## 3 Simulated Results and Discussion
Furthermore, Figure 4a shows the phase difference between the five frequency bands as mentioned above, which is nearly equal to \(\pm 90^{\lx@math@degree}\) or an odd multiple of \(90^{\lx@math@degree}\). Thus, both conditions for the LP-CP conversion have been satisfied in the frequency ranges 12.29-12.63, 16.08-24.16, 27.82-32.21, 33.75-38.74, and 39.70-39.79 GHz. In addition, we express the \(AR\) to calculate the CP waves. In the design,an \(AR\) of less than 3 dB is generally considered a CP wave, and the \(AR\) can be determined using the following equation [9]:  
\[AR=10\log_{10}(|\tan\chi|) \tag{4}\]  
where '\(\chi\)' denotes the elliptical angle, and follows this equation:  
\[\chi=\frac{1}{2}\text{arcsin}(\beta) \tag{5}\]  
where '\(\beta\)' is ellipticity and can be calculated as:  
\[\beta=\frac{2R\sin\Delta\varphi}{1+R^{2}}\text{ and }R=\frac{r_{xy}}{r_{yy}} \tag{6}\]  
where \(\Delta\varphi=\varphi_{yy}-\varphi_{xy}\) denotes the phase difference of the reflection coefficients. Where the corresponding co- and cross-polarization phases are \(\varphi_{yy}\) and \(\varphi_{xy}\), respectively. According to EM wave theory, the reflected wave is RHCP if \(\chi=-45^{\circ}\big{(}\Delta\varphi=-90^{\circ}\big{)}\) and LHCP if \(\chi=45^{\circ}\big{(}\Delta\varphi=90^{\circ}\big{)}\). Also, the reflected wave is LHCP if \(\beta=+1\) and RHCP if \(\beta=-1\), respectively. Figure 4b, c show the \(AR\) and elliptical angle with the ellipticity curves of the proposed structure. The \(AR\) is less than 3 dB in the five frequency bands of 12.29-12.63, 16.08-24.16, 27.82-32.21, 33.75-38.74, and 39.70-39.79 GHz; therefore, the LP incident waves in these bands will be reflected as CP waves. The blue dotted line indicates the 3 dB region. Figure 3: The simulated results for the magnitudes (\(r_{xy}\), \(r_{yx}\), \(r_{yy}\), and \(r_{xx}\)): **(a)** semicircle (type I); **(b)** slotted rectangular patch (type II); **(c)** proposed metasurface (yellow region indicates the CP region where \(r_{xy}=r_{yy}\) and \(r_{yx}=r_{xx}\)); **(d)** PCR (%) (dotted circle shows the PCR reaches 100%). Figure 4c shows that the ellipticity is almost \(\pm 1\) within the five frequency bands of 12.46, 16.78-23.14, 28.84-32.02, 35.04-38.46, and 39.76 GHz, respectively. Three frequency bands have RHCP waves, namely 16.78-23.14, 28.84-32.02, and 35.04-38.46 GHz; the two frequency bands that have LHCP waves are 12.46 and 39.76 GHz. Additionally, Figure 4c demonstrates that the elliptical angle is approximately \(-45^{\circ}\) in three frequency ranges, namely 16.78-23.14, 28.84-32.02, and 35.04-38.46 GHz, and the elliptical angle is close to \(+45^{\circ}\) in two frequency ranges, 12.46 and 39.76 GHz, demonstrating that the reflected polarized waves are RHCP and LHCP, respectively. Figure 4d shows that the reflection components \(r_{yy}\) and \(r_{xy}\) have nearly the same magnitude \(\left(|r_{xy}|/|r_{yy}|\approx 1\right)\) for the frequencies 12.46, 16.88-23.11, 26.1-32.44, 34.97-38.49, and 39.75 GHz, where yellow area represents that the ratio of co-and cross-polarization are nearly equal to 1. There are several bands between 10 and 40 GHz where circular polarization is satisfied. It is worth mentioning that the five frequency bands offer near-ideal CP conversion. These ideal characteristics are attributed to the negligible loss in the substrate, equal power distribution, and \(\pm 90^{\circ}\) (or an odd integral multiple of \(90^{\circ}\)) phase difference between the two orthogonal reflection components.