Acoustic mirage in two-dimensional gradient-index phononic crystals

We report the design of a two-dimensional gradient-index phononic crystal (GRIN PC) structure, which effectively demonstrates the "acoustic mirage" effect on the wavelength scale. Using the GRIN PC, the propagating direction of acoustic waves can be continuously bent along an arc-shaped trajectory by gradually tuning the filling ratio of PCs. We investigate the acoustic mirage effect through both plane wave expansion and finite-difference time-domain methods. By controlling the incident angle or operating frequency, the arc-shaped trajectory of acoustic wave propagation can be dynamically adjusted. The GRIN PC structure is composed of steel cylinders, positioned in a square lattice, and immersed in an epoxy. It can be fabricated through a simple process and seamlessly integrated with existing acoustic devices. In addition, we establish that such an acoustic effect can be used in the design of tunable acoustic waveguides, which could find applications in acoustic switching, filtering, and biosensing.