Imaging an off-plane shear wave source with two-dimensional phononic-crystal lens

TL;DR

This paper proposes a two-dimensional phononic crystal lens that uses self-collimation and Dirichlet-to-Neumann Maps to focus off-plane shear waves, achieving subwavelength imaging in the far field.

Contribution

It introduces a novel 2D phononic crystal lens design employing a triangular lattice and advanced computational methods for off-plane shear wave imaging.

Findings

Subwavelength imaging achieved in the far field.

Good agreement between multiple-scattering simulations and ray-trace predictions.

Effective guidance of shear waves via self-collimation in the lens.

Abstract

A two dimensional flat phononic crystal (PC) lens for focusing off-plane shear waves is proposed. The lens consists of a triangular lattice hole-array, embedded in solid matrix. Self-collimation effect is employed to guide the shear waves propagating through the lens along specific directions. Dirichlet-to-Neumann Maps (DtN) method is employed to calculate the band structure of the PC, which can avoid the problems of bad convergence and fake bands automatically in the void-solid PC structure. When the lens is illuminated by the off-plane shear waves emanating from a point source, a subwavelength image appears in the far-field zone. The imaging characteristics are investigated by calculating the displacement fields explicitly using the multiple-scattering method, and the results are in good agreement with the ray-trace predictions. Our results may provide insights for designing new phononic devices.