David C. Calvo

Highly anisotropic elements for acoustic pentamode applications.

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 3 orders of magnitude, and that it can be realistically tailored for transformation acoustic applications.

Demonstration at sea of the decomposition-of-the-time-reversal-operator techniquea)

This paper presents a derivation of the time reversal operator decomposition (DORT) using the sonar equation. DORT is inherently a frequency-domain technique, but the derivation is shown in the time-frequency domain to preserve range resolution. The magnitude of the singular values is related to sonar equation parameters. The time spreading of the time-domain back-propagation image is also related to the sonar equation. Noise-free, noise-only, and signal-plus-noise data are considered theoretically. Contamination of the echo singular component by noise is shown quantitatively to be very small at a signal-to-noise ratio of 0dB. Results are shown from the TREX-04 experiment during April 22 to May 4, 2004 in 94m deep, shallow water southwest of the Hudson Canyon. Rapid transmission of short, 500Hz wide linear frequency modulated beams with center frequencies of 750, 1250, 1750, 2250, 2750, and 3250Hz are used. Degradation caused by a lack of time invariance is found to be small at 750Hz and nearly complete a...

Thin Fresnel zone plate lenses for focusing underwater sound

A Fresnel zone plate (FZP) lens of the Soret type creates a focus by constructive interference of waves diffracted through open annular zones in an opaque screen. For underwater sound below MHz frequencies, a large FZP that blocks sound using high-impedance, dense materials would have practical disadvantages. We experimentally and numerically investigate an alternative approach of creating a FZP with thin (0.4λ) acoustically opaque zones made of soft silicone rubber foam attached to a thin (0.1λ) transparent rubber substrate. An ultra-thin (0.0068λ) FZP that achieves higher gain is also proposed and simulated which uses low-volume fraction, bubble-like resonant air ring cavities to construct opaque zones. Laboratory measurements at 200 kHz indicate that the rubber foam can be accurately modeled as a lossy fluid with an acoustic impedance approximately 1/10 that of water. Measured focal gains up to 20 dB agree with theoretical predictions for normal and oblique incidence. The measured focal radius of 0.68λ (peak-to-null) agrees with the Rayleigh diffraction limit prediction of 0.61 λ/NA (NA = 0.88) for a low-aberration lens.

Underwater acoustic omnidirectional absorber

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 shells 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.

Experimental realization of a variable index transmission line metamaterial as an acoustic leaky-wave antenna

Development and experimental realization of an acoustic leaky wave antenna are presented. The antenna uses a one-dimensional composite right/left hand transmission line approach to tune radiation angle continually from backfire-to-endfire, including broadside, as a function of input frequency. An array of acoustically loaded membranes and open channels form a structure with negative, zero, or positive refractive index, depending on excitation frequency. The fast-wave radiation band of the antenna is determined using acoustic circuit analysis. Based on the designs specified by circuit and finite element analysis, an acoustic leaky wave antenna was fabricated, and the radiation direction measured at discrete frequencies.

Enhanced sound transmission from water to air at low frequencies.

Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the sources acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.

Experimental Demonstration of Underwater Acoustic Scattering Cancellation.

We explore an acoustic scattering cancellation shell for buoyant hollow cylinders submersed in a water background. A thin, low-shear, elastic coating is used to cancel the monopole scattering from an air-filled, neutrally buoyant steel shell for all frequencies where the wavelength is larger than the object diameter. By design, the uncoated shell also has an effective density close to the aqueous background, independently canceling its dipole scattering. Due to the significantly reduced monopole and dipole scattering, the compliant coating results in a hollow cylindrical inclusion that is simultaneously impedance and sound speed matched to the water background. We demonstrate the proposed cancellation method with a specific case, using an array of hollow steel cylinders coated with thin silicone rubber shells. These experimental results are matched to finite element modeling predictions, confirming the scattering reduction. Additional calculations explore the optimization of the silicone coating properties. Using this approach, it is found that scattering cross-sections can be reduced by 20 dB for all wavelengths up to k0a = 0.85.

A higher-order on-surface radiation condition derived from an analytic representation of a Dirichlet-to-Neumann map

On-surface radiation conditions are useful for obtaining approximate solutions to scattering problems involving compact obstacles. An analytic representation of the Dirichlet-to-Neumann map for a circle is derived and used to construct a higher-order on-surface radiation condition for a generally convex perfectly conducting body in two dimensions. This approach is based on a Hankel function in which a tangential operator appears in the index. In the high-frequency limit, this analytic representation approaches the square root of a differential operator which commonly arises in the application of parabolic equation techniques to propagation problems. Treating the scattered field propagation angle relative to the surface normal and the surface curvature as independent parameters, the representation is fit to a rational function to provide an accurate and efficient on-surface radiation condition that is tested for various examples.

Designing acoustic transformation devices using fluid homogenization of an elastic substructure

The design of devices using finite embedded coordinate transformations presents an unique approach to control acoustic waves. Though combining the use of conformal mappings may provide a pathway to more realizable material properties, many device geometries still require combinations of density and sound speed which are unavailable in isotropic materials. Here, we present a design strategy based on a multiple scattering homogenization method to approximate the unique values required within such a device. We apply the method, using full-wave simulations, to the design of an aqueous cylindrical-to-plane wave lens, which can be constructed from simple materials.

Acoustical scattering by arrays of cylinders in waveguides

Multiple scattering of acoustic waves in a planar horizontal waveguide by finite-length cylinders is considered. Cylinder height equals the waveguide depth, and both are vertically constrained by the pressure-release boundaries. An analytically exact solution is obtained via normal mode expansion method in conjunction with the concept of the T matrix. The problem is decomposed into an infinite number of two-dimensional multiple scattering problems, modulated by waveguide mode shapes. Examples are presented for an isovelocity waveguide in which the medium is uniform and the waveguide depth is constant. It is found that, in numerical computations, including one or two evanescent modes captures the essence of the evanescent modes. Multiple scattering in the waveguide is compared with the corresponding two-dimensional case. It is concluded that, in low frequencies, the wave patterns in the two cases are very similar, with a shift in the frequency. The similarity diminishes when there are multiple propagating modes. Despite the mode mixing, some key features in the scattering as observed in the two-dimensional problem remain observable in the waveguide case.