# Efficient Analysis of Metasurfaces in Terms of Spectral-Domain GSTC Integral Equations

## TL;DR

This paper introduces a spectral-domain method for efficiently analyzing metasurfaces using GSTCs, reducing computational complexity by focusing on the surface rather than the entire domain, and demonstrating its effectiveness with practical examples.

## Contribution

The paper develops a spectral-domain integral equation approach for metasurface analysis that is more efficient than traditional volumetric methods, focusing on surface equations.

## Key findings

- Significant reduction in memory and computation time compared to finite-difference and finite-element methods.
- Successful application to generalized-refractive and focusing metasurfaces.
- Validation of the method's accuracy with illustrative examples.

## Abstract

We present a spectral-domain (SD) technique for the efficient analysis of metasurfaces. The metasurface is modeled by generalized sheet transition conditions (GSTCs) as a zero-thickness sheet creating a discontinuity in the electromagnetic field. The SD expression of these GSTCs for a specified incident field leads to a system of four surface integral equations for the reflected and transmitted fields, which are solved using the method of moments in the spectral domain. Compared to the finite-difference and finite-element techniques that require meshing the entire computational domain, the proposed technique reduces the problem to the surface of the metasurface, hence eliminating one dimension and providing substantial benefits in terms of memory and speed. A monochromatic generalized-refractive metasurface and a polychromatic focusing metasurface are presented as illustrative examples.