Windowed Green Function MoM for Second-Kind Surface Integral Equation Formulations of Layered Media Electromagnetic Scattering Problems

This article presents a second-kind surface integral equation (SIE) method for the numerical solution of frequency-domain electromagnetic (EM) scattering problems by locally perturbed layered media in three spatial dimensions. Unlike standard approaches, the proposed methodology does not involve the use of layer Green functions (LGFs). It instead leverages an indirect Muller formulation in terms of free-space Green functions that entails integration over the entire unbounded penetrable boundary. The integral equation domain is effectively reduced to a small-area surface by means of the windowed Green function (WGF) method, which exhibits high-order convergence as the size of the truncated surface increases. The resulting (second-kind) windowed integral equation is then numerically solved by means of the standard Galerkin method of moments (MoM) using the Rao-Wilton-Glisson (RWG) basis functions. The methodology is validated by comparison with the Mie series and Sommerfeld integral exact solutions as well as against an LGF-based MoM. Challenging examples including realistic structures relevant to the design of plasmonic solar cells and all-dielectric metasurfaces demonstrate the applicability, efficiency, and accuracy of the proposed methodology.