## 2 Materials and Methods  
Figure 1 depicts the schematic of the proposed mirror-induced MAS-based metasurfaces, which consist of silicon nanostrip arrays placed on the optically thick silver film. The dielectric material hydrogenated amorphous silicon is used due to its high refractive index and accessible third-order nonlinearity [32], while the noble metal Ag is selected due to its low loss at the near-infrared [33]. An x-polarized plane wave normally illuminates onto the metasurfaces. Commercial software COMSOL Multiphysics (v.4.4) based on the finite element method is employed for both the linear and nonlinear simulations. For a single nano device, a perfect matching layer is used in the x, y, and z directions to truncate the space [34], and the periodic device uses a \(P_{\text{x}}\) = \(P_{\text{y}}\) = 1500 nm periodic structure, while the perfect matching layer is still used in the z direction to truncate the space. The practical fabrication can be readily accomplished by the combination of evaporation, lithography, and lift-off procedures [35; 36]. In order to elucidate the physical mechanism of the resonance inside the high-refractive-index silicon nanostrip, we start with the scattering of one single-unit cell extracted from the arrayed metasurface in Figure 1a, and analyze its features induced by the PEC mirror effect [37]. Figure 2a and 2b show the multipolar decompositions [38] of the scattering cross-section (SCS) spectra for a high-refractive-index silicon nanostrip placed on the air (silicon on air, SOA) and silver film (silicon on metal, SOM), respectively. It should be noted that the height of the nanostrip in the SOA configuration is \(2H\), which is two times higher than that of the SOM configuration. For SOA in Figure 2a, a suppression of MD (red solid line) scattering appeared at the wavelength \(\lambda\) = 1090 nm, which resulted from the destructive interference of the Cartesian MD [denoted as MD(C), magenta dashed line] and MTD (yellow dotted line) moments. Consequently, the dominant resonance at this wavelength can be determined as an MAS. This can be further validated by the field and current distributions presented in Figure 3a. It can be seen from the upper panel of Figure 3a that four electric hotspots emerge within the silicon nanostrip, together with four unidirectional currents in the corresponding regions, as denoted by the black arrows. These four currents can thus form three circulating current loops, leading to three magnetic hotspots, as shown in the lower panel of Figure 3a. The features of these current and magnetic hotspot distributions are schematically illustrated in the inset of Figure 2a, which vividly demonstrates the characteristic of an MAS [34; 39]. Next, by observing the centrosymmetry of the currents in the silicon nanostrip depicted in the insets of Figures 2a and 3a, the PEC mirror effect can be readily introduced by cutting off the lower half of the nanostrip and placing the remaining part onto a Ag film, thus forming the SOM structure with a nanostrip height of H. Figure 2b shows the multipolar decomposition of the silicon part, and the corresponding overall multipolar decomposition is presented. Notably, an obvious resonance peak can be observed at \(\lambda\) = 1145.7 nm, where the ED peak and the MD peak are the predominant peaks. However, the introduction of the silver metal film makes it infeasible to accurately calculate the SCS spectrum and its multipole decomposition of the whole system. Under such circumstances, the silicon component and some metal reflectors near the silicon component can be consid  
Figure 1: Schematic diagram of the proposed mirror-induced MAS-based metasurfaces. Optical bistability originates from the silicon with third-order susceptibility. (**a**) Before asymmetrical optimization. Geometric parameters: length of silicon strip \(L_{1}=L_{2}\) = 250 nm, width \(W_{1}=W_{2}\) = 230 nm, height \(H\) = 360 nm, Ag film thickness \(D\) = 200 nm, and period \(P\) = 1500 nm. (**b**) After asymmetrical optimization.