## 2 Materials and Methods
Geometric parameters: \(L_{1}\) = 190 nm, \(W_{1}\) = 210 nm, \(H_{2}\) = 120 nm, and \(H_{1}+H_{2}\) = \(H\), while others remain unchanged as in (**a**). ered for approximate calculation. The selected physical solution domain is located at the interface between the silicon component and the silver film, and the size of the calculation region selected below the interface is 1500 nm \(\times\) 1500 nm \(\times\) 1000 nm. The right inset of Figure 2b shows the multipolar decomposition of the silicon nanostrip within the SOM, and the left inset shows the schematic diagram of the mirror-induced MAS. Although the geometric parameters are the same, the structure of the SOM differs from that of the SOA. Consequently, the resonance of the total SCS scattering (indicated by the black dashed line) becomes narrower, and the resonance wavelength shifts to \(\lambda\) = 1145.7 nm. The ED peak (blue solid line) dominates the scattering and is hybridized with EQ (green dotted line) and MD(C). Nevertheless, at this point, the magnetic dipole (MD) peak (red solid line) is strongly suppressed, corresponding to two currents and one and a half magnetic hotspots inside the SOM nanostrip, as shown in the uncovered part of the inset of Figure 2b. When two currents are placed on the surface of the silver film, the PEC mirror effect generates virtual images that are centrosymmetric with the original images, enabling the real image and the virtual image to jointly form a mirror-induced MAS. Figure 3b provides further verification. The field and current distributions inside the SOM nanostrip have similar patterns to half of those in the SOA [34]. The mirror effect significantly contributes to the electromagnetic enhancement and localization within the dielectric of the nano resonator [37]. As can be seen from Figure 3b, \(\mid\!E_{\text{max}}/E_{\text{inc}}\!\mid\!=\!11.7\) and \(\mid\!H_{\text{max}}/H_{\text{inc}}\!\mid\!=\!68.7\), which are nearly three times larger than the corresponding values in Figure 3a. Additionally, the electromagnetic field is more concentrated within the specific dielectric. This can be quantified by the average enhancement factor (average EF  
to be 151.8 at the resonant wavelength, while that of SOA is 7.1. This factor is usually used to quantize the ability to enhance the performance of nonlinear harmonic generation and optical switch. The large average EF of the proposed mirror-induced MAS-based metasurfaces indicates its potential for optical bistability. In order to apply efficient optical bistability, we further optimize the geometry. As can be observed from Figure 3b, one and a half magnetic hotspots occupy different positions inside the silicon nanostrip. This provides the possibility for further optimization by adjusting their geometry parameters. First of all, we set the period of the proposed metasurfaces in Figure 1 to be \(P\) = 1500 nm. This is because the period array on metal surfaces tends to excite propagating surface plasmon resonance (PSPR), and the choice of period can keep the PSPR away from the mirror-induced MAS to avoid the coupling effect [9]. Then, the average EFs are investigated by dividing the height of the silicon nanostrip into two parts and letting \(L_{1}\
eq L_{2}\), \(W_{1}\
eq W_{2}\), as shown in Figure 1b. The average EFs as functions of length L\({}_{1}\) and height duty ratio \(H_{2}/(H_{1}+H_{2})\) are given in Figure 4a, with \(W_{1}\) = 210 nm and \(W_{2}\) = 230 nm. It can be seen that, for every \(H_{2}/(H_{1}+H_{2})\), the average EFs have an optimal value within the \(L_{1}\) range, and the highest value is 1524.8 happening at \(L_{1}\) = 190 nm and \(H_{2}/(H_{1}+H_{2})=1/3\). Figure 4b gives those as functions of width \(W_{1}\) and \(H_{2}/(H_{1}+H_{2})\), with \(L_{1}\) = 190 nm, \(L_{2}\) = 250 nm. Although other \(W_{1}\) or \(L_{1}\) were performed, a higher average EF could not be found, so the results are not presented here form simplicity.