Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals

TL;DR

This paper provides a theoretical analysis of acoustic wave focusing by two-dimensional sonic crystals, exploring how shape, filling factor, and disorder influence focusing, and comparing results with experimental data.

Contribution

It offers a detailed theoretical investigation into acoustic focusing by sonic crystals, highlighting the effects of shape, filling factor, and disorder, and validating findings against experiments.

Findings

Shape and filling factor significantly influence focusing.

Focusing robustness varies with positional disorder.

Theoretical results align well with experimental observations.

Abstract

Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependance of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. (Phys. Rev. Lett. 88, 023902 (2002)).