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Subwavelength resonances of encapsulated bubbles

by H. Ammari and B. Fitzpatrick and H. Lee and E. Orvehed Hiltunen and S. Yu

(Report number 2018-40)

Abstract
The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance can be efficiently computed using the multipole method.

Keywords: bubble, subwavelength resonance, encapsulated bubble, thin coating.

@Techreport{AFLOY18_794,
  author = {H. Ammari and B. Fitzpatrick and H. Lee and E. Orvehed Hiltunen and S. Yu},
  title = {Subwavelength resonances of encapsulated bubbles},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-40},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-40.pdf },
  year = {2018}
}

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