Metasurfaces comprising arrays of film-coupled, nanopatch antennas are a promising platform for low-energy, all-optical switches. The large field enhancements that can be achieved in the dielectric spacer region between the nanopatch and the metallic substrate can substantially enhance optical nonlinear processes. Here we consider a dielectric material that exhibits an optical Kerr effect as the spacer layer and numerically calculate the optical bistability of a metasurface using the finite element method (FEM). We expect the proposed method to be highly accurate compared with other numerical approaches, such as those based on graphical post-processing techniques, because it self-consistently solves for both the spatial field distribution and the intensity-dependent refractive index distribution of the spacer layer. This method offers an alternative approach to finite-difference time-domain (FDTD) modeling. We use this numerical tool to design a metasurface optical switch and our optimized design exhibits exceptionally low switching intensity of , corresponding to switching energy on the order of tens of attojoules per resonator, a value much smaller than those found for most devices reported in the literature. We propose our method as a tool for designing all-optical switches and modulators.
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