## 3 Results and Discussion  
Based on the proposed anisotropic metasurface, a linear polarization beam splitter is firstly designed to independently deflect \(x\)- and \(y\)-polarized waves at opposite oblique angles of \(-28.4^{\circ}\) and \(28.4^{\circ}\) in the \(x\)-\(z\) plane, by engineering the phase gradient along the \(x\)-direction, respectively. As is well known, for a surface with phase gradient of \(\partial\Phi/\partial x\) along the interface, the reflected beam can be described by generalized Snell's law, as follows [2]:  
\[\sin\theta_{\rm r}-\sin\theta_{\rm i}=\frac{\lambda_{0}}{2\pi\omega_{\rm i}} \frac{\partial\Phi}{\partial x} \tag{1}\]  
Figure 3: **(a)** The amplitude and (**b**) phase of S\({}_{11}\) of the proposed unit cell as a function of dx. **(c)** The amplitude and (**d**) phase of S\({}_{11}\) of a unit cell without square ring as a function of dx. Here, dy = 4.5 mm. where \(\theta_{\rm r}\) and \(\theta_{\rm i}\) are the angles of reflection and incidence, respectively. \(\lambda_{0}\) is the incident wavelength in a vacuum. \(n_{\rm i}\) is the refractive index of the incidence space, which equals 1 in our case. Therefore, we select six cells with different geometric parameters to satisfy the phase gradient, achieving linear polarization beam splitting. Table 1 summarizes the sizes and phase distributions of the six unit cells along the \(x\)-axis, where n is the number of the unit cell, and \(\Phi_{\rm x}\) and \(\Phi_{\rm y}\) are the phase response of the cells for incident \(x\)- and \(y\)-polarized waves, respectively. The phase gradient for \(x\)- and \(y\)-polarization are \(-60^{\circ}\) and \(60^{\circ}\), therefore resulting in reflection angles of \(-28.4^{\circ}\) and \(28.4^{\circ}\), respectively. In addition, for the sake of a better result, we design a beam splitter consisting of \(3\times 2\) element arrays of the supercell. Figure 4a,b schematically shows the supercell and the prospect view of our designed beam splitter, respectively. To simulate, the periodic boundary condition is set only in the \(y\) direction, while the open boundary condition is used in both \(x\) and \(z\) directions [31]. The incidence is set as a waveguide port, irritating the quasi-plane wave. To depict the phenomenon of the polarization beam splitting, the near-field distributions of the electric field for the \(x\)- and \(y\)-polarized waves are plotted in Figure 5a,b, respectively. Both polarization components are not reflected normally, but at an oblique angle of \(-28.4^{\circ}\) and \(28.4^{\circ}\) for the \(x\)- and \(y\)-polarized waves, respectively. This is in a good agreement with the theoretical value of generalized Snell's law. In addition, the return loss of the polarization beam splitter at the incident port is shown in Figure 5c, presenting the dips lying at around 15 GHz for both the \(x\)- and \(y\)-polarized waves. It indicates that the energy is deflected at oblique angles, and it does not return to the incident port. Thus, it is further demonstrated in that the anisotropic metasurface has a great potential in the application of microwave polarization manipulation. It should be noted that the deviation of the simulated \(x\)-polarized wave from the theoretical design results from the coupling along the \(x\)-axis between the neighboring unit cells. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**n** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline dx (mm) & \(4.00\) & \(4.71\) & \(4.88\) & \(5.00\) & \(5.16\) & \(5.73\) \\ dy (mm) & \(5.73\) & \(5.16\) & \(5.00\) & \(4.88\) & \(4.71\) & \(4.00\) \\ \(\Phi_{\rm x}\) (deg) & \(-45.6\) & \(-105.6\) & \(-165.6\) & \(-225.6\) & \(-285.6\) & \(-345.6\) \\ \(\Phi_{\rm y}\) (deg) & \(-345.6\) & \(-285.6\) & \(-225.6\) & \(-165.6\) & \(-105.6\) & \(-45.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sizes and phase distributions of the six unit cells. Figure 4: The schematic of the designed metasurface.