Part 2: Spatially Dispersive Metasurfaces -- IE-GSTC-SD Field Solver with Extended GSTCs

TL;DR

This paper introduces an advanced integral equation field solver for spatially dispersive metasurfaces, extending GSTCs to include spatial derivatives, and validates it through multiple numerical examples involving practical metasurface structures.

Contribution

The work extends GSTCs to include spatial derivatives and integrates them into an IE solver, enabling accurate modeling of spatially dispersive metasurfaces with validation against established methods.

Findings

Successfully modeled spatially dispersive metasurfaces

Validated results against Fourier decomposition and full-wave simulations

Demonstrated applicability to practical metasurface structures

Abstract

An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, $\boldsymbol{k}$. By representing the angular dependence of the surface susceptibilities in $\boldsymbol{k}$ as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IE-GSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.