## 3 Simulated Results and Discussion  
The proposed meta-atom was designed and simulated using CST Microwave Studio 2021, in the reflection mode. The boundary conditions were defined as a unit cell on the \(x\)- and \(y\)-planes, and a Floquet port was used for excitation in the \(z\)-direction. We used the \(x\)- and \(y\)-polarized wave as the incident wave and defined the co- and cross-polarization reflection coefficients as follows:  
\[r_{xx}=\frac{E_{xr}}{E_{xi}}\text{ and }r_{yy}=\frac{E_{yr}}{E_{yi}} \tag{1}\]  
\[r_{yx}=\frac{E_{yr}}{E_{xi}}\text{ and }r_{xy}=\frac{E_{xr}}{E_{yi}} \tag{2}\]  
An electric field is denoted by \(E\). Moreover, '\(i\)' and '\(r\)' denote the incident and reflected EM wave, respectively. The polarization conversion ratio (\(PCR\)) can be employed to evaluate the CPC performance of a meta-atom. The \(PCR\) for an incident wave with linear polarization can be calculated using the following formulas [37]:  
\[PCR_{x}=\frac{\left|r_{yx}\right|^{2}}{\left|r_{yx}\right|^{2}+\left|r_{xx} \right|^{2}}\text{ and }PCR_{y}=\frac{\left|r_{xy}\right|^{2}}{\left|r_{xy}\right|^{2}+\left|r_{yy} \right|^{2}} \tag{3}\]  
where the reflection coefficients for cross-polarization are \(r_{xy}\) and \(r_{yx}\). The co-polarization reflection coefficients are expressed by \(r_{yy}\) and \(r_{xx}\), respectively. In Equation (3), \(PCR_{x}\) and \(PCR_{y}\) represent the polarization conversions for \(x\)- and \(y\)-polarized incidence waves, respectively. The simulated results under normal \(x\)- and \(y\)-polarized incidence waves are illustrated in Figure 3. In the unit cell's evolution stages, the semicircle patch structure, depicted in Figure 3a, performs as an LP-LP converter at 39.74 GHz, with a magnitude value of 1.0 for \(r_{xy}\) and \(r_{yx}\), respectively. In general, an amplitude of more than 80% or a magnitude of less than \(-10\) dB (\(r_{yy}\) or \(r_{xx}<-10\) dB) is deemed effective for co-polarization. Furthermore, an efficient performance requirement for the cross-polarization reflection coefficient is \(0\) dB \(<r_{yx}<-3\) dB or \(0\) dB \(<r_{xy}<-3\) dB. As depicted in Figure 3b, in single-frequency bands, covering from 17.77 to 26.01 GHz, the cross-polarization coefficient (\(r_{yx}\)) has a magnitude that is expressively greater than the co-polarization coefficient (\(r_{xx}\)). Finally, the slotted rectangular patch was added with a semicircle to enhance the polarization conversion mechanism. By integrating a slotted rectangular patch with a semicircle, the improvement in the \(r_{xy}\) and \(r_{yx}\) values can be tailored for particular frequency bands. As shown in Figure 3c, the resulting \(r_{xy}\) and \(r_{yx}\) values at the frequencies 13.81 GHz, 25.75 GHz, and 39.65 GHz, are about one, demonstrating effective CPC. Hence, in the subsequent Equation (3), the PCR values achieve 100% at 13.10-14.72, 25.43-26.00, 32.46-32.56, and 39.14-39.59 GHz, as indicated in Figure 3d. The simulated result verifies the efficiency of the proposed structure as an LP converter in the above frequency ranges. In addition, the proposed structure also performs another important function known as LP-CP conversion, or the quarter-wave plate operation (QWP). In reflection mode, two main conditions must be satisfied to accomplish LP-CP conversion. The amplitude of the reflected co- and cross-polarization components must be nearly equal \(\left(\left|r_{xy}\right|=\left|r_{yy}\right|\right)\) and \(\left(\left|r_{yx}\right|=\left|r_{xx}\right|\right)\), and the phase difference \(\left(\Delta\varphi_{yx}\right)\) between the co- and cross-polarization components should be \(\pm 90^{\lx@math@degree}\), or an odd multiple of \(90^{\lx@math@degree}\). Figure 3c shows that the co- and cross-polarization reflection coefficients of the proposed structure, which has an LP-CP function, have a comparable amplitude in five frequency bands: 12.29-12.63, 16.08-24.16, 27.82-32.21, 33.75-38.74, and 39.70-39.79 GHz.