Transparent gradient index lens for underwater sound based on phase advance

Spatial gradients in refractive index have been used extensively in acoustic metamaterial applications to control wave propagation through phase delay. This study reports the design and experimental realization of an acoustic gradient index lens using a sonic crystal lattice that is impedance matched to water over a broad bandwidth. In contrast to previous designs, the underlying lattice features refractive indices that are lower than the water background, which facilitates propagation control based on a phase advance as opposed to a delay. The index gradient is achieved by varying the filling fraction of hollow, air-filled aluminum tubes that individually exhibit a higher sound speed than water and matched impedance. Acoustic focusing is observed over a broad bandwidth of frequencies in the homogenization limit of the lattice, with intensity magnifications in excess of 7 dB. An anisotropic lattice design facilitates a flat-faceted geometry with low backscattering at 18 dB below the incident sound pressure level. Three dimensional Rayleigh-Sommerfeld integration that accounts for the anisotropic refraction is used to accurately predict the experimentally measured focal patterns.