# An Optically Transparent Metasurface for Microwave Amplitude-Phase Manipulation
## 2 Results  
### Design of the Meta-Atom  
The schematic of the proposed meta-atom is illustrated in Figure 1b. To achieve visible transparency, first, optically transparent dielectric material polymethyl methacrylate (PMMA) with a thickness of \(h=3\) mm and a dielectric constant of \(2.25(1-j0.01)\) is used as the substrate. Next, the metal backplane of a traditional reflection-type metasurface is replaced by metallic meshes with a period of \(p_{m}\) and a linewidth of \(w_{m1}\). In terms of the top resonant layer, a widely used H-shaped anisotropic configuration is adopted to enable satisfactory polarization conversion efficiency [32; 33]. More significantly, the entire  
Figure 1: (**a**) Schematic of the proposed metasurface for simultaneously transmitting visible light and generating a multiplane complex-amplitude hologram. (**b**) Unit cell of the designed metasurface consisting of an anisotropic H-shaped resonator based on a metal frame and a metallic mesh separated by a PMMA substrate. (**c**) Top view of the unit cell. The geometric parameters are \(p_{m}=1\), \(w_{m1}=w_{m2}=0.05\), \(h=3\), \(p=8\), \(w=1.1\), \(a=2.6\), all in millimeters. metallic pattern of the H-shaped resonator is deliberately replaced by a metal frame with a linewidth of \(w_{m2}\), as shown in Figure 1b,c. In addition, we denote the two principal axes of the H-shaped resonator as \(u\) and \(v\), respectively, and the \(u\) axis is rotated counterclockwise by an angle of \(\beta\) with respect to the \(x\) axis of the laboratory coordinate system. After the optimization process, other geometric parameters of the designed H-shaped resonator are provided in Figure 1c, and they will not change throughout the paper unless otherwise indicated. Both the top metal frame and the bottom metallic mesh are deposited on a 50 \(\upmu\)m thick polyethylene terephthalate (PET) substrate with a dielectric constant of 3(\(1-j0.03\)), which can be easily fabricated by using mature and low-cost FPC technology. As mentioned above, the relationship between optical transparency and microwave performance should be balanced, which is mainly affected by the period and linewidth of the top metal frame and the bottom mesh layer. Here we used CST Microwave Studio 2020 commercial software based on the finite element method (FEM) to optimize the geometric parameters of the proposed meta-atom. During the simulation process, periodic boundary conditions were adopted in the \(x\)- and \(y\)-directions, while an open boundary condition was applied along the \(z\)-axis. In addition, adaptive tetrahedral mesh refinement was used to ensure the mesh convergence as well as the numerical accuracy. Figure 2a,b plot the simulated cross-polarized reflection amplitude (\(1\,r_{yx}\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)) of the designed meta-atom (\(l\) = 6.3 mm, \(\beta\) = 45\({}^{\circ}\)) with various periods (\(p_{m}\)) and linewidths (\(w_{m1}\)) of the bottom mesh layer, respectively. It is obvious that the bandwidth and efficiency of \(1\,r_{yx}\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)\(\,\)\  
Thus, we can conclude from Equation (3) that for a given meta-atom with certain \(r_{u}\) and \(r_{v}\), the cross-polarized reflection amplitude can be tuned from zero to a maximum value as \(\beta\) is varied from zero to \(\pi/4\), whereas the phase undergoes a \(\pi\) shift when \(\beta\) is \(\pi/2\). To quantitatively investigate the influence of rotation angle on the cross-polarized reflection coefficient, we simulated the amplitude and phase of \(r_{yx}\) versus \(\beta\), as shown in Figure 3a,b, respectively. It can be seen that the simulated results fit the theoretical ones well, verifying that our proposed meta-atom enables the continuous manipulation of amplitude from 0 to 0.9 by varying the rotation angle.