# Ultrawideband Cross-Polarization Converter Using Anisotropic Reflective Metasurface
## 2 Design of a Unit Cell  
For EM waves absorption, isotropic reflective metasurfaces are typically used with low co\(-\) and cross\(-\)polarized reflection components. If we break the symmetry of the isotropic unit cell, its cross\(-\)polarized coefficient increases due to the anisotropic effect faced by the geometry [35]. It signifies that EM waves convert from \(x-\)polarized to \(y-\)polarized or (\(y-\)polarized to \(x-\)polarized). Following a similar idea, we proposed an ultra\(-\)broadband and highly efficient reflective metasurface based on a hollow rhombus\(-\)type\(-\)shaped unit cell, as depicted in Figure 1, with the physical dimensions of a unit cell as P = 7 mm, l = 4 mm, h = 1.6 mm, a = 0.4 mm, and b = 2.8 mm. The postulated unit cell is made up of three layers: the top and bottom layers are composed of copper, each with a thickness of 0.035 mm and electrical conductivity of \(\sigma\) = 5.80 \(\times\) 10\({}^{7}\) S/m. The central layer consists of FR\(-\)4 with a thickness of h = 1.6 mm and dielectric constant and loss tangent of \(\epsilon_{r}\) = 4.3, tan\(\delta\) = 0.025, respectively. We follow four steps to convert this isotropic shape into anisotropic to achieve an efficient polarization conversion. * First, a \(4\times 4\) mm copper patch is rotated at 45\({}^{\circ}\) w.r.t. \(x-\)axis and simulated. Co\(-\)polarized (\(r_{yy}\)) and cross\(-\)polarized (\(r_{xy}\)) coefficients are depicted in Figure 2a. It can be observed that \(r_{yy}\) approaches 0 dB, whereas \(r_{xy}\) is below \(-\)75 dB. It is evident that there is no polarization conversion;
* A cut with a width of 0.4 mm is applied at 45\({}^{\circ}\) to the \(x-\) and \(y-\)axes. Figure 2b illustrates simulated results. In the frequency ranges of 14.2 GHz to 18 GHz, \(r_{yy}\) is less than \(-\)10 dB, whereas \(r_{xy}\) is more significant than \(-\)1 dB. It is evident that there is polarization conversion, but the operating bandwidth is narrow, so we move forward for further modifications;
* Figure 2c shows simulated results after eliminating a triangular patch from the inner side of one slice. This provides a broadband polarization conversion over the frequency range of 12 GHz to 26 GHz. However, the efficiency does not improve across all frequency ranges. To improve the efficiency of polarization conversion, we further modify the structure;
* A triangular shape of the same size is removed from the second slice; the structure adopts a shape similar to a hollow rhombus. It is noteworthy that \(r_{yy}\) is below \(-\)10 dB, and \(r_{xy}\) is approaching 0 dB over the frequency bands of 13 GHz to 26.2 GHz. The polarization conversion results are relatively efficient, up to 90%, and the operating bandwidth is also high (Figure 2d). Figure 1: Schematic diagram of the proposed meta\(-\)unit cell structure: (**a**) front view, (**b**) side view. Mathematically, the relation between effective electric and magnetic dipole moments i.e., \(\mathbf{p}\) and \(\mathbf{m}\) respectively, and the incident fields (\(E\) and \(H\)) can be described through the following equations [35]:  
\[\left[ \begin{array}{c}\mathbf{p}\\ \mathbf{m}\end{array} \right]=\left[ \begin{array}{c}p_{x}\\ p_{y}\\ m_{x}\\ m_{y}\end{array} \right]=\left[ \begin{array}{c}P_{exx}\\ P_{exy}\\ P_{mexy}\\ P_{mex}\\ P_{meyx}\\ P_{meyx}\\ P_{meyx}\\ P_{meyx}\\ \end{array} \right]\left[ \begin{array}{c}E_{x}\\ E_{y}\\ H_{x}\\ H_{y}\end{array} \right] \tag{1}\]  
where \(P_{em}\) represent for electric-magnetic polarizability and \(P_{exx}\) can be defined as \(P_{exx}=\frac{P_{x}}{E_{x}}|_{F_{y},H_{x},H_{y}=0}\). Moreover, the relation between effective surface electric current and magnetic current densities i.e., \(\mathbf{J_{s}}\) and \(\mathbf{M_{s}}\) respectively, and the incident fields can also be written as [35]:  
\[\left[ \begin{array}{c}\mathbf{J_{s}}\\ \mathbf{M_{s}}\end{array} \right]=\left[ \begin{array}{c}J_{x}\\ J_{y}\\ M_{x}\\ M_{y}\end{array} \right]=\left[ \begin{array}{c}P_{exx}\\ P_{exy}\\ P_{mexx}\\ P_{meyx}\\ P_{meyx}\\ P_{meyx}\\ P_{meyx}\\ \end{array}