## 2 Unit Cell Design and Properties of LC Materials  
### Unit Cell Structure Design  
Figure 1 illustrates the geometry and corresponding dimensional parameters of the optimized polarization-converting RMS unit cell. The unit cell has dimensions of 16 \(\times\) 16 \(\times\) 2.794 mm\({}^{3}\) and consists of a 6-layer stacked structure, as shown in Figure 1a,b, from top to bottom, the polarization conversion radiation layer, orientation layer 1, LC middle layer, orientation layer 2, ground layer, and bias layer. The dielectric substrates of both the polarization conversion radiation layer and the LC middle layer are made of Rogers RT5880 material, which has a relative dielectric constant of 2.2 and a loss angle tangent of 0.0009. The polarization conversion radiation layer contains two drill holes: one for exhaust and the other for LC injection. The outer surface of the top layer is designed based on the logarithmic function expression \(G=ln(t+1)\), where \(t\) ranges from 0 to 3.7 mm. The inner surface is slotted with a cross-like slit structure to facilitate caliber coupling feed, and the patch serves as the positive electrode for the biased DC power supply. Both patches are symmetric with respect to the \(u\)- and \(v\)-axes, where the \(u\)-axis is oriented at +45\({}^{\circ}\) relative to the \(x\)-axis, and the \(v\)-axis is oriented at +45\({}^{\circ}\) relative to the \(y\)-axis. The LC middle layer contains skeletonized grooves for LC filling. The second and fourth layers are orientation layers, which are made by spin-coating a polyimide solution, high-temperature curing, and friction processing. They have a relative dielectric permittivity of 4.3 and a loss angle tangent of 0.004, and they are primarily used to pre-orient the LC molecules. The ground and other metal radiation patches are made of copper, with a conductivity \(\sigma\) = 5.8 \(\times\) 10\({}^{7}\) S/m and a thickness of 35 um. The grounded metal patch acts as the negative electrode for the DC power supply. The sixth layer is the DC bias layer, and Rogers 4350B is used as the dielectric substrate with a relative permittivity of 3.66 and a loss angle tangent of 0.0037. The DC bias circuit features a fan-shaped branch structure. Table 1 demonstrates the specific values of the optimized MS parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Para.** & **Value** & **Para.** & **Value** & **Para.** & **Value** & **Para.** & **Value** & **Para.** & **Value** \\ \hline \(L_{\text{sub}}\) & 16 & \(L_{1}\) & 3.4 & \(L_{2}\) & 2.8 & \(g_{1}\) & 0.6 & \(g_{2}\) & 3.6 \\ \(g_{3}\) & 2.7 & \(L_{\text{w}}\) & 1.5 & \(R_{\text{f}}\) & 1 & \(\hat{d}_{\text{s1}}\) & 0.3 & \(h_{1}\) & 1.524 \\ \(L_{\text{a}}\) & 9 & \(L_{\text{f}}\) & 2.5 & \(L_{\text{s1}}\) & 10.2 & \(L_{\text{s2}}\) & 0.9 & \(w_{\text{s}}\) & 0.6 \\ \(w_{\text{f}}\) & 0.4 & \(d_{\text{f}}\) & 1 & \(R_{\text{vcc}}\) & 0.9 & \(L_{\text{a}}\) & 9 & \(R_{\text{ex}}\) & 1.4 \\ \(h_{2}\) & 0.762 & \(h_{3}\) & 0.508 & \(R_{\text{gnd}}\) & 0.8 & \(R_{\text{bs}}\) & 5 & \(L_{\text{vcc}}\) & 2.5 \\ \(w_{\text{vcc}}\) & 2.4 & \(w_{\text{f1}}\) & 1 & \(d_{\text{s2}}\) & 1.5 & & & & \\ \hline \end{tabular}
\end{table}
Table 1: Optimized value (in mm) of the proposed RMS unit cell (Para. is parameter).