## 2 The Principle and Element Design of the CPFRA
### Geometry and Performance of the Metasurface-Based Element on the Primary Reflector Surface
#### 2.3.1 Design of the Transmissive Linear-to-Circular Polarization Converter  
Based on the architecture proposed in Section 2.1, the sub-reflector surface needs to have the functions of converting LP to CP and polarization selection. Inspired by the linearly polarized grids and the transmission-type circularly polarized mender lines, a transmissive linear-to-circular polarization converter based on polarized grids and mender lines is proposed as the sub-reflector surface element. The geometry is shown in Figure 7. As shown in Figure 7a, \(\overset{\rightharpoonup}{E}_{y}^{t}\) represents the electric field of the transmitted EW along the \(y\)-polarization direction, \(\overset{\rightharpoonup}{E}_{x}^{t}\) represents the electric field of the transmitted EW along the \(x\)-polarization direction, \(\overset{\rightharpoonup}{E}_{y}^{m}\) represents the electric field of the incident EW in the \(v\)-polarization direction, and \(\overset{\rightharpoonup}{E}_{u}^{r}\) represents the electric field of the reflective EW in the \(u\)-polarization direction. The polarization converter is composed of a four-layer dielectric substrate, which is made of Rogers Duroid 4350 material with the same thickness \(h\). Under each layer of dielectric substrate layer is an air layer. The thicknesses of the air layers are \(d_{1}\), \(d_{2}\), and \(d_{3}\). Each layer of the dielectric substrate is covered with metal on the bottom and without metal on the top. The top metal layer to the third metal layer are mender lines, and the top and third mender lines are the same. The top and second metal layers are displayed in Figure 7b,c. Figure 7d shows the bottom metal layer, which is composed of polarized grids. The detailed parameter values of the transmissive linear-to-circular polarization converter are listed in Table 1.  
The working principle of the proposed transmissive linear-to-circular polarization converter is as follows: When the linearly polarized EWs along the \(u\)-polarization direction are incident to the transmissive linear-to-circular polarization converter on the sub-reflector surface, they are reflected back and cannot pass through this polarization converter because of the polarization selection characteristic of the polarized grids. However, the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameters** & \(\mathbf{h}\) & \(\mathbf{d_{1}}\) & \(\mathbf{d_{2}}\) & \(\mathbf{d_{3}}\) & \(\mathbf{w_{1}}\) & \(\mathbf{w_{2}}\) & \(\mathbf{sur\_w}\) \\ \hline Value & 0.508 mm & 0.508 mm & 1 mm & 3.3 mm & 2 mm & 1.85 mm & 2.2 mm \\ \hline
**Parameters** & \(\mathbf{l_{1}}\) & \(\mathbf{l_{2}}\) & \(\mathbf{l_{3}}\) & \(\mathbf{l_{4}}\) & \(\mathbf{w}\) & \(\mathbf{s}\) & \(\mathbf{sur\_s}\) \\ \hline Value & 0.3 mm & 1.46 mm & 0.2 mm & 0.4 mm & 0.2 mm & 0.4 mm & 0.3 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Values of the polarization converter.  
Figure 6: Surface current distribution of a \(2\times 2\) patch layer based on metasurface-based element.  
linearly polarized incident EWs along the \(v\)-polarization direction can pass through this structure and be converted into two orthogonal components with equal amplitudes and a phase difference of \(-90^{\circ}\). These two components can be synthesized to achieve a circular polarization characteristic.