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Honeycomb-lattice Minnaert bubbles

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

(Report number 2018-42)

Abstract
The aim of this paper is to rigorously show the existence of a Dirac dispersion cone in a bubbly honeycomb phononic crystal comprised of bubbles of arbitrary shape. The main result is an asymptotic formula for the quasi-periodic Minnaert resonance frequencies close to the symmetry points K in the Brilloun zone. This shows the linear dispersion relation of a Dirac cone. Our findings in this paper are illustrated in the case of circular bubbles, where the multipole expansion method provides an efficient technique for computing the band structure.

Keywords: Honeycomb lattice, Dirac cone, bubble, Minnaert resonance, subwavelength bandgap.

@Techreport{AFHLY18_796,
  author = {H. Ammari and B. Fitzpatrick and E.O. Hiltunen and H. Lee and S. Yu},
  title = {Honeycomb-lattice Minnaert bubbles},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-42},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-42.pdf },
  year = {2018}
}

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