Double-negative acoustic metamaterials

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

doi:10.1090/qam/1543

Authors: Habib Ammari, Brian Fitzpatrick, Hyundae Lee, Sanghyeon Yu and Hai Zhang
Journal: Quart. Appl. Math. 77 (2019), 767-791
MSC (2010): Primary 35C20, 74J20
DOI: https://doi.org/10.1090/qam/1543
Published electronically: June 3, 2019
MathSciNet review: 4009331
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Abstract: 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 double-negative 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.

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