Simulation of Metasurfaces in Finite Difference Techniques

TL;DR

This paper presents a new, rigorous finite difference method for analyzing metasurfaces as zero-thickness sheets, capable of handling both electric and magnetic discontinuities, applicable in frequency and time domain simulations.

Contribution

The paper introduces a novel virtual structure approach using GSTCs for metasurfaces in FD methods, improving accuracy and generality over previous techniques.

Findings

Method accurately models electric and magnetic discontinuities.

Applicable to both FDFD and FDTD schemes.

Validated by five illustrative examples.

Abstract

We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the metasurface as a virtual structure, located between nodal rows of the Yee grid, using a finite difference version of Generalized Sheet Transition Conditions (GSTCs). In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution in computational electromagnetics. It is presented here in the framework of the FD Frequency Domain (FDFD) method but also applies to the FD Time Domain (FDTD) scheme. The theory is supported by five illustrative examples.