A Thin Sheet Volume Integral Equation Solver for Simulation of Bianisotropic Metasurfaces

TL;DR

This paper introduces a novel volume integral equation method for simulating 3D bianisotropic metasurfaces, accurately modeling both tangential and normal field interactions.

Contribution

It presents a thin-sheet volume integral equation formulation incorporating GSTCs that rigorously enforces bianisotropic conditions, including normal field interactions.

Findings

Accurately models polarization rotation and perfect reflection.

Demonstrates robustness for multi-directional attenuation.

Validates effectiveness for oblique phase-shift transformation.

Abstract

A thin-sheet (TS) volume integral equation (VIE) formulation incorporating generalized sheet transition conditions (GSTCs) is presented for the simulation of three-dimensional (3D) bianisotropic metasurfaces. The metasurface is represented as an equivalent TS, with its constitutive tensors derived from the GSTC susceptibility tensors. Invoking the TS approximation, the governing VIEs are reduced to surface integral equations (SIEs), in which tangential and normal flux density components are treated as distinct sets of unknowns and discretized using Rao-Wilton-Glisson and pulse basis functions, respectively. In contrast to conventional GSTC approaches based on conventional SIEs, which represent only tangential fields, the proposed framework rigorously enforces the bianisotropic GSTCs, including normal field interactions, while retaining the flux-based VIE character of the formulation. Numerical examples demonstrate the accuracy and robustness of the proposed TS-VIE-GSTC solver for polarization rotation, perfect reflection, multi-directional attenuation, and oblique phase-shift transformation.