## 3 Theoretical Analysis
The \(\Delta\varphi_{uv}\) will be altered to \(\pm 90^{\circ}\) when \(\Delta\varphi_{uv}=90^{\circ}\), resulting in a perfect LTC polarization conversion. We used the preceding study to simulate the anticipated polarization reflective converter under \(v\)- and \(u\)-polarized incidence to determine the fundamental cause of linear-to-circular polarization converters. The simulated results of a dual-frequency wideband LTC polarization, especially the \(\Delta\varphi_{uv}\) (phase difference) between \(r_{vv}\) and \(r_{uu}\), are shown in Figure 7a. The frequency bands between 16.27-23.79 GHz and 27-35.23 GHz show that the phase difference of a dual-frequency wideband always remains close to \(+90^{\circ}\). It is implied that the calculated LTC-polarization converter of a dual-wideband will be comprehended in a wide frequency range. Why is the resulting phase difference (\(\Delta\varphi_{uv}\)) so effective? To ensure the root cause, the other simulation results, such as the magnitude (\(r_{uu}\) and \(r_{vv}\)) along with the phases (\(\varphi_{uu}\) and \(\varphi_{vv}\)) of a dual-wideband, are presented in Figure 7b,c. The formula \(\varphi_{ii}=Arg(\text{R}_{ii})+2k_{0}\ S\) 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 \(\Delta\varphi_{uv}\) 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). 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 It is implied that the calculated LTC-polarization converter of a dual-wideband will be comprehended in a wide frequency range. Why is the resulting phase difference (\(\Delta\varphi_{uv}\)) so effective? To ensure the root cause, the other simulation results, such as the magnitude (\(r_{uu}\) and \(r_{vv}\)) along with the phases (\(\varphi_{uu}\) and \(\varphi_{vv}\)) of a dual-wideband, are presented in Figure 7b,c.