# Ultrawideband Cross-Polarization Converter Using Anisotropic Reflective Metasurface
## 3 Performance Analysis and Simulation Results  
The commercially available CST Microwave Studio was used to analyze and optimize the proposed metasurface unit cell design. To perform the simulation analysis, the \"unit cell\" boundary conditions option is specified for \(x_{min}\), \(x_{max}\), \(y_{min}\), and \(y_{max}\), and the open add space option is employed for \(z_{min}\) and \(z_{max}\). Finally, a frequency\(-\)domain solver is used for simulation. When electromagnetic waves strike the metasurface, the reflected waves have two components: a co\(-\)polarized field, represented by \(r_{yy}\) and \(r_{xx}\), which have the same polarization to the incident field, and a cross\(-\)polarized field coefficient, represented as \(r_{xy}\) and \(r_{yx}\), which are orthogonal to the incident field. The co\(-\) and cross\(-\)polarized coefficients can be defined as \(\left|r_{yy}\right|=E_{yr}/E_{yi}\) and \(\left|r_{xy}\right|=E_{xr}/E_{yi}\), respectively, whereas the analogous coefficients for an \(x-\)polarized wave are \(\left|r_{xx}\right|=E_{xr}/E_{xi}\) and \(\left|r_{yx}\right|=E_{yr}/E_{xi}\). The co\(-\)polarization and cross\(-\)polarization reflection coefficients of the TE or TM polarized incident wave are \(r_{yy}\) and \(r_{xy}\) or (\(r_{xx}\) and \(r_{yx}\)).  
For this analysis, we solely evaluated the TE mode. Due to diagonal symmetry in the geometry, the designed meta\(-\)unit cell is equally effective for the TM mode. When the co\(-\)polarized coefficient decreases and the cross\(-\)polarized coefficient raises, cross\(-\)polarization conversion occurs. The results are identical for the \(x-\)polarized incidence wave or \(y-\)polarized incidence wave due to the unit cell's diagonal symmetry. The main criterion for an above 90% cross\(-\)polarization conversion is that the co\(-\)polarized coefficients should be less than \(-\)10 dB and the cross\(-\)polarization coefficient value should be greater than \(-1\) dB, respectively, (\(r_{xx}<-10\) dB and \(r_{yy}<-10\) dB) and (\(r_{xy}>-1\) dB and \(r_{yx}>-1\) dB). The co\(-\)polarized and cross\(-\)polarized coefficients in the operative frequency range of 13 GHz to 26.2 GHz are (\(r_{yy}<-10\) dB) and (\(r_{xy}>-1\) dB), respectively, according to these conditions, as shown in Figure 3a. The polarization conversion efficiency is anticipated to be better than 90% for the assessment frequency range.  
To further understand the performance of the proposed metasurface, we scrutinize the _PCR_ in the operating frequency band. To calculate the _PCR_, divide the square of the cross\(-\)polarized reflection coefficient \(\left|r_{xy}\right|^{2}\) by the sum of the squares of the co\(-\)polarized coefficient \(\left|r_{yy}\right|^{2}\) and cross\(-\)polarized reflection coefficient \(\left|r_{xy}\right|^{2}\)[29]. Equation (11) shows the _PCR_ for the case of linearly \(y-\)polarized waves.  
\[PCR=\frac{\left|r_{xy}\right|^{2}}{\left|r_{yy}\right|\!\!\left|z\!+\!\left|r_ {xy}\right|\right|^{2}} \tag{11}\]  
For the specified frequency range of 13 GHz to 26.2 GHz, the _PCR_ \(>0.9\), as shown in Figure 3b. Hence, the polarization conversion efficiency is greater than 90%.