Xiaoshi Su

Broadband focusing of underwater sound using a transparent pentamode lens

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.

Focusing, refraction, and asymmetric transmission of elastic waves in solid metamaterials with aligned parallel gaps

Gradient index (GRIN), refractive, and asymmetric transmission devices for elastic waves are designed using a solid with aligned parallel gaps. The gaps are assumed to be thin so that they can be considered as parallel cracks separating elastic plate waveguides. The plates do not interact with one another directly, only at their ends where they connect to the exterior solid. To formulate the transmission and reflection coefficients for SV- and P-waves, an analytical model is established using thin plate theory that couples the waveguide modes with the waves in the exterior body. The GRIN lens is designed by varying the thickness of the plates to achieve different flexural wave speeds. The refractive effect of SV-waves is achieved by designing the slope of the edge of the plate array, and keeping the ratio between plate length and flexural wavelength fixed. The asymmetric transmission of P-waves is achieved by sending an incident P-wave at a critical angle, at which total conversion to SV-wave occurs. An array of parallel gaps perpendicular to the propagation direction of the reflected waves stop the SV-wave but let P-waves travel through. Examples of focusing, steering, and asymmetric transmission devices are discussed.

Elastic metasurfaces for splitting SV- and P-waves in elastic solids

Although recent advances have made it possible to manipulate electromagnetic and acoustic wavefronts with sub-wavelength metasurface slabs, the design of elastodynamic counterparts remains challenging. We introduce a novel but simple design approach to control SV-waves in elastic solids. The proposed metasurface can be fabricated by cutting an array of aligned parallel cracks in a solid such that the materials between the cracks act as plate-like waveguides in the background medium. The plate array is capable of modulating the phase change of SV-wave while keeping the phase of P-wave unchanged. An analytical model for SV-wave incidence is established to calculate the transmission coefficient and the transmitted phase through the plate-like waveguide explicitly. A complete

Isotropic transformation acoustics and applications

2\pi

Acoustic-like behavior in periodic metal structures

range of phase delay is achieved by selecting different thicknesses for the plates. An elastic metasurface for splitting SV- and P-waves is designed and demonstrated using full wave finite element (FEM) simulations. Two metasurfaces for focusing plane and cylindrical SV-waves are also presented.

Willis coupling in underwater elastic Helmholtz resonators

A novel class of acoustic metamaterial is proposed for directional collimation of a cylindrical source into a plane wave beam. The effect is based on transformation acoustics which retains the exact form of the wave equation under conformal mapping from a circular region to a triangular area. The transformation is adjustable, allowing the acoustic energy to be equally radiated in three directions, or preferentially in a single direction. Importantly, the material properties in the physical domain are isotropic and therefore practically realizable. Two example devices are proposed using cylindrical elastic shells in water as the metamaterial elements and demonstrated using full wave simulations. This approach has potential applications beyond acoustic antenna design in beam-steering and wavefront manipulation.

Highly directional source radiation using isotropic transformation acoustics

Pentamode materials are of interest for acoustic metamaterials because of their property of having only one elastic mode, similar to the hydrostatic response of an acoustic fluid. This static property does not take into account dynamic frequency dependent effects related to the necessary spatial inhomogeneity in the structural realization. In this talk, we argue that pure pentamode behavior is not desirable, and instead AMM users should focus on the one-wave dynamic response. Experience with metal structures designed to provide acoustic properties close to those of water using metal structures, e.g., Su et al. (JASA 2017, doi: 10.1121/1.498519), shows that the most useful response is in a one-wave band gap in which shear waves are non-propagating. Surprisingly, the one-wave region is generally broadband relative to the cutoff frequency of the shear waves at low frequencies, and is non-dispersive, with constant phase speed over the one-wave gap. The talk will attempt to explain these surprising and unexpected features using numerical and analytical results. The latter include an approximation of the dynamic effective properties of 2D and 3D metallic structures displaying broadband one-wave regions using simplistic models.Pentamode materials are of interest for acoustic metamaterials because of their property of having only one elastic mode, similar to the hydrostatic response of an acoustic fluid. This static property does not take into account dynamic frequency dependent effects related to the necessary spatial inhomogeneity in the structural realization. In this talk, we argue that pure pentamode behavior is not desirable, and instead AMM users should focus on the one-wave dynamic response. Experience with metal structures designed to provide acoustic properties close to those of water using metal structures, e.g., Su et al. (JASA 2017, doi: 10.1121/1.498519), shows that the most useful response is in a one-wave band gap in which shear waves are non-propagating. Surprisingly, the one-wave region is generally broadband relative to the cutoff frequency of the shear waves at low frequencies, and is non-dispersive, with constant phase speed over the one-wave gap. The talk will attempt to explain these surprising and unexpec...

Anomalous refraction and asymmetric transmission of SV-waves through elastic metasurfaces

Helmholtz resonators (HRs) have been central in many acoustic metamaterial devices. For example, one can use an array of HRs to obtain negative effective bulk modulus or a panel of HRs to achieve total absorption of low-frequency sound. The aforementioned applications are based on the local monopolar resonance of each HR. However, the HR behaves differently in water. The elastic modulus of the resonator wall can become comparable to the modulus of water making the resonant frequency much lower than the rigid wall case. Moreover, considering the wall elasticity and mass leads to large structural asymmetry and induces cross-coupling between pressure and velocity fields. In this talk, we provide a lumped element model in order to predict the resonant frequency of the elastic HR. The model is demonstrated by sound scattering from an elastic HR in the context of acoustic bianisotropy, or Willis behavior, following a recent paper [Li Quan et al., Phys. Rev. Lett., 2018]. It is found that both the pressure and velocity fields can generate monopole and dipole responses from an elastic HR. The explicit example of an elastic HR in a one-dimensional waveguide will be discussed.Helmholtz resonators (HRs) have been central in many acoustic metamaterial devices. For example, one can use an array of HRs to obtain negative effective bulk modulus or a panel of HRs to achieve total absorption of low-frequency sound. The aforementioned applications are based on the local monopolar resonance of each HR. However, the HR behaves differently in water. The elastic modulus of the resonator wall can become comparable to the modulus of water making the resonant frequency much lower than the rigid wall case. Moreover, considering the wall elasticity and mass leads to large structural asymmetry and induces cross-coupling between pressure and velocity fields. In this talk, we provide a lumped element model in order to predict the resonant frequency of the elastic HR. The model is demonstrated by sound scattering from an elastic HR in the context of acoustic bianisotropy, or Willis behavior, following a recent paper [Li Quan et al., Phys. Rev. Lett., 2018]. It is found that both the pressure and v...

Optimizing sound transmission through 3D pentamode materials in water

Recent developments in transformation acoustics (TA) have taken advantage of the isotropic nature of conformal mappings to form gradient index lens devices, such as a two-dimensional monopole-to-quadropole lens. While this TA precisely maintains the wave equation solution within the lens the radiated field is still multi-directional and not fully efficient due to impedance mismatch and non-planar radiation. A three-fold strategy is outlined here to achieve highly directional and impedance matched devices. First, most of the rays leaving the original circular region are mapped to a single face of a polygon. Second, the center of the radiating face is impedance matched by simply scaling the size up or down. Finally, the polygon is replaced by a two-sided crescent moon mapping which optimizes the radiation across the face of higher curvature, allowing near-field focusing and quasi-planar far-field radiation. These ideas are illustrated by example simulations. Practical design methods, including water matrix ...

Deconvolution methods to obtain the impulse response of acoustic metamaterial samples of finite extent

Recent advances in acoustic metasurface design make it possible to manipulate sound waves in an almost arbitrary way. Here, we present several elastic metasurfaces comprised of an array of subwavelength plates for controlling SV-wave in solids. The underlying physics are the coupling between the SV-wave in the elastic body and the flexural wave in plates, and the coupling between the P-wave in the elastic body and the longitudinal wave in plates. By varying the thicknesses of the plates, a wide range of phase delay for flexural waves can be obtained, while keeping constant the phase delay for longitudinal waves. The anomalous refraction of SV-waves is achieved by selecting the thickness of each plate to engineer the phase change according to the generalized Snell’s law. This metasurface has another feature that it redirects SV-waves only, which enables it to be used to split SV- and P-wavefronts into different directions. In addition, this metasurface can be paired with a uniform metasurface to break spat...