# Scattering Field Solutions of Metasurfaces based on the Boundary Element Method (BEM) for Interconnected Regions

## TL;DR

This paper introduces a Boundary Element Method (BEM) approach to compute electromagnetic scattering from interconnected regions with metasurfaces, validated through Gaussian beam and diffraction grating examples.

## Contribution

It develops a BEM-based framework incorporating GSTCs for analyzing EM scattering from complex metasurfaces in interconnected regions.

## Key findings

- Validated with semi-analytical method for Gaussian beam scattering.
- Confirmed results with FDFD for diffraction grating.
- Demonstrated effectiveness of BEM in metasurface scattering problems.

## Abstract

A methodology for determining the scattered Electromagnetic (EM) fields present for interconnected regions with common metasurface boundaries is presented. The method uses a Boundary Element Method (BEM) formulation of the frequency domain version of Maxwell's equations - which expresses the fields present in a region due to surface currents on the boundaries. Metasurface boundaries are represented in terms of surface susceptibilities which when integrated with the Generalized Sheet Transition Conditions (GSTCs), gave rise to an equivalent configuration in terms of electric and magnetic currents. Such a representation is then naturally incorporated into the BEM methodology. Two examples are presented for EM scattering of a Gaussian beam to illustrate the proposed method. In the first example, metasurface is excited with a diverging Gaussian beam, and the scattered fields are validated using a semi-analytical method. Second example concerned with a non-uniform metasurface modeling a diffraction grating, whose results were confirmed with conventional Finite Difference Frequency Domain (FDFD) method.