TY - JOUR

T1 - Dirac Integral Equations for Dielectric and Plasmonic Scattering

AU - Helsing, Johan

AU - Rosén, Andreas

PY - 2021/10

Y1 - 2021/10

N2 - 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.

AB - 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.

KW - Boundary integral equation

KW - Clifford–Cauchy integral

KW - Maxwell scattering

KW - Non-smooth object

KW - Nyström discretization

KW - Spurious resonances

KW - Surface plasmon wave

U2 - 10.1007/s00020-021-02657-1

DO - 10.1007/s00020-021-02657-1

M3 - Article

AN - SCOPUS:85112285416

SN - 1420-8989

VL - 93

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 5

M1 - 48

ER -