当前位置: X-MOL 学术SIAM J. Math. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Honeycomb-Lattice Minnaert Bubbles
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-11-03 , DOI: 10.1137/19m1281782
Habib Ammari , Brian Fitzpatrick , Erik Orvehed Hiltunen , Hyundae Lee , Sanghyeon Yu

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5441-5466, January 2020.
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.


中文翻译:

蜂窝格Minnaert气泡

SIAM数学分析杂志,第52卷,第6期,第5441-5466页,2020年1月。
对于许多不同的物理应用而言,在亚波长范围内操纵波的传播的能力很重要。在本文中,我们考虑了亚波长谐振器的蜂窝晶格,并首次证明了在亚波长范围内存在狄拉克色散锥。如[Ammari,Hiltunen和Yu,Arch。配给。机甲 Anal。,238(2020),pp。1559--1583],在Dirac点附近,将亚波长谐振器的蜂窝晶体用作接近零的材料具有很大的潜力。在这里,我们对气泡晶体的例子进行分析,这是亚波长谐振的经典例子,其中单个气泡的谐振频率称为Minnaert谐振。我们的第一个结果是导出接近Brilloun区中对称点K的准周期Minnaert共振频率的渐近公式。然后我们获得狄拉克锥的线性色散关系。本文在圆形气泡的情况下说明了我们的发现,其中多极膨胀方法为计算能带结构提供了一种有效的技术。
更新日期:2020-11-04
down
wechat
bug