# Dual-Polarization Conversion and Coding Metasurface for Wideband Radar Cross-Section Reduction
## 2 Metasurface Design  
Figure 1a illustrates the proposed modified circular ring meta-atom-based unit cell designed to operate as a polarization converter. As shown in Figure 1b, the proposed unit cell is composed of two stacked layers: air and a commercially available Rogers RT5880  
substrate. The unit cell is printed on top of an RT5880 substrate with \(\epsilon_{r}=2.2\), tan\(\delta=0.0009\), where the bottom copper layer is entirely removed. The thin layer of Rogers RT5880 is also separated from the ground copper sheet by an air gap. The bottom layer and top structure are composed of copper, with a thickness of 35 \(\upmu\)m and an electrical conductivity of \(5.8\times 10^{7}\) S/m. The CST Microwave Studio is a well-known commercial full-wave simulation program used for simulating unit cells. Specifically, we incorporated a Floquet port to direct electromagnetic waves onto the proposed meta-atom in the z-direction, as illustrated in Figure 1c. For the z-direction, an open boundary was implemented, while unit cell boundary conditions were applied for the x and y axes. Figure 1 depicts the geometry of the proposed unit cell, where the initial cell dimensions are considered as \(P=6\) mm, w = 1.2 mm, \(r=2.4\) mm, \(r_{i}=1.2\) mm, \(h=0.127\) mm, and \(h_{\text{air}}=1.4\) mm. To investigate the polarization conversion property, a \(y\)-polarized incident wave is allowed to impinge on the unit cell converter. Figure 1c displays the simulation setup. Due to the anisotropic nature of the structure, the reflected wave contains both co- and cross-polarized components. These components can be expressed as follows:  
\[r_{yy}=\left|E_{yr}\right|/\left|E_{yi}\right|\text{ and }r_{xy}=\left|E_{xr} \right|/\left|E_{yi}\right| \tag{1}\]  
where \(r_{yy}\) and \(r_{xy}\) represent the reflection coefficients for co- and cross-polarization, respectively, and the electric field is denoted by \(E\). \(E_{xr}\) is an electric field of reflected waves, and \(E_{yi},E_{yr}\) are the reflected fields. The reflected and incident subscripts are denoted by the symbols \(r\) and \(i\), respectively. The linear polarization conversion performance of the converter is assessed using the following expressions for the polarization conversion ratio (PCR) and polarization conversion efficiency (PCE). \[PCR=\left|r_{xy}\right|^{2}/\left(\left|r_{yy}\right|^{2}+\left|r_{xy}\right|^{ 2}\right) \tag{2}\]  
\[PCE=PCR\times 100\% \tag{3}\]  
Figure 1: The schematic diagram of the proposed unit cell: (**a**) top view, (**b**) side view of proposed meta-atom, and (**c**) isometric view and simulation setup. Figure 2 displays the \(r_{yy}\)- and \(r_{xy}\)-polarized reflection responses, as well as the polarization conversion efficiency from the converter. Figure 2a demonstrates that within the dual-frequency range of 12.37-13.03 GHz and 18.96-32.37 GHz, the magnitude of cross-polarization reflection exceeds \(-1\) dB, while the magnitude of co-polarization reflection remains below \(-10\) dB. Figure 2b depicts the calculated polarization conversion efficiency using Equation (3). It is evident that within the dual-frequency bands of 12.37-13.03 GHz and 18.96-32.37 GHz, the PCE value exceeds 95%. This substantiates the effectiveness of the proposed converter as a linear polarization converter within the mentioned frequency bands. Another significant functionality of the proposed metasurface is its capability to convert linear to circular polarization or operate as a quarter-wave plate (QWP). In an ideal scenario, a design that offers LP-CP conversion must satisfy two conditions: The co- and cross-polarized reflected components must be approximately equal. Simultaneously, the phase difference between these two components should be \(\pm 90^{\circ}\) or an odd multiple of \(\pm 90^{\circ}\), which can be expressed as \(\left|r_{xy}\right|/\left|r_{yy}\right|\cong 1\), and \(\angle r_{yy}-\angle r_{xy}=\pm n\pi/2\), where \(n\) is an odd number.