Daniel Torrent

Acoustic cloaking in two dimensions: a feasible approach

This work proposes an acoustic structure feasible to engineer that accomplishes the requirements of acoustic cloaking design recently introduced by Cummer and Schurig (2007 New J. Phys. 9 45). The structure, which consists of a multilayered composite made of two types of isotropic acoustic metamaterials, exactly matches the conditions for the acoustic cloaking. It is also shown that the isotropic metamaterials needed can be made of sonic crystals containing two types of material cylinders, whose elastic parameters should be properly chosen in order to satisfy (in the homogenization limit) the acoustic properties under request. In contrast to electromagnetic cloaking, the structure here proposed verifies the acoustic cloaking in a wide range of wavelengths; its performance is guaranteed for any wavelength above a certain cutoff defined by the homogenization limit of the sonic crystal employed in its fabrication.

Acoustic metamaterials for new two-dimensional sonic devices

It has been shown that two-dimensional arrays of rigid or fluidlike cylinders in a fluid or a gas define, in the limit of large wavelengths, a class of acoustic metamaterials whose effective parameters (sound velocity and density) can be tailored up to a certain limit. This work goes a step further by considering arrays of solid cylinders in which the elastic properties of cylinders are taken into account. We have also treated mixtures of two different elastic cylinders. It is shown that both effects broaden the range of acoustic parameters available for designing metamaterials. For example, it is predicted that metamaterials with perfect matching of impedance with air are now possible by using aerogel and rigid cylinders equally distributed in a square lattice. As a potential application of the proposed metamaterial, we present a gradient index lens for airborne sound (i.e. a sonic Wood lens) whose functionality is demonstrated by multiple scattering simulations.

Anisotropic mass density by two-dimensional acoustic metamaterials

We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.

Sound focusing by gradient index sonic lenses

Gradient index sonic lenses based on two-dimensional sonic crystals are here designed, fabricated, and characterized. The index-gradient is achieved in these type of flat lenses by a gradual modification of the sonic crystal filling fraction along the direction perpendicular to the lens axis. The focusing performance is well described by an analytical model based on ray theory as well as by numerical simulations based on the multiple-scattering theory.

Omnidirectional broadband acoustic absorber based on metamaterials

We present the design, construction, and experimental characterization of the acoustic analogue of the so called photonic black-hole. The fabricated sample has cylindrical symmetry and consists of two parts, a shell that bends the sound towards the center and a core that dissipates its energy. The shell is made of a metamaterial that perfectly matches the acoustic impedance of air and behaves like a gradient index lens. The experimental data obtained in a multi-modal impedance chamber demonstrate that the proposed acoustic black-hole acts like an onmidirectional broadband absorber with strong absorbing efficiency.

Sonic gradient index lens for aqueous applications

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.

Noise control by sonic crystal barriers made of recycled materials

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is reported here. The barriers consist of only three rows of perforated metal shells filled with rubber crumb. Measurements of reflectance and transmittance by these barriers are reported. Their attenuation properties result from a combination of sound absorption by the rubber crumb and reflection by the periodic distribution of scatterers. It is concluded that the porous cylinders can be used as building blocks whose physical parameters can be optimized in order to design efficient barriers adapted to different noisy environments.

Acoustic resonances in two-dimensional radial sonic crystal shells

Radial sonic crystals (RSC) are fluidlike structures infinitely periodic along the radial direction that verify the Bloch theorem and are possible only if certain specially designed acoustic metamaterials with mass density anisotropy can be engineered (see Torrent and S?nchez-Dehesa 2009 Phys. Rev. Lett.?103 064301). A comprehensive analysis of two-dimensional (2D) RSC shells is reported here. A given shell is in fact a circular slab with a central cavity. These finite crystal structures contain Fabry?Perot-like resonances and modes strongly localized at the central cavity. Semi-analytical expressions are developed to obtain the quality factors of the different resonances, their symmetry features and their excitation properties. The results reported here are completely general and can be extended to equivalent 3D spherical shells and to their photonic counterparts.

Gradient index lenses for flexural waves based on thickness variations

This work presents a method for the realization of gradient index devices for flexural waves in thin plates. Unlike recent approaches based on phononic crystals, the present approach is based on the thickness-dependence of the dispersion relation of flexural waves, which is used to create gradient index devices by means of local variations of the plates thickness. Numerical simulations of known circularly symmetrical gradient index lenses have been performed. These simulations have been done using the multilayer multiple scattering method and the results prove their broadband efficiency and omnidirectional properties. Finally, finite element simulations employing the full three-dimensional elasticity equations also support the validity of the designed approach.

Multiple scattering formulation of two-dimensional acoustic and electromagnetic metamaterials

A multiple scattering formulation of two-dimensional (2D) acoustic metamaterials is presented. This approach is comprehensive and can lead to frequency-dependent effective parameters (scalar bulk modulus and tensorial mass density), as it is possible to have not only positive or negative ellipsoidal refractive index, but also positive or negative hyperbolic refractive index. The correction due to multiple scattering interactions is included in the theory and it is demonstrated that its contribution is important only for lattices with high filling fractions. Since the surface fields on the scatterers are mainly responsible for the anomalous behavior of the resulting effective medium, complex scatterers can be used to engineer the frequency response. Anisotropic effects are also discussed within this formulation and some numerical examples are reported. A homogenization theory is also extended to electromagnetic wave propagation in 2D lattices of dielectric structures, where Mie resonances are found to be responsible for the metamaterial behavior.