## 3 Simulation Results of Unit Cell and Theory Analysis of LCPC
The reflection coefficients for the LCPC are LHCP and RHCP, and the right-handed circular polarization conversion rate (\(PCR_{RHCP-y}\)) for a \(y\)-polarized incident wave can be expressed as follows:  
\[r_{RHCP-x}=\frac{\sqrt{2}}{2}(R_{xx}+iR_{yx})r_{LHCP-x}=\frac{\sqrt{2}}{2}(R_ {xx}-iR_{yy})r_{RHCP-y}=\frac{\sqrt{2}}{2}(R_{xy}+iR_{yy})r_{LHCP-y}=\frac{ \sqrt{2}}{2}(R_{xy}-iR_{yx}) \tag{9}\]  
\[PCR_{RHCP-y}=\frac{\left|r_{RHCP-y}\right|^{2}}{\left|r_{RHCP-y}\right|^{2}+ \left|r_{LHCP-y}\right|^{2}} \tag{10}\]  
The simulation results of the MS unit cell under an incident \(y\)-polarized EM wave are shown in Figure 3. Figure 3a shows the co- and cross-polarized (\(r_{yy}\) and \(r_{xy}\)) amplitude components for different LC dielectric constants. Figure 3b displays the phase difference \(\Delta\varphi_{xy}\) between the co- and cross-polarized components for different LC dielectric constants. By combining Figure 3a,b, it can be observed that the LCPC conditions are met as follows: for \(\varepsilon_{r}=2.8\), frequency intervals within 8.14-8.48 GHz and 9.84-12.52 GHz, \(r_{yy}\approx r_{xy},\Delta\varphi_{xy}\) are \(-90^{\circ}\) and \(90^{\circ}\), respectively. For \(\varepsilon_{r}=3.9\), frequency intervals within 8.32-8.43 GHz, 9-9.11 GHz, and 9.86-11.83 GHz, and \(r_{yy}\approx r_{xy},\Delta\varphi_{xy}\) are \(90^{\circ}\), \(-90^{\circ}\), and \(90^{\circ}\), respectively. \(\varepsilon_{r}=4.6\), and \(r_{yy}\approx r_{xy}\) for frequency intervals within 8.96-9.11 GHz and 9.95-11.51 GHz, with phase differences of \(-90^{\circ}\) and \(90^{\circ}\), respectively. The results calculated for the incidence of \(x\)- or \(y\)-polarized EM waves are shown in Figure 4. Figure 4a,b show the magnitude components of the reflection coefficients of the reflection coefficients for the two CP reflections, calculated under the incidence of \(x\)- and \(y\)-polarized EM waves, respectively. It is evident that the reflected CP waves, obtained for an incident \(x\)- or \(y\)-polarized EM wave, propagate in opposite directions at the same frequency. This behavior results from the orthogonal symmetry of the unit cell, which has a diagonal 45\({}^{\circ}\) structure. The system is reciprocal, meaning that the unit cell exhibits symmetric behavior in the direction of signal transmission. For an incident \(x\)-polarized EM wave, with \(\varepsilon_{r}=2.8\), the reflected EM waves are primarily composed of LHCP and RHCP, with amplitudes exceeding 0.98 in the frequency ranges 8.15-8.46 GHz and 9.84-12.52 GHz, respectively. When \(\varepsilon_{r}=3.9\), the reflected EM waves are dominated by LHCP with amplitudes above 0.96 in the frequency range 9-9.11 GHz. In the frequency interval of 9.86-11.81 GHz, the reflected EM waves are dominated by RHCP with amplitudes above 0.98. For \(\varepsilon_{r}=4.6\), the reflected EM waves are dominated by LHCP and RHCP with amplitudes greater than 0.96 in the frequency ranges 8.96-9.11 GHz and 9.95-11.51 GHz, respectively. Figure 4: Calculated results at the incidence of an \(x\)- or \(y\)-polarized EM wave. Two CP reflection coefficient magnitude components (LHCP and RHCP) for (**a**) an incident \(x\)-polarized and (**b**) \(y\)-polarized EM waves and different LC dielectric constants. Figure 3: Simulation results of the MS unit cell under an incident \(y\)-polarized EM wave. (**a**) Co- and cross-polarized (\(r_{yy}\) and \(r_{xy}\)) amplitude components and (**b**) phase difference (\(\Delta\varphi_{yx}\)) for different LC dielectric constants. Figure 5 shows the computationally obtained results after simulating the MS unit cell at the incidence of a y-polarized EM wave. In Figure 5a, as the dielectric constant of the LC decreases, the ARBW gradually increases, which also corresponds to different frequency ranges in the x-band, making it suitable for flexible scheduling of the resulting circularly polarized waves. For \(\varepsilon_{r}=2.8\), AR < 3 dB in the frequency intervals 8.14-8.48 GHz and 9.84-12.52 GHz, with fractional bandwidths (FBWs) of 4.09% and 23.97%, respectively.