Metasurfaces, comprising large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an efficient boundary element method specifically tailored for metasurfaces, leveraging the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. Our method combines the Multilevel Fast Multipole Algorithm (MLFMA) with a representation of surface current density unknowns using static modes, a set of entire domain basis functions dependent only on object shape. The reduction in the number of unknowns by the static mode expansion (SME), combined with the \(O(N log N)\) complexity of MLFMA matrix-vector products, significantly reduces CPU time and memory requirements for solving scattering problems from metasurfaces compared to classical MLFMA with RWG basis functions. The MLFMA-SME method offers substantial benefits for the analysis and optimization of metalenses and metasurfaces.
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Corsaro et al. (2024) studied this question.
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