## 2 Design, Simulation, and Theoretical Analysis
shows that \(r_{uu}\) and \(r_{vv}\) are both close to unity with only a slight distinction related to the dielectric loss in the substrate. As shown in Figure 3d, the phase difference (\(\Delta\varphi\)) at both 10.67 and 12.23 GHz is equivalent to \(-180^{\circ}\) and \(\Delta\varphi\) at both 16.19 and 19.67 GHz is \(180^{\circ}\). These four frequencies are nearly identical to the frequencies indicated in Figure 2a. The phase difference between the EM waves polarized along the \(u\)- and \(v\)-directions after reflection is in the \(-180^{\circ}\pm 20^{\circ}\) range, within the frequency range from 9.84 to 13.15 GHz. However, \(\Delta\varphi\) is in the \(180^{\circ}\pm 20^{\circ}\) range within the frequency range from 15.25 to 20.33 GHz. According to the phase difference formula \(\Delta\varphi=\varphi_{uu}-\varphi_{vv}=2n\pi\pm\pi\) (\(n\in Z\)), the direction of the reflected EM wave changes to \(\hat{u}-\hat{v}\), which is perpendicular to the polarization direction of the incoming EM wave \(\hat{u}+\hat{v}\). This indicates that the polarization direction of the EM wave can rotate by \(90^{\circ}\). In addition, \(\Delta\varphi\) is exactly equal to \(0^{\circ}\) at the frequency of 14.03 GHz, where there is hardly any cross-polarized refection, as indicated in Figure 2d. Therefore, the designed polarization converter is able to change the \(y\)- or \(x\)-polarized illuminating waves into their mutually perpendicular counterparts within the two broadbands. Additionally, the polarization conversion efficiency is very nearly 100%. To further study the operational principle of the designed linear polarization converter, the surface current distributions on the top metasurface structure and bottom metallic ground sheet at the four resonance frequencies of 10.67 GHz, 12.22 GHz, 16.18 GHz, and 19.51 GHz in the case of \(y\)-polarized incidence are shown in Figure 4. The types of resonance at these resonance frequencies are related to the flow directions of the induced currents. Figure 4a1,a4 show that the induced surface currents on the inner ring are parallel to those on the outer ring at 10.67 and 19.51 GHz. These surface current distributions correspond to electric dipole resonances [47]. In contrast, at 12.22 and 16.18 GHz, the anti-parallel inducted currents are generated between the outer ring and the inner ring, and the magnetic dipole resonances are formed, as indicated in Figure 4a2,a3. In addition, the directions of surface current on the top and bottom layers are the same at 19.51 and opposite at 10.67 GHz, which lead to electrical coupling and magnetic coupling between the top and bottom layers, respectively. At  
Figure 3: (**a**) Definitions of the \(u\)- and \(v\)-axes, (**b**) reflected amplitudes of the cross-polarization, (**c**) reflected amplitudes of the co-polarization, and (**d**) phase difference of the co-polarization for the electric fields in the \(u\)- and \(v\)-axis directions. 12.22 and 16.18 GHz, there are currents in the same and opposite directions between the top and bottom layers, which result in cross-coupling between the induced electric and magnetic fields. Therefore, it is crucial that the dual-broadband and high-efficiency performance is achieved for these four resonances. It can be considered that the extended bandwidth of the cross-polarized reflection is primarily caused by the overlying magnetic resonance and electrical resonance. This also implies that the proposed metasurface is able to work over a broadband through reasonable optimization of its geometrical parameters as a result of the multiple resonance characteristics [48; 49; 50]. Interference theory can be used to further determine the reasons for the high polarization conversion efficiency.