TY - JOUR

T1 - HONEYCOMB-LATTICE MINNAERT BUBBLES

AU - Ammari, Habib

AU - Fitzpatrick, Brian

AU - Hiltunen, Erik Orvehed

AU - Lee, Hyundae

AU - Yu, Sanghyeon

N1 - Funding Information:
The work of the fourth author was supported by the National Research Fund of Korea (NRF) grants 2015R1D1A1A01059357, 2018R1D1A1B07042678. The work of the fifth author was supported by NRF grant 2020R1C1C1A01010882.
Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics

PY - 2020

Y1 - 2020

N2 - The ability to manipulate the propagation of waves on subwavelength scales is important for many different physical applications. In this paper, we consider a honeycomb-lattice of subwavelength resonators and prove, for the first time, the existence of a Dirac dispersion cone at subwavelength scales. As shown in [Ammari, Hiltunen, and Yu, Arch. Ration. Mech. Anal., 238 (2020), pp. 1559-1583], near the Dirac points, the use of honeycomb crystals of subwavelength resonators as near-zero materials has great potential. Here, we perform the analysis for the example of bubbly crystals, which is a classic example of subwavelength resonance, where the resonant frequency of a single bubble is known as the Minnaert resonance. Our first result is to derive an asymptotic formula for the quasi-periodic Minnaert resonance frequencies close to the symmetry points K in the Brilloun zone. Then we obtain 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.

AB - The ability to manipulate the propagation of waves on subwavelength scales is important for many different physical applications. In this paper, we consider a honeycomb-lattice of subwavelength resonators and prove, for the first time, the existence of a Dirac dispersion cone at subwavelength scales. As shown in [Ammari, Hiltunen, and Yu, Arch. Ration. Mech. Anal., 238 (2020), pp. 1559-1583], near the Dirac points, the use of honeycomb crystals of subwavelength resonators as near-zero materials has great potential. Here, we perform the analysis for the example of bubbly crystals, which is a classic example of subwavelength resonance, where the resonant frequency of a single bubble is known as the Minnaert resonance. Our first result is to derive an asymptotic formula for the quasi-periodic Minnaert resonance frequencies close to the symmetry points K in the Brilloun zone. Then we obtain 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.

KW - Bubble

KW - Dirac cone

KW - Honeycomb lattice

KW - Minneart resonance

KW - Subwavelength bandgap

UR - http://www.scopus.com/inward/record.url?scp=85096741031&partnerID=8YFLogxK

U2 - 10.1137/19M1281782

DO - 10.1137/19M1281782

M3 - Article

AN - SCOPUS:85096741031

SN - 0036-1410

VL - 52

SP - 5441

EP - 5466

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -