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Perturbations of the scattering resonances of an open cavity by small particles. Part II: The transverse electric polarization case

by H. Ammari and A. Dabrowski and B. Fitzpatrick and P. Millien

(Report number 2018-39)

Abstract
This paper is concerned with the scattering resonances of open cavities. It is a follow-up of a work by the same authors, where the transverse magnetic polarization was assumed. In that case, using the method of matched asymptotic expansions, the leading-order term in the shifts of scattering resonances due to the presence of small particles of arbitrary shapes was derived and the effect of radiation on the perturbations of open cavity modes was characterized. The derivations were formal. In this paper, we consider the transverse electric polarization and prove a small-volume formula for the shifts in the scattering resonances of a radiating dielectric cavity perturbed by small particles. We show a strong enhancement in the frequency shift in the case of plasmonic particles. We also consider exceptional scattering resonances and perform small-volume asymptotic analysis near them. Our method in this paper relies on pole-pencil decompositions of volume integral operators.

Keywords: Open dielectric resonator, shift of scattering resonances, plasmonic nanoparticles, exceptional scattering resonances, pole-pencil decomposition.

@Techreport{ADFM18_793,
  author = {H. Ammari and A. Dabrowski and B. Fitzpatrick and P. Millien},
  title = {Perturbations of the scattering resonances of an open cavity by small particles. Part II: The transverse electric polarization case},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-39},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-39.pdf },
  year = {2018}
}

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