We study the acoustic scattering properties of a phononic crystal designed to behave as a gradient index lens in water, both experimentally and theoretically. The gradient index lens is designed using a square lattice of stainless-steel cylinders based on a multiple scattering approach in the homogenization limit. We experimentally demonstrate that the lens follows the graded index equations derived for optics by mapping the pressure intensity generated from a spherical source at 20 kHz. We find good agreement between the experimental result and theoretical modeling based on multiple scattering theory.

Pentamode metamaterials are a class of acoustic metafluids that are characterized by a divergence free modified stress tensor. Such materials have an unconventional anisotropic stiffness and isotropic mass density, which allow themselves to mimic other fluid domains. Here we present a pentamode design formed by an oblique honeycomb lattice and producing customizable anisotropic properties. It is shown that anisotropy in the stiffness can exceed three orders of magnitude, and that it can be realistically tailored for transformation acoustic applications. [16][17][18][19]. Such devices are defined as metafluids, which are effective materials with unconventional fluid-like properties whose particular bulk realization typically requires an anisotropic mass density. Experimental demonstration has been sparse, with most studies relying on a superlattice approach of alternating isotropic layers [20]. However, such an approach is difficult to realize and limited by the so-called mass catastrophe, which requires infinite mass density in the effective material profile.An alternative approach is to generalize the conventional stress strain relationship to include pentamode metamaterials. Pentamode materials [21][22][23] are metafluids that support five easy infinitesimal strains (i.e. there is only one non-zero eigenvalue of the elasticity tensor which is of a pure pressure type), and satisfies the invariance of the governing equations by virtue of maintaining a harmonic transformation. Pure pentamodes, in general, have an isotropic density and anisotropic stiffness with a negligible shear modulus. Recently, isotropic pentamode materials have become experimental reality, and it was shown that the structure's effective bulk modulus exceeded the shear modulus by three orders of magnitude [24]. However, it has yet to be reported that anisotropic pentamode metamaterials can be realistically implemented for specific applications, since an elastic solid with a zero shear modulus would have no stability and immediately flow away.In this Letter, we show that an oblique honeycomb lattice can be utilized as a simple yet versatile building block for pentamode device construction, which exerts highly anisotropic control over sound waves. The method presents a distinctly different approach to acoustic metamaterials, in that it does not require the difficult to achieve high value anisotropy in the effective mass density in addition to removing frequency bandwidth problems associated with inertial metafluids. Potential applications include extraordinary scattering reduction and arbitrary wave manipulation, low loss acoustic delay lines [25], and phase controlled logic gates [26].Anisotropy in pentamode metafluids. We consider elastic wave propagation in a microstructure having the general characteristics presented in Fig. 1. For simplicity we present our results in a two-dimensional (2D) plain strain space, however, the analysis can straightforwardly be extended to three dimensions. Only wavelengths much larger than the lattice constant...

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Gradient index media, which are designed by varying local element properties in given geometry, have been utilized to manipulate acoustic waves for a variety of devices. This study presents a cylindrical, two-dimensional acoustic “black hole” design that functions as an omnidirectional absorber for underwater applications. The design features a metamaterial shell that focuses acoustic energy into the shell's core. Multiple scattering theory was used to design layers of rubber cylinders with varying filling fractions to produce a linearly graded sound speed profile through the structure. Measured pressure intensity agreed with predicted results over a range of frequencies within the homogenization limit.

Vortex waves, which carry orbital angular momentum, have found use in a range of fields from quantum communications to particle manipulation. Due to their widespread influence, significant attention has been paid to the methods by which vortex waves are generated. For example, active phased arrays generate diverse vortex modes at the cost of electronic complexity and power consumption [1][2][3][4] . Conversely, analog apertures, such as spiral phase plates 1,5 , metasurfaces 6 , and gratings 7 require separate apertures to generate each mode. Here we present a new class of metamaterial-based acoustic vortex generators, which are both geometrically and electronically simple, and topologically tunable. Our metamaterial approach generates vortex waves by wrapping an acoustic leaky wave antenna 8 back upon itself. Exploiting the antennas frequency-varying refractive index, we demonstrate experimentally and analytically that this analog structure generates both integer, and noninteger vortex modes. The metamaterial design makes the aperture compact and can thus be integrated into high-density systems.The total angular momentum of a system can be divided into two components, spin angular momentum, and orbital angular momentum (OAM). Although acoustic waves do not possess spin angular momentum they have been shown to carry OAM 1,2 . A drawing of a single mode helical wave with value L = −2 is shown in Fig. 1(a) where L is the OAM topological mode number. A wave with OAM index L = 0 describes a system with no helical phase front. The phase front of the propagating wave is a corkscrew-type phase advance with the sign of the topological charge positive, for clockwise rotation, or negative, for counter-clockwise rotation. These vortex waves have been found to be useful in an extremely diverse range of applications from communications 6,9-13 and imaging 14-16 to particle manipulation 17-19 over a wide range of length scales. In the most widely examined application, vortex waves have been harnessed for use in electromagnetic and quantum 2 communications.The importance of both topological diversity, and aperture simplicity in vortex mode generation becomes immediately evident when considering the applications of vortex waves. Inspired by recent research on acoustic leaky-wave antennas 8,23 , we present an air-acoustic vortex beam emitter which generates topologically diverse vortex waves using a single transducer coupled to a single analog metamaterial aperture. A leaky wave antenna is a device comprised of a one-or two-dimensional waveguide which leaks power along it's length with either a continuous leaking slot or sub-wavelength radiating shunts. Leaky wave antennas rely on geometry-controlled dispersion to tune the refractive index of the fluid inside the waveguide. The leaked energy then refracts from the antenna at an angle θ(ω), similar to the refraction mechanism of a prism. The value of θ(ω) is determined by the ratio of 3 wavenumber β(ω) inside the waveguide to the wavenumber in the surrounding area kAlthough not in...