thickness was 0.07 mm. The dielectric substrate was Rogers RT5880 with a dielectric constant of 2.2 and a loss tangent of 0.0009. The thickness of the upper and the lower dielectric substrate was \(H_{1}\) and \(H_{2}\), respectively. To isolate two layers of graphene, a spacer was inserted between them. The spacer was made of hexagonal boron nitride (h-BN) with a thickness of 0.05 mm and the relative permittivity was 2.5. The DC feed was loaded between the upper and lower layers of the graphene. In this design, graphene was modeled and analyzed as a thickness-free 2-D material. The upper graphene served as the positive stage for DC excitation, while the lower graphene acted as the negative stage. Consequently, two vias with radius \(r_{1}\) were inserted into the substrate, as shown in Figure 1a. It should be emphasized that holes must be punched at the position where the longer via intersects with the lower graphene and the ground. The radius \(r_{2}\) of the hole should be greater than the radius \(r_{1}\) of the via. Table 1 presents the unit parameters of the graphene metasurface. The practical application of DC feeding for each graphene unit was considered during the design process. The upper graphene layer has a via that connects to the back of the bottom dielectric substrate, enabling some electromagnetic waves to be transmitted to the bottom. In order to make the simulation results as close as possible to the actual application scenario, a DC feed-line was incorporated behind each unit and a fan structure was positioned next to the feeder as a low-resistance node that isolated the RF signal from the DC circuit. To confirm the relationship between the phase and amplitude of the coding unit, the frequency domain simulator of the CST Studio Suite software was used to simulate and analyze the graphene metasurface unit. For this study, all discussions and results correspond to normal direction incidence scenario. The Fermi level of both upper and lower layers of graphene were simultaneously regulated, tuning it from 0 eV to 1.8 eV in steps of 0.2 eV. Figure 2 displays the reflection amplitudes corresponding to the graphene metasurface units at different Fermi energy levels. The unit reflection amplitude at the Fermi energy level of 0 eV was extremely low, but gradually increased with the applied Fermi level. This can be explained by Equation (5), as the conductivity of graphene was particularly low at the Fermi level of 0 eV, resulting in a significantly higher resistance value compared to that observed when the Fermi energy level state was applied. Therefore, in the absence of a Fermi level, the metasurface unit of graphene acted as an absorber, absorbing most of the electromagnetic waves and resulting in a low reflection amplitude \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Parameter** & **a** & **b** & **c** & **d** & \(m\) & \(n\) & \(r_{1}\) & \(r_{2}\) & \(r_{3}\) & \(H_{1}\) & \(H_{2}\) & \(H_{pcc}\) & \(H_{\text{h-BN}}\) \\ \hline Value (mm) & 2.5 & 2 & 1.4 & 0.3 & 1.45 & 0.2 & 0.1 & 0.15 & 0.4 & 0.508 & 0.254 & 0.07 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Graphene-based Metasurface Unit Parameters. Figure 1: Metasurface unit structure. (**a**) 3D-view; (**b**) front view; (**c**) side view; (**d**) bottom view. of electromagnetic waves. When voltage was applied to the graphene, the resistance value of the metasurface unit gradually decreased, resulting in an increase in the reflection amplitude of electromagnetic waves. In amplitude encoding metasurfaces, the difference in amplitude between the two states should generally be greater than or equal to 0.5.