Acoustic resonances in two dimensional radial sonic crystals shells

TL;DR

This paper analyzes two-dimensional radial sonic crystal shells, revealing they support Fabry-Perot-like resonances and localized modes, with potential extensions to 3D structures and photonic analogs.

Contribution

It provides a comprehensive analytical study of RSC shells with defects, highlighting their resonance and localization properties, and generalizing to higher dimensions and photonic systems.

Findings

RSC shells exhibit Fabry-Perot-like resonances.

Localized modes are supported by the shells.

Results applicable to 3D and photonic structures.

Abstract

Radial sonic crystals (RSC) are fluidlike structures infinitely periodic along the radial direction. They have been recently introduced and are only possible thanks to the anisotropy of specially designed acoustic metamaterials [see Phys. Rev. Lett. {\bf 103} 064301 (2009)]. We present here a comprehensive analysis of two-dimensional RSC shells, which consist of a cavity defect centered at the origin of the crystal and a finite thickness crystal shell surrounded by a fluidlike background. We develop analytic expressions demonstrating that, like for other type of crystals (photonic or phononic) with defects, these shells contain Fabry-Perot like resonances and strongly localized modes. The results are completely general and can be extended to three dimensional acoustic structures and to their photonic counterparts, the radial photonic crystals.