Sonic crystal lenses that obey Lensmaker's formula

TL;DR

This paper demonstrates that sonic crystal arrays can function as acoustic lenses following Lensmaker's formula, supported by theoretical analysis of wave scattering and band structures, with potential applications in acoustic imaging.

Contribution

It provides a theoretical framework showing sonic crystal lenses obey Lensmaker's formula, combining multiple scattering theory and band structure calculations.

Findings

Sonic crystal arrays can act as acoustic lenses.

Focusing effects follow Lensmaker's formula.

Potential applications in acoustic imaging.

Abstract

This paper presents a theoretical study of the phenomenon of acoustic imaging by sonic crystals, which are made of two-dimensional regular arrays of rigid cylinders placed in parallel in air. The scattering of acoustic waves is computed using the standard multiple scattering theory, and the band structures are computed by the plane-wave expansion method. It is shown that properly arranged arrays not only can behave as acoustic lenses, but also the focusing effect can be well described by Lensmaker's formula. Possible applications are also discussed.