# Dual-Polarization Conversion and Coding Metasurface for Wideband Radar Cross-Section Reduction
## 5 Configuration and Analysis of RCS Reduction with Coding Metasurface  
The radar cross-section determines a target's detectability to an approaching radar system. Although a low RCS hinders enemy radar from identifying combat targets like missiles, planes, and rockets, it is crucial for stealth technology because it improves their surveillance capabilities. Given the significance of a low radar cross-section, the remarkable ability of a coding metasurface to scatter the EM wave in several directions to reduce scattering energy in all directions and reduce the radar cross-section is of great interest. Different coding elements with distinct phases distributed over a constant amplitude produce a coding metasurface. With the addition of the PB phase, an anisotropic structure can easily be rotated to produce the phase difference instead of requiring several isotropic elements or adjusting its size attributes. The PB phase indicates that rotating the top metal pattern by \(\beta\) results in a reflection phase change of \(\pm 2\beta\). In order to obtain a 180\({}^{\circ}\) phase difference for a 1-bit CM, \(\beta\) is rotated by 90\({}^{\circ}\). Figure 7 shows the mechanism. Figure 7a depicts the layout of the meta-atoms '1' and '0'. From Figure 7b, the phase difference of meta-atoms '1' and '0' is equal to \(\pm 180^{\circ}\). Ref. [35] states that the far-field scattering caused by a coding metasurface can be written as follows:  
\[f(\theta,\varphi)=f_{m,n}(\theta,\varphi).AF(\theta,\varphi) \tag{8}\]  
\[ \begin{array}{c}AF(\theta,\varphi)=\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{ N}\exp\{-j\{\varphi(m,n)+kD\sin\theta\big{[}(m-1/2)\\ \qquad\qquad\qquad\qquad\times\cos\varphi+(n-1/2)\sin\varphi\big{]}\}\}\end{array}  \tag{9}\]  
where \(f_{m,n}(\theta,\varphi)\) and \(AF(\theta,\varphi)\) stand for the radiation intensity of each element and array factor, respectively, whereas \(k\) stands for the wavenumber vector, and \(D\) is the lattice size. \(\varphi\) and \(\theta\) are the azimuth and elevation angle. We suppose that \(\varphi(m,n)\), which can be either 0\({}^{\circ}\) or 180\({}^{\circ}\), represents the scattering phase of each lattice. Hence, the phase difference between  
Figure 6: Surface current distribution at different resonance frequencies: (**a**) 12.47 GHz, (**b**) 20.08 GHz, and (**c**) 32.56 GHz. \"0\" and \"1\" causes \(f_{m,n}(\theta,\varphi)\), and the directivity function \(Dir(\theta,\varphi)\) of the metasurface can be written as follows:  
\[Dir(\theta,\varphi)=\frac{4\pi|f(\theta,\varphi)|^{2}}{\int\limits_{0}^{2\pi} \int\limits_{0}^{\pi/2}|f(\theta,\varphi)|^{2}\sin\theta d\theta d\varphi} \tag{10}\]  
The RCS reduction caused by the CM compared to a metallic plate of the same size is determined as follows:  
\[RCS\_reduction=\frac{\lambda^{2}}{4\pi N^{2}D^{2}}Max[Dir(\theta,\varphi)] \tag{11}\]  
where \(N\) is optimized codes for different numbers of lattices. The coding metasurface elements provide control over the scattered fields, as shown by the above Equations (9)-(11). For example, the main scattering beam will be reflected to the incident indirection when 00/00 or 11/11 CM is used, since the coding sequences 00/00 and 11/11 indicate fully electrified conductors with finite size, which is consistent with real physics. Hence, the coding metasurface with all \"0\" or \"1\" does not exhibit the characteristics of RCS reduction under normal incidence. The two main scattering beams for coding sequences 01/01 and 10/10 align with the directions of 90\({}^{\circ}\) and 270\({}^{\circ}\). On the other hand, the reflected energy is distributed in four scattering beams, 45\({}^{\circ}\), 135\({}^{\circ}\), 225\({}^{\circ}\), and 315\({}^{\circ}\), when the coding sequence is 01/01. Thus, to achieve the properties of scattering and diffuse reflection, the two fundamental elements must be encoded in distinct coding sequences. According to the preceding analysis, an aperiodic coding sequence can effectively suppress the incident EM waves, which causes the RCS reduction in a target.