Spectral Numerical Mode Matching Method for Metasurfaces

A novel 3-D spectral numerical mode-matching (SNMM) method is proposed and developed as a highly efficient rigorous solver for metasurfaces on the interface of a half-space with Bloch (Floquet) periodic boundary conditions. In addition to full electromagnetic (EM) fields, the SNMM solver can provide with ease the characteristics of metasurfaces including their absorptance, anomalous reflection/refraction, and surface plasmon polaritons (SPPs). The SNMM method is a semianalytical solver: it solves for the Bloch eigenmodes in the horizontal directions by using the mixed spectral-element method (MSEM) numerically, but determines the scattering in the vertical direction analytically through eigenmode propagation. As there is no need for discretization in the vertical direction, it can efficiently and accurately simulate EM wave interactions with metasurfaces. Numerical experiments indicate that the SNMM method is efficient and accurate for the metasurfaces compared with the well-developed 3-D finite-element method (FEM). Applications to homogeneous isotropic/anisotropic, inhomogeneous isotropic, and the gradient metasurfaces are demonstrated. Typically, the computational speed of the proposed solver is one to two orders of magnitude higher than the FEM as implemented in a commercial software package.