Subwavelength localized modes for acoustic waves in bubbly crystals with a defect

Abstract

The ability to control wave propagation is of fundamental interest in many areas of physics. Photonic and phononic crystals have proved very useful for this purpose but, because they are based on Bragg interference, these artificial media require structures with large dimensions. In [Ammari et al., Subwavelength phononic bandgap opening in bubbly media, J. Diff. Eq., 263 (2017), 5610--5629], it has been proved that a subwavelength bandgap opening occurs in bubbly phononic crystals. To demonstrate the opening of a subwavelength phononic bandgap, a periodic arrangement of bubbles is considered and their subwavelength Minnaert resonance is exploited. In this paper, this subwavelength bandgap is used to demonstrate cavities, very similar to those obtained in photonic and phononic crystals, albeit of deeply subwavelength dimensions. The key idea is to perturb the size of a single bubble inside the crystal, thus creating a defect. The goal is then to analytically and numerically show that this crystal has a localized eigenmode close to the defect bubble.

arXiv comment19 pages, 4 figures, typos corrected, added argument to account for dilute regime

References in corpus (6)

• Composite 3D-printed meta-structures for low frequency and broadband vibration absorption
• A mathematical theory of super-resolution by using a system of sub-wavelength Helmholtz resonators
• Defect Modes and Homogenization of Periodic Schrödinger Operators
• Sub-wavelength focusing of acoustic waves in bubbly media
• Homogenized description of defect modes in periodic structures with localized defects
• Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes

Cited by in corpus (6)

• Topologically protected edge modes in one-dimensional chains of subwavelength resonators
• Honeycomb-lattice Minnaert bubbles
• Functional analytic methods for discrete approximations of subwavelength resonator systems
• A high-frequency homogenization approach near the Dirac points in bubbly honeycomb crystals
• Subwavelength resonances of encapsulated bubbles
• Double Dirac cones in band structures of periodic Schrödinger operators