Microscopic Modeling of Metasurfaces by the Mixed Finite Element Numerical Mode-Matching Method

A semi-analytical finite element numerical mode-matching (FNMM) method is developed to simulate microscopic structures of metasurfaces on the interfaces of the 3-D multilayered structure. Similar to the recently developed spectral element NMM method, the FNMM method reduces the original 3-D problem into a series of 2-D waveguide eigenvalue problems plus a 1-D layered medium problem, which can be analytically described by a recursion procedure. The 2-D eigenvalue problems in the horizontal directions are solved numerically by the mixed finite element method (MFEM) to remove the spurious modes in the conventional FEM. Therefore, it can effectively and accurately simulate electromagnetic wave interactions with the detail metasurfaces, especially for thick layers. Metasurfaces embedded on the interfaces of 3-D structures are treated by the generalized impedance boundary conditions, thus enabling their rapid yet accurate computation. This method is applied to characterize metasurfaces consisting of microscopic patterns with complex geometric construction with details much smaller than the wavelength. Numerical experiments indicate that the FNMM method is highly efficient and accurate for the microscopic metasurface models.