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Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect

by H. Ammari and E. Orvehed Hiltunen and S. Yu

(Report number 2019-22)

Abstract
The recent development of subwavelength photonic and phononic crystals shows the possibility of controlling wave propagation at deep subwavelength scales. Subwavelength bandgap phononic crystals are typically created using a periodic arrangement of subwavelength resonators, in our case small gas bubbles in a liquid. In this work, a waveguide is created by modifying the sizes of the bubbles along a line in a dilute two-dimensional bubbly crystal, thereby creating a line defect. Our aim is to prove that the line defect indeed acts as a waveguide; waves of certain frequencies will be localized to, and guided along, the line defect. The key result is an original formula for the frequencies of the defect modes. Moreover, these frequencies are numerically computed using the multipole method, which numerically illustrates our main results.

Keywords: Bubble, subwavelength resonance, subwavelength phononic crystal, subwavelength waveguide, line defect, weak localization

@Techreport{AOY19_826,
  author = {H. Ammari and E. Orvehed Hiltunen and S. Yu},
  title = {Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-22.pdf },
  year = {2019}
}

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