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Modal approximation for plasmonic resonators in the time domain: the scalar case

by L. Baldassari and P. Millien and A. Vanel

(Report number 2021-05)

Abstract
We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non-Hermitian problem as perturbations of electrostatic modes, and obtain a modal approximation of the scattered field in the frequency domain. The poles of the expansion correspond to the eigenvalues of a singular boundary integral operator and are shown to lie in a bounded region near the origin of the lower-half complex plane. Finally, we show that this modal representation gives a very good approximation of the field in the time domain. We present numerical simulations in two dimensions to corroborate our results.

Keywords: plasmonic resonance, time-domain modal expansion, subwavelength resonators, quasi-normal modes

@Techreport{BMV21_947,
  author = {L. Baldassari and P. Millien and A. Vanel},
  title = {Modal approximation for plasmonic resonators in the time domain: the scalar case},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-05.pdf },
  year = {2021}
}

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