## 3 Simulation Results of Unit Cell and Theory Analysis of LCPC  
To achieve the proposed MS with dual polarization conversion properties, the unit cell needs to be capable of controlling both the amplitude and phase of EM waves. When an \(x\)- or \(y\)-polarization plane wave is incident on the top surface of the RMS unit cell, the incident electric field can be represented as:  
\[\overset{\rightarrow}{E_{ix(y)}}=\ E_{ix(y)}\text{exp}(j\varphi_{ix(y)})e_{ix( y)} \tag{5}\]  
Figure 2: Deflection characteristics of nematic phase LC molecules with applied bias voltage are listed as: (**a**) without a bias voltage, (**b**) with a bias voltage (\(0<V<V_{max}\)), (**c**) with a bias voltage (\(V\geqslant V_{max}\)), and (**d**) elements labeling. where \(e_{ix(y)}\) denotes the unit vector of the incident wave. Due to the anisotropy of the structure, the polarization direction of the EM wave is altered, and the reflected wave can be decomposed into two orthogonal field components. Consequently, the reflected electric field can be expressed as:  
\[\overrightarrow{E_{r}}=\ E_{rx}\text{exp}(j\varphi_{rx})e_{rx}+\ E_{ry}\text{ exp}(j\varphi_{ry})e_{ry} \tag{6}\]  
where \(E_{rx}\) and \(E_{ry}\) are the amplitudes of the reflected wave in the \(x\)- and \(y\)-direction electric field components, respectively. \(\varphi_{rx}\) and \(\varphi_{ry}\) are the corresponding phases of the reflected wave in the \(x\)- and \(y\)-direction electric field components. Additionally, \(e_{rx}\) and \(e_{ry}\) are the unit vectors of the reflected wave in the \(x\)- and \(y\)-directions, respectively. Similarly, as shown in [31], the reflected electric field, \(\overrightarrow{E_{r}}\), can also be expressed as:  
\[\overrightarrow{E_{r}}= \begin{bmatrix}E_{x}^{r}\\ E_{y}^{y}\end{bmatrix} =R\cdot E_{i}= \begin{bmatrix}r_{xx}&r_{xy}\\ r_{yx}&r_{yy}\end{bmatrix}\begin{bmatrix}E_{x}^{i}\\ E_{y}^{i}\end{bmatrix}  \tag{7}\]  
where \(r_{xx}\) and \(r_{yy}\) represent the co-polarized reflection coefficient amplitude components for vertical polarization (VP) and horizontal polarization (HP) waves, respectively. Meanwhile, \(r_{xy}\) and \(r_{yx}\) denote the cross-polarized reflection coefficient amplitude components for both. For instance, considering \(x\)-polarization (i.e., horizontal polarization), where \(r_{xx}= \begin{vmatrix}E_{x}^{r}/E_{x}^{i}\end{vmatrix} \),\(r_{yx}= \begin{vmatrix}E_{y}^{r}/E_{x}^{i}\end{vmatrix} \). When \(r_{xx}=\ r_{yx}\) and the phase difference \(\Delta\varphi_{yx}=\ \varphi_{xx}-\varphi_{yx}=\ 2k_{0}\pi\ \pm\ \pi/2\) (\(k_{0}\) takes an integer), LCPC is achieved. If the AR of the reflected EM wave is less than 3 dB, the reflected wave can be considered as a CP wave, and the formula for calculating the \(AR\) is as follows [23; 32]:  
\[AR=\ \left(\frac{\left|R_{+,+}\right|^{2}+\left|R_{-,+}\right|^{2}+\sqrt{a}}{ \left|R_{+,+}\right|^{2}+\left|R_{-,+}\right|^{2}-\sqrt{a}}\right)^{1/2} \tag{8}\]  
where a = \(\left|R_{+,+}\right|^{4}+\left|R_{-,+}\right|^{4}\)+2 \(\left|R_{+,+}\right|^{2}\)\(\left|R_{-,+}\right|^{2}\) cos(2\(\Delta\varphi_{-,+}\)), \(+\) and \(-\) refer to the polarization signs of the incident and reflected waves, respectively. Additionally, \(\Delta\varphi_{-,+}=\varphi_{++}-\varphi_{-+}\). To specifically probe the LCPC, some parameters are introduced, where the incident EM wave is either \(x\) or \(y\)-polarized.