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Modal expansion for plasmonic resonators in the time domain

by H. Ammari and P. Millien and A. Vanel

(Report number 2020-19)

Abstract
We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low frequency regime. We use asymptotic analysis and spectral theory to diagonalise a singular integral operator, which allows us to write the field inside and outside the particle in the form of a complete and orthogonal modal expansion. We find the eigenvalues of the volume operator to be associated, via a non-linear relation, to the resonant frequencies of the problem. We prove that all resonances lie in a bounded region near the origin. Finally we use complex analysis to compute the Fourier transform of the scattered field and obtain its modal expansion in the time domain.

Keywords: plasmonic resonance, normal modes, dispersive scatterer, time domain expansion

@Techreport{AMV20_892,
  author = {H. Ammari and P. Millien and A. Vanel},
  title = {Modal expansion for plasmonic resonators in the time domain},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-19},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-19.pdf },
  year = {2020}
}

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