Dirac Integral Equations for Dielectric and Plasmonic Scattering
Artikel i vetenskaplig tidskrift, 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.

Clifford–Cauchy integral

Spurious resonances

Surface plasmon wave

Non-smooth object

Boundary integral equation

Nyström discretization

Maxwell scattering


Johan Helsing


Andreas Rosén

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Integral Equations and Operator Theory

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

Vol. 93 5 48



Annan fysik

Matematisk analys



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