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Perturbation of the scattering resonances of an open cavity by small particles. Part I: The transverse magnetic polarization case

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

(Report number 2018-38)

Abstract
This paper aims at providing a small-volume expansion framework for the scattering resonances of an open cavity perturbed by small particles. The induced shift of the scattering frequencies by the small particles is derived without neglecting the radiation effect. The formula holds for arbitrary-shaped particles. It shows a strong enhancement in the frequency shift in the case of plasmonic particles. The formula is used to image small particles located near the boundary of an open resonator which admits whispering-gallery modes. Numerical examples of interest for applications are presented.

Keywords: Open cavity, shift of scattering resonances, whispering-gallery modes, bio-sensing, plasmonic nanoparticles.

@Techreport{ADFM18_792,
  author = {H. Ammari and A. Dabrowski and B. Fitzpatrick and P. Millien},
  title = {Perturbation of the scattering resonances of an open cavity by small particles. Part I: The transverse magnetic polarization case},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-38},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-38.pdf },
  year = {2018}
}

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