## 3 Theoretical Analysis
The formula \(\varphi_{ii}=Arg(R_{ii})+2k_{0}\)\(S\) is applied to determine their phase changes, where \(S\) is the separation between the proposed converter surface and the Floquet port in the simulation structure. According to Figure 7b, the magnitude of a dual-frequency wideband is nearly 1.0 throughout all frequencies, indicating minimal dielectric loss of the proposed polarization converter. The curve of \(r_{vv}\) and \(r_{uu}\) still has a great many variations, which have two and two in dual-frequency wideband local minimum values, respectively, which are found at 13.56 GHz and 40.24 GHz, as well as at 24.94 GHz and 40.65 GHz. The two and two in dual-wideband resonant modes are assumed to be simulated by \(v\)- and \(u\)-polarized incident waves, created by these local maximum dielectric losses. Additionally, the curves of \(r_{uu}\) and \(r_{vv}\) have quite distinct curvatures at various resonant frequencies, suggesting that the Q values of these resonant modes vary. Moreover, Figure 7c shows that the phase variation rate of \(r_{vv}\) and \(r_{uu}\) at each resonance frequency varies only due to the variance in Q values across different resonance modes. At a lower frequency, the phase difference \(\Delta\)\(\dots\)\(uv\) can remain close to +90\({}^{\circ}\) over the frequency band of 16.27-23.79 GHz, whereas at a higher frequency it is an integral multiple of 90\({}^{\circ}\) (in the frequency band of 27-35.23 GHz), which is primarily due to the following two causes. Firstly, compared to the first resonance mode (13.56 and 24.94 GHz) at \(v\)- and \(u\)-polarized incident in a dual-frequency wideband, it has a higher Q value in addition to possessing a lower resonant frequency. It causes the phase \(\varphi_{vv}\) in a dual-wideband to decline earlier and more quickly, and, when keeping the phase difference (\(\Delta\varphi_{uv}\)) in the 11-13.75 GHz range, is close to +90\({}^{\circ}\). Secondly, the second pair of resonant modes in a dual-frequency wideband at \(v\)- and \(u\)-polarized incidences are identical, and both are very clear. This causes the phases of \(\varphi_{uu}\) and \(\varphi_{vv}\) to change the same way as the frequency increase in the range of 15-39 GHz, allowing the phase difference (\(\Delta\varphi_{uv}\)) is close to +90\({}^{\circ}\) or an integral multiple of \(\pm\)90\({}^{\circ}\) in the following band. Finally, Figure 7d shows the axial ratio of the reflected wave via Equation (10), based on the phase difference (\(\Delta\varphi_{uv}\)) in a dual-frequency wideband obtained in Figure 7a. It is evident from Figure 3a that the anticipated axial ratio substantially agrees with Figure 7d. The above analysis has clarified that the polarization converter in a dual-frequency wideband can carry out such a high-efficiency and ultrawideband LTC reflective polarization conversion. Excluding the first two resonant modes at \(v\)- and \(u\)-polarized incidences, it can be generally ascribed to the second pair of resonance modes. A sufficient difference between the two first resonance modes causes the \(\Delta\varphi_{uv}\) in the frequency range of 10-15 GHz to be close to \(\pm\)90\({}^{\circ}\). However, due to the similarity and low Q values of the second pair of resonance modes, the phase difference (\(\Delta\varphi_{uv}\)) remains nearby +90\({}^{\circ}\) or an integral multiple of \(\pm\)90\({}^{\circ}\) in the adjacent band of 16.27-23.79 GHz and 27.0-35.23 GHz. Comparisons of the performance of this novel LTC reflective polarization conversion metasurface in a dual-wideband with those in previously published papers are tabulated in Table 2. Hence, the calculated LTC polarization conversion of 99 % of a dual-frequency wideband has been achieved in the ultrawideband frequency range.