Dirac integral equations for dielectric and plasmonic scattering

TL;DR

This paper introduces a novel Dirac integral equation formulation for electromagnetic scattering in Lipschitz domains, overcoming limitations of existing methods and applicable in both 2D and 3D, with demonstrated numerical effectiveness.

Contribution

The paper presents a new Dirac integral equation approach for Maxwell transmission problems that avoids false eigenwavenumbers and low-frequency breakdown, applicable to magnetic materials and in multiple dimensions.

Findings

Numerical results show competitiveness with existing methods in 2D.

The formulation is free from false eigenwavenumbers for a wider permittivity range.

It performs well in 3D, as shown in a companion study.

Abstract

A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities than other known formulations, can be used for magnetic materials, is applicable in both two and three dimensions, and does not suffer from any low-frequency breakdown. Numerical results for the two-dimensional version of the formulation, including examples featuring surface plasmon waves, demonstrate competitiveness relative to state-of-the-art integral formulations that are constrained to two dimensions. However, our Dirac integral equation performs equally well in three dimensions, as demonstrated in a companion paper.