Acoustic cloaking transformations from attainable material properties

We propose a general methodology and a set of practical recipes for the construction of ultra-broadband acoustic cloaks -structures that can render themselves and a concealed object undetectable by means of acoustic scattering. The acoustic cloaks presented here are designed and function analogously to electromagnetic cloaks. However, acoustic cloaks in a fluid medium do not suffer the bandwidth limitations imposed on their electromagnetic counterparts by the finite speed of light in vacuum. In the absence of specific metamaterials having arbitrary combinations of quasi-static speed of sound and mass density, we explore the flexibility of continuum transformations that produce approximate cloaking solutions. We show that an imperfect, eikonal acoustic cloak (that is, one which is not impedance matched but is valid in the geometrical optics regime) with negligible dispersion can be designed using a simple layered geometry. Since a practical cloaking device will probably be composed of combinations of solid materials rather than fluids, it is necessary to consider the full elastic properties of such media, which support shear waves in addition to the compression waves associated with the acoustic regime. We perform a systematic theoretical and numerical investigation of the role of shear waves in elastic cloaking devices. We find that for elastic metamaterials with Poisson's ratio nu > 0.49, shear waves do not alter the cloaking effect. Such metamaterials can be built from nearly incompressible rubbers (with nu approximate to 0.499) and fluids. We expect this finding to have applications in other acoustic devices based on the form-invariance of the scalar acoustic wave equation.