Achromatic acoustic gradient-index phononic crystal lens for broadband focusing

The aim of this study is to realize an achromatic acoustic gradient-index (GRIN) phononic crystal (PC) lens system with a spatially invariant focal length over a broad operating frequency range. To this end, we propose an approach of introducing thin achromatic coating layers that can be easily assembled into the front and rear regions of the acoustic GRIN PC lens. A systematic design method based on topology optimization (TO) is developed to inversely design the achromatic coating components. The topology-optimized achromatic coating components are fabricated using 3D printing and coupled with the acoustic GRIN PC lens for acoustic characterization. Both numerical simulation and experimental characterization demonstrate the achromatic focusing capabilities of the GRIN PC lens with the designed achromatic coating layers in a wide range of frequencies (2.5kHz-5.5kHz). The proposed concept of applying achromatic coating layers along with the TO-based design method is expected to provide remarkable versatility to design GRIN PC lens-based applications such as energy harvesting, acoustic imaging, and acoustic wireless power transfer in broadband operation.