FMM IE-GSTC Simulation of Metasurfaces with Complete Dyadic Surface Susceptibilities

Abstract

An accelerated Integral Equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces, with both normal and tangential susceptibilities, utilizing Fast Multipole Method (FMM) is proposed and demonstrated in 2D. In the proposed method, practical general metasurfaces are modeled as a zero thickness sheet model described with surface susceptibilities, and where the total fields around it satisfy the Generalized Sheet Transition Conditions (GSTCs). While the standard IE-GSTC offers fast field computation compared to other numerical methods, it is still computationally demanding when solving electrically large problems, with a large number of unknowns. Here we accelerate the IE-GSTC method using the FMM technique. Using a numerical example, the speed improvement of the FMM IE-GSTC method <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left\{ {O\left({{N^{3/2}}} \right)} \right\}$</tex> over the standard IE-GSTC <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\left\{O\left(N^{3}\right)\right\}}$</tex> method is confirmed, when both tangential and normal surface susceptibilities are present.