Gradient-index phononic crystals

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.