Multilevel Fast Multipole Algorithm for Electromagnetic Scattering by Large Metasurfaces using Static Mode Representation

TL;DR

This paper presents a novel multilevel fast multipole algorithm using static mode representation for efficient electromagnetic scattering analysis of large metasurfaces, significantly reducing computational resources.

Contribution

It introduces a boundary element method combining MLFMA with static mode basis functions, enabling efficient large-scale metasurface simulations with reduced complexity.

Findings

Achieved accurate full-wave simulations of large metasurfaces

Reduced CPU time and memory compared to classical methods

Demonstrated effectiveness on a 100λ×100λ metalens

Abstract

Metasurfaces, consisting of 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 the unknown equivalent surface current density by means of static modes, a set of entire domain basis functions dependent only on object shape but independent of the material and frequency. The compression of the number of unknowns enabled by the Static Mode Representation (SMR), combined with the \(\mathcal{O}(N \log N)\) complexity of MLFMA matrix-vector products, significantly reduces CPU time and memory requirements compared to classical MLFMA with RWG basis functions. We demonstrate the accuracy, time, and memory requirements of this method through several test cases including the full-wave simulation of a $100 \lambda \times 100 \lambda$ canonical metalens. The MLFMA-SMR method offers substantial benefits for the analysis and optimization of metasurfaces and metalenses.