## 3 Results and Discussion
This phenomenon occurs because the constant \(\lambda_{\text{in}}\) reads a different reflectance when the resonance moves by the intensity-dependent permittivity of the Kerr material [26], as depicted in Equation (2). Next, the lower hysteresis branch is obtained by decreasing the intensity of incident light from a high level. As it decreases to the threshold \(I_{\text{OFF-ON}}=7.1\) MW/cm\({}^{2}\) from the right-hand side of Figure 5a, the reflectance dramatically jumps to a high value of R = 0.85 from R = 0.06, which shows a great OFF/ON ratio of 14.2. Figure 6a shows the variation in the nonlinear reflection spectra with the incident wavelength when the incident light intensity is increased. The red curve in it corresponds to the upper branch of the two red curves in Figure 5a. We chose five different intensities of incident light to comprehensively observe the change process of bistability. The observation results show that, when the incident light intensity is lower than 3 MW/cm\({}^{2}\), the resonant position of the spectrum has a slight redshift, but the overall line shape is still symmetric, as shown by the cyan curve and the green curve in Figure 6. It can be seen that the Kerr effect has almost no influence at a lower incident light intensity. As the incident light intensity gradually increases, the resonant wavelength gradually redshifts. At this time, due to the influence of the Kerr effect, the line shape of the spectrum also becomes asymmetric, and it shows a sharper characteristic on the long-wave side, and the corresponding reflectivity also gradually increases. When the incident light intensity increases to \(I_{\text{ON-OFF}}=8.5\) MW/cm\({}^{2}\), the resonant wavelength is close to the incident wavelength. Consistent with the behavior of the upper branch of the red curve in Figure 5a, the reflectivity drops sharply from the initial 0.79 to 0.14. The yellow dotted line and the black dotted line correspond to the resonant wavelength and the incident wavelength, respectively. This also proves that the \(I_{\text{ON-OFF}}\) obtained in Figure 5a is correct. Next, using the Kerr effect again, we continue to  
Figure 5: (**a**) Optical bistability of mirror-induced MAS metasurfaces. (**b**) Reflection spectra. The insets are the field distribution. verify the correctness of \(I_{\text{OFF-ON}}\) from the spectra of the variation in reflectivity, with the incident wavelength obtained when reducing the incident light intensity. Contrary to Figure 6a, Figure 6b shows the variation in the nonlinear reflection spectra with the incident wavelength when the incident light intensity is reduced. The red curve therein corresponds to the lower branch of the two red curves in Figure 5a. Here, five different intensities of incident light are also chosen for observation. The observation results show that, under the condition of a lower incident light intensity, the nonlinear reflection spectra in Figure 6a,b have high similarity and are similar to the linear spectrum. With the influence of the Kerr effect, the decrease in the incident light intensity leads to a gradual blue shift of the resonant wavelength, and the line shape of the spectrum gradually changes from asymmetric to symmetric, and also shows a sharp characteristic on the long-wave side. When the input intensity is reduced to the threshold \(I_{\text{OFF-ON}}\) = 7.1 MW/cm\({}^{2}\), the reflectivity jumps sharply from 0.06 to 0.85, which is consistent with the behavior of the lower branch in Figure 5a. Figure 6 shows the evolution process of optical bistability induced by the nonlinear Kerr effect, and is consistent with the results calculated in Figure 5. In addition, by connecting Figure 6a,b corresponding to different fixed incident light intensities in series for observation, the bistability of reflectivity and wavelength can also be obtained. For the sake of comparison, the hysteresis loop generated from the proposed before-optimization metasurface is also presented.