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

Habib Ammari, Erik Orvehed Hiltunen, Sanghyeon Yu

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2279-2313
Number of pages35
JournalJournal of the European Mathematical Society
Issue number7
Publication statusPublished - 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 European Mathematical Society Publishing House. All rights reserved.


  • Bubble
  • line defect
  • subwavelength phononic crystal
  • subwavelength resonance
  • subwavelength waveguide
  • weak localization

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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