# Ultrawideband Cross-Polarization Converter Using Anisotropic Reflective Metasurface
## 5 Working Mechanism  
When the EM wave interacts with the meta\(-\)atom, it produces electric and magnetic dipole moments. Due to the resonator's bi\(-\)anisotropy, electric and magnetic fields can be coupled to these dipole moments. Equation (17) depicts the link between incident fields and effective dipole moments:  
\[\left[ \begin{array}{c}p\\ m\end{array} \right]=\left[ \begin{array}{cc}p_{ee}&p_{em}\\ p_{me}&p_{mm}\end{array} \right]\left[ \begin{array}{c}E\\ H\end{array} \right], \tag{14}\]  
where \(p=\left[ \begin{array}{c}p_{x}\\ p_{y}\end{array} \right]\) represents electric dipole moments and \(m=\left[ \begin{array}{c}m_{x}\\ m_{y}\end{array} \right]\) magnetic dipole moments, respectively, and the electric and magnetic fields are \(E\), \(H\). \(p_{me}\) represents magneto\(-\)electric polarizability. The effective impedance of the metasurface is given by Equation (15). \[Z(\omega)=\sqrt{\mu(\omega)/\epsilon(\omega)}, \tag{15}\]  
where \(\mu(\omega)\) and \(\epsilon(\omega)\) are the magnetic permeability and electric permittivity, \(Z(\omega)\) is the surface impedance of the metasurface, and all are frequency dependent. At the normal incidence, the reflection coefficient is given as:  
\[R(\omega)=(Z(\omega)-Z_{\circ})/(Z(\omega)+Z_{\circ}) \tag{16}\]  
where \(Z_{\circ}=377\:\Omega\) denotes the free space impedance and \(\omega_{r}\) represents the resonance frequency. When the impedance of the metasurface is greater than the impedance of free space, \(Z(\omega_{r})>Z_{0}\), the reflection coefficient approaches unity, and the surface behaves like a high impedance surface (HIS). An incident EM waves on such a surface will be reflected with an in\(-\)phase and unity magnitude, unlike a normal reflective surface, which reflects waves out of phase. As discussed earlier, when orthogonal components reflect \(180^{\circ}\) or \(0^{\circ}\), the polarization of the incident wave will be rotated by \(90^{\circ}\), leading to cross\(-\)polarization conversion. It can be concluded that the structure behaves as a HIS for one component and a common reflector for another component. To justify the above discussion and ultra\(-\)wideband polarization conversion, the surface current distributions are studied and induced by the time\(-\)varying dipole moment induced by time\(-\)harmonic electric and magnetic fields. Equation (17) explains the following relationship:  
\[\left[ \begin{array}{c}J\\ M\end{array} \right]=\omega\omega\left[ \begin{array}{cc}\alpha_{ee}&\alpha_{ em}\\ \alpha_{me}&\alpha_{mm}\end{array} \right]\left[ \begin{array}{c}E\\ H\end{array} \right], \tag{17}\]  
where \(J=\left[ \begin{array}{cc}J_{x}&J_{y}\end{array} \right]^{T}\) is the electric surface current density, \(M=\left[ \begin{array}{cc}M_{x}&M_{y}\end{array} \right]^{T}\) is a magnetic surface current density, \((\omega)\) is the angular frequency, and \(\alpha_{me}\) is the magnetic and electric polarizability. According to [PERSON]'s law, the time\(-\)varying magnetic field B sandwiched between the top metallic structure and the metallic groundsheet produces an opposite\(-\)direction surface current. As a result, the resonances of the entire system operate as magnetic responses. At the resonance frequency, \(\mu\) is divergent, resulting in a relatively large surface impedance \(z=\sqrt{\mu/\epsilon}\) and in\(-\)phase reflection. According to the previous discussion, when the current direction on the top and bottom metallic layer is antiparallel, the resonance will be magnetic; otherwise, there will be electric resonance. These resonances are also known as plasmonic resonances. The unit cell's Plasmon resonance is illustrated in Figure 3c. The exciting unit cell has three plasmon resonances, where 1 and 3 are \(u-\)polarized excited states, whereas 2 is \(v-\)polarized excited state plasmon resonance. As a result of the multiple resonances, ultra\(-\)wideband polarization conversion is achieved.