Dirac Integral Equations for Dielectric and Plasmonic Scattering
Journal article, 2021

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.

Surface plasmon wave

Nyström discretization

Clifford–Cauchy integral

Spurious resonances

Non-smooth object

Maxwell scattering

Boundary integral equation

Author

Johan Helsing

Lund University

Andreas Rosén

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Integral Equations and Operator Theory

0378-620X (ISSN) 1420-8989 (eISSN)

Vol. 93 5 48

Subject Categories

Computational Mathematics

Other Physics Topics

Mathematical Analysis

DOI

10.1007/s00020-021-02657-1

More information

Latest update

11/4/2021