## 4 Design and Simulation of Gradient and Code Metasurface  
The Pancharatnam-Berry phase theory plays a vital role in manipulating circularly polarized waves. According to the Pancharatnam-Berry phase theory, when the top structure of the polarizer rotates \(\Psi\), the co-polarized reflectance of the circularly polarized waves remains unchanged and the phase difference is \(2\Psi\), which generates a phase gradient in the polarizer, denoted as follows:  
\[\
abla\alpha=\frac{\pm 2\psi}{P}=\frac{\pm 2\pi}{L}, \tag{4}\]  
where \(L=NP\), \(N\) is the number of sub-units of the polarizer. According to the generalized Snell's law, the co-polarized reflected waves will be redirected, and the abnormal reflection angle is defined as follows:  
\[\theta_{r}=\frac{\mathbf{k}_{0}\sin\theta_{i}+\
abla\alpha}{\mathbf{k}_{0}}, \tag{5}\]  
where \(\mathbf{k}_{0}\) represents the wave vector in free space. If \(\theta_{i}=0\), \(\mathbf{k}_{0}=2\pi/\lambda\), the anomalous reflection angle of the EM waves under normal incidence can be calculated theoretically by Equation (5). Figure 6a,b shows the relationship between the rotation angle \(\Psi\) and the reflection magnitude and phase of the polarizer, respectively. It can be noticed that, as the rotation  
Figure 5: Surface current distributions at three resonance points: (**a**) 15.45 GHz, (**b**) 20.82 GHz and (c) 26.94 GHz. angle increases in steps of 22.5\({}^{\circ}\), the reflection amplitude of the left-handed circularly polarized waves under normal incidence remains stable, and the corresponding reflection phase increases linearly in steps of 45\({}^{\circ}\) over a range of 360\({}^{\circ}\), which implies the existence of a phase gradient of the reflected waves. In the following, we describe the designed one-dimensional gradient metasurface, as depicted in Figure 7a. The gradient metasurface consists of 8 sub-units, each with the same structural parameters as those shown in Figure 1. In order to study the characteristics of the gradient metasurface, numerical simulations were carried out in CST, and the simulated results are displayed in Figure 7b. In Figure 7b, the anomalous reflection angle decreases with increasing frequency under the incident left-hand circularly polarized waves. The anomalous reflection angles at 15 GHz, 18 GHz, 21 GHz, 24 GHz and 27 GHz are \(-\)23.0\({}^{\circ}\), \(-\)20.0\({}^{\circ}\), \(-\)17.0\({}^{\circ}\), \(-\)15.0\({}^{\circ}\) and \(-\)12.0\({}^{\circ}\), respectively, which are basically consistent with the theoretical calculation results (\(-\)24.58\({}^{\circ}\), 20.3\({}^{\circ}\), 17.27\({}^{\circ}\), 15.07\({}^{\circ}\), 13.35\({}^{\circ}\)). The simulated results show that the maximum error between the anomalous reflection angle of the gradient metasurface and the theoretical calculation is 1.58\({}^{\circ}\), suggesting that the proposed gradient metasurface has satisfactory performance in anomalous reflection. From the electric field distribution of the reflected waves in Figure 7c,d, we can find that the angle of the reflected waves varies at different frequencies, demonstrating the correctness of the above design. Moreover, we designed a 1-bit coded metasurface to reduce the RCS. When the reflection phase is 0\({}^{\circ}\) and 180\({}^{\circ}\), the metasurface is defined as \"0\" and \"1\" in the digitally encoding state. To achieve a 10 dB reduction in RCS, the phase difference between adjacent units should meet 180\({}^{\circ}\)\(\pm\) 37\({}^{\circ}\). On this basis, we built the basic unit and performed the simulation as shown in Figure 8a,b. From Figure 8b, it can be observed that the reflection phase difference between two cells is 180\({}^{\circ}\)\(\pm\) 37\({}^{\circ}\) in the range of 15.3-28.0 GHz, which implies that a 10 dB RCS reduction can be realized in this frequency band. We randomly generate a 1-bit coding sequence to achieve a 10 dB RCS reduction.