Static surface mode expansion for the full-wave scattering from penetrable objects

TL;DR

This paper introduces static surface modes as a shape-dependent basis to efficiently solve full-wave electromagnetic scattering problems from penetrable objects, reducing computational complexity and time.

Contribution

The paper presents a novel static surface mode expansion that simplifies solving electromagnetic scattering by shape-dependent basis functions, independent of frequency and material.

Findings

Reduces the number of unknowns compared to traditional discretization.

Regularizes singular integral operators in the scattering problem.

Significantly decreases CPU time for particle array scattering simulations.

Abstract

We introduce the longitudinal and transverse static surface modes and use them to solve the full-wave electromagnetic scattering problem from penetrable objects. The longitudinal static modes are the eigenmodes with zero surface curl of the electrostatic integral operator that gives the tangential component of the electric field, as a function of the surface charge density. The transverse static modes are the eigenmodes with zero surface divergence of the magnetostatic integral operator that returns the tangential component of the vector potential, as a function of the surface current distribution. The static modes only depend on the shape of the object, thus, the same static basis can be used regardless of the frequency of operation and of the material constituting the object. We expand the unknown surface currents of the Poggio-Miller-Chang-Harrington-Wu-Tsai surface integral equations in terms of the static surface modes and solve them using the Galerkin-projection scheme. The static modes expansion allows the regularization of the singular integral operators and yields a drastic reduction of the number of unknowns compared to a discretization based on sub-domain basis functions. The introduced expansion significantly reduces the cpu-time required for the numerical solution of the scattering problem from particle arrays.