# Dual-Polarization Conversion and Coding Metasurface for Wideband Radar Cross-Section Reduction
## 4 Operating Principle  
In order to understand the proposed metasurface functions as a linear polarizer, the E-field component beside the \(y\)-axis can be decomposed into two orthogonal \(u\) and \(v\) components, which are on \(\pm 45^{\circ}\) concerning the \(x\)- and \(y\)-axes. The \(u\) and \(v\) components of an incident \(y\)-polarized electromagnetic wave can be divided, as shown in Figure 5a. We evaluate the incident and reflected electric field along the \(u\)- and \(v\)-axes, which are represented, respectively, by \(E_{ui}\) and \(E_{vi}\), and \(E_{ur}\) and \(E_{ur}\). The decomposed \(u\) and \(v\) components of the incident and reflected electric field are expressed as follows:  
\[E_{i}=\hat{y}E_{i}e^{i\varphi}=\hat{u}E_{iu}e^{i\varphi}+\hat{v}E_{iv}e^{i\varphi} \tag{6}\]  
\[E_{r}=\hat{u}r_{u}E_{iu}e^{i(\varphi+\varphi_{u})}+\hat{v}r_{v}E_{iv}e^{i( \varphi+\varphi_{v})} \tag{7}\]  
When \(u\)- and \(v\)-polarized incident electromagnetic waves are the incoming waves, the unit vectors in the equation above are \(\hat{u}\) and \(\hat{v}\), and the co-polarized components are represented by \(r_{u}\) and \(r_{v}\) with their relative phases \(\varphi_{u}\) and \(\varphi_{v}\), respectively. Because of its asymmetric design, the converter shows anisotropic characteristics such as dispersive relative permittivity and permeability. Thus, there can be variations in the phase \((\Delta\varphi=|\varphi_{u}-\varphi_{v}|)\) between \(E_{ru}\) and \(E_{rv}\). Figure 5b illustrates that the synthetic field \(E_{r}\) along the \(y\)-direction results when \(r_{u}=r_{v}\approx 1\) and \(\Delta\varphi\approx\pm 180^{\circ}+2\pi k\) (\(k\) is an integer); \(E_{iv}\) will be opposite to \(E_{rv}\), and \(E_{iu}\) remains the same as \(E_{ru}\), respectively. Figure 5b shows the amplitude and phase difference in the reflection coefficients. It is noted that the reflection amplitudes (\(r_{u}\) and \(r_{v}\)) are nearly equal to unity with \(\Delta\varphi=\pm 180^{\circ}\) between 12.37-13.03 GHz and 20.10-28.30 GHz. In dual-frequency bands, it implies the proposed structure is capable of LP-LP conversion.  
Nonetheless, the phase difference of \(\pm 90^{\circ}+2\pi k\) is required for LP-CP conversion. Furthermore, at the frequency bands of 12.06, 13.76-16.44, and 36.75-38.80 GHz, a phase difference of nearly \(\pm 90^{\circ}\) is realized, indicating LP-CP conversion. To provide more details about the physical process causing the polarization conversion, we evaluate the surface currents on the metasurface at resonance frequencies. At resonant frequencies, Figure 6a-c show the surface current orientations on the top copper layer and bottom ground copper layer of the proposed converter. To be more precise, magnetic resonance occurs when the current causes the top and bottom metallic plates to be in opposite directions from one  
Figure 5: (**a**) Proposed meta-atom with \(UV\)-coordinates, and (**b**) magnitude (\(r_{u}\) and \(r_{v}\)) and reflection phase difference (\(\Delta\varphi=|\varphi_{u}-\varphi_{v}|\)) in \(u\)- and \(v\)-polarized waves.  
another, and electric resonance occurs when the surface current distribution is parallel on the top metallic pattern and bottom ground plane. At the resonant frequency of 12.47 GHz, Figure 6a renders that the surface currents at the top layer are parallel to the ones at the bottom. In the case of 20.08 GHz and 32.56 GHz resonance frequencies, magnetic resonance occurs due to the opposite surface currents at the top layer and the ground plate, as shown in Figure 6b,c. Thus, current loops that occur in the dielectric layer provide a cause for magnetic resonance. The magnetic field produced by these antiparallel currents is amplified in the dielectric area, leading to a high magnetic permeability value. The surface impedance of the structure is significantly higher than that of air or free space because of the high magnetic permeability. Consequently, high-impedance surface behavior shows up by the surface, which is essential for cross-polarization conversion.