Double-negative acoustic metamaterials

Habib Ammari, Brian Fitzpatrick, Hyundae Lee, Sanghyeon Yu, Hai Zhang

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


The aim of this paper is to provide a mathematical theory for understanding the mechanism behind the double-negative refractive index phenomenon in bubbly fluids. The design of double-negative metamaterials generally requires the use of two different kinds of subwavelength resonators, which may limit the applicability of doublenegative metamaterials. Herein we rely on media that consists of only a single type of resonant element, and show how to turn the acoustic metamaterial with a single negative effective property obtained in [SIAM J. Math. Anal., 49 (2017), pp. 3252-3276] into a negative refractive index metamaterial, which refracts waves negatively, hence acting as a superlens. Using bubble dimers made of two identical bubbles, it is proved, under the assumption that their volume fraction is small and their orientation is uniformly distributed, that both the effective mass density and the bulk modulus of the bubbly fluid can be negative at frequencies slightly higher than the dipole hybridized frequency for a single constituent bubble dimer.

Original languageEnglish
Pages (from-to)767-791
Number of pages25
JournalQuarterly of Applied Mathematics
Issue number4
Publication statusPublished - 2019
Externally publishedYes

Bibliographical note

Funding Information:
Received February 6, 2019. 2010 Mathematics Subject Classification. Primary 35C20, 74J20. Key words and phrases. Acoustic wave propagation, double-negative metamaterial, Minnaert resonance, hybridization. The work of the third author was supported by National Research Fund of Korea (NRF-2015R1D1A1A01059357, NRF-2017R1A4A1014735). The work of the fifth author was partially supported by Research Grant Council of Hong Kong (GRF grant 16304517) and startup fund R9355 from HKUST.. Email address: Email address: Email address: Email address: Email address:

Publisher Copyright:
© 2019 Brown University.


  • Acoustic wave propagation
  • Double-negative metamaterial
  • Hybridization
  • Minnaert resonance

ASJC Scopus subject areas

  • Applied Mathematics


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