# Design of an Optically Transparent Microwave Absorber Based on Coding Metasurface
## 2 Design and Simulation
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(h_{\text{s}}\) & \(h_{\text{p}}\) & \(w\) & \(p\) & \(r\) & \(R_{\text{S1}}\) & \(R_{\text{S2}}\) \\ \hline
0.3 mm & 5.6 mm & 13 mm & 30 mm & 3 mm & 110 \(\Omega\) & 8 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of the unit structure shown in Figure 1.  
Figure 2: (a) Phase difference of absorber unit as a function of frequency. (b) Reflection coefficient of absorber unit as a function of frequency. particle position, i.e., the coding sequence is optimized and considered as a random matrix (containing only 0 and 1), as is the particle velocity. The metasurface cell structure has an initial value of 0 or 1 corresponding to 0 or \(\pi\). The curve of the fitness function obtained by numerical optimization using Matlab is shown in Figure 3. It can be seen that the curve decreases rapidly in the initial stage and then stabilizes, indicating that the APS-PSO algorithm has high efficiency. The APS module calculates the RCS reduction with the current phase arrangement, and then calculates the fitness function value and returns it to the PSO module. After several iterations, the phase arrangement of the coding metasurface with the maximum RCS reduction is obtained. The structure of the coding sequence absorber is shown in Figure 4.  
The simulation of the optically transparent absorber is performed by finite integration technique using the CST MWS software. Floquet ports with normal incident plane transverse electric (TE) waves and transverse magnetic (TM) waves were set in the z-direction for excitation. Periodic boundary conditions (PBCs) along the x and y directions were used to simulate the infinite periodic element, and frequency-dependent complex S parameters can be simulated by the frequency domain solver. To maximize the absorptance \(A(\omega)\), we need to minimize the reflectance \(R(\omega)\) and transmittance \(T(\omega)\). The absorptance of a microwave absorber is usually expressed by the  
Figure 4: (**a**) Absorber structure. (**b**) Top view of the absorber. Figure 3: Adaptive evolution curve. reflectance \(R(\omega)\) and transmittance \(T(\omega)\), both of which depend on the frequency of the incident electromagnetic wave. They can be defined as:  
\[A(\omega)=1-R(\omega)-T(\omega) \tag{1}\]  
\[A(\omega)=1-\left|S_{11}\right|^{2}-\left|S_{21}\right|^{2} \tag{2}\]  
Transmittance (\(T(\omega)=\left|S_{21}\right|^{2}\)\(T(\omega)=\left|S_{21}\right|^{2}\)) and reflectance (\(R(\omega)=\left|S_{11}\right|^{2}\)) are shown separately in the form of \(S\) parameters [25]. To describe the characteristics of microwave absorbers, the effective medium parameters, the effective permittivity \(\varepsilon_{\textit{eff}}(\omega)\), and the effective permeability \(\mu_{\textit{eff}}(\omega)\) can be used. Figure 5a,b show the effective permittivity \(\varepsilon_{\textit{eff}}(\omega)\) and the effective permeability \(\mu_{\textit{eff}}(\omega)\), respectively. It can be observed that the real part of both parameters is close to zero at the absorptance frequency, which indicates that the reflectivity is close to zero. Figure 5c shows the simulated effective impedance normalized by the free-space impedance, and the effective impedance of the absorbing structure can be expressed as [26]:  
\[Z_{\textit{eff}}=\sqrt{\frac{\mu_{\textit{eff}}(\omega)}{\varepsilon_{\textit{ eff}}(\omega)}}=\sqrt{\frac{\left(1+S_{11}\right)^{2}-S_{21}^{2}}{\left(1-S_{11} \right)^{2}-S_{21}^{2}}} \tag{3}\]  
The real part of the effective impedance fluctuates around 1 in the 4.5-9.45 GHz frequency range, while the imaginary part is almost zero in the 6.3-8.7 GHz frequency range. We can conclude that the input impedance of the structure is almost matched with the impedance matching free space Z0 of the structure, and the impedance of the microwave absorber is perfectly matched with the free space due to the rational and optimal design of the unit structure.