An inhomogeneous acoustic metamaterial lens based on spatial variation of refractive index for broadband focusing of underwater sound is reported. The index gradient follows a modified hyperbolic secant profile designed to reduce aberration and suppress side lobes. The gradient index (GRIN) lens is comprised of transversely isotropic hexagonal microstructures with tunable quasi-static bulk modulus and mass density. In addition, the unit cells are impedance-matched to water and have in-plane shear modulus negligible compared to the effective bulk modulus. The flat GRIN lens is fabricated by cutting hexagonal centimeter scale hollow microstructures in aluminum plates, which are then stacked and sealed from the exterior water. Broadband focusing effects are observed within the homogenization regime of the lattice in both finite element simulations and underwater measurements (20-40 kHz). This design approach has potential applications in medical ultrasound imaging and underwater acoustic communications.

A metamaterial of particular interest for underwater applications is the three-dimensional (3D) anisotropic pentamode (PM), i.e., a structure designed to support a single longitudinal wave with a sound speed that depends on the propagation direction. The present work attempts to experimentally verify anisotropic sound speeds predicted by finite element simulations using additively manufactured anisotropic 3D PM samples made of titanium. The samples were suspended in front of a plane wave source emitting a broadband chirp in a water tank to measure time of flight for wavefronts with and without the PM present. The measurement utilizes a deconvolution method that extracts the band limited impulse response of data gathered by a scanning hydrophone in a plane of constant depth behind the samples. Supporting material takes the form of finite element simulations developed to model the response of a semi-infinite PM medium to an incident normal plane wave. A technique to extract the longitudinal PM wave speed for frequency domain simulations based on Fourier series expansions is given.

This paper presents a method to characterize the effective properties of inertial acoustic metamaterial unit cells for underwater operation. The method is manifested by a fast and reliable parameter retrieval procedure utilizing both numerical simulations and measurements. The effectiveness of the method was proved to be self-consistent by a metamaterial unit cell composed of aluminum honeycomb panels with soft rubber spacers. Simulated results agree well with the measured responses of this metamaterial in a water-filled resonator tube. A sub-unity density ratio and an anisotropic mass density are simultaneously achieved by the metamaterial unit cell, making it useful in implementations of transformation acoustics. The metamaterial, together with the approach for its characterization, are expected to be useful for underwater acoustic devices.