Gradient-index phononic crystals

TLDR

The study designs and characterizes a two-dimensional gradient‑index phononic crystal to control acoustic wave propagation. The GRIN PC consists of solid cylinders in a square lattice immersed in epoxy, with a hyperbolic secant refractive‑index gradient modulated by cylinder density and elastic moduli; effective indices were derived from band diagrams via plane‑wave expansion, and acoustic propagation was simulated with finite‑difference time‑domain and compared to analytical beam trajectories. The GRIN PC achieves acoustic focusing across a broad frequency range, enabling flat acoustic lenses and couplers.

Abstract

We designed and characterized a two-dimensional, gradient-index phononic crystal (GRIN PC) to control the propagation of acoustic waves. The GRIN PC was composed of solid cylinders arranged in a square lattice and immersed in an epoxy. The refractive index along the direction transverse to the phononic propagation was designated as a hyperbolic secant gradient distribution. This distribution was modulated by means of the density and elastic moduli of the cylinders. The effective refractive indices in each row of the GRIN PC were determined from band diagrams obtained via a plane-wave expansion method. The acoustic wave propagation was numerically investigated by a finite-difference time-domain method, and the results were compared to the analytical beam trajectories derived from the hyperbolic secant profile. These results show that the GRIN PC allows acoustic focusing over a wide range of working frequencies, making it suitable for applications such as flat acoustic lenses and couplers.