Acoustic cloaking theory

Abstract

An acoustic cloak envelopes an object so that sound incident from all directions passes through and around the cloak as though the object were not present. A theory of acoustic cloaking is developed using the transformation or change-of-variables method for mapping the cloaked region to a point with vanishing scattering strength. We show that the acoustical parameters in the cloak must be anisotropic: either the mass density or the mechanical stiffness or both. If the stiffness is isotropic, corresponding to a fluid with a single bulk modulus, then the inertial density must be infinite at the inner surface of the cloak. This requires an infinitely massive cloak. We show that perfect cloaking can be achieved with finite mass through the use of anisotropic stiffness. The generic class of anisotropic material required is known as a pentamode material. If the transformation deformation gradient is symmetric then the pentamode material parameters are explicit, otherwise its properties depend on a stress like tensor which satisfies a static equilibrium equation. For a given transformation mapping the material composition of the cloak is not uniquely defined, but the phase and wave speeds of the pseudo-acoustic waves in the cloak are unique. Examples are given from 2D and 3D.

20 pages, 3 figures

References in corpus (2)

• Confirmation of Cylindrical Perfect Invisibility Cloak Using Fourier-Bessel Analysis
• Full-wave invisibility of active devices at all frequencies

Cited by in corpus (16)

• Achieving control of in-plane elastic waves
• Acoustic metafluids
• Employing pre-stress to generate finite cloaks for antiplane elastic waves
• Special transformations for pentamode acoustic cloaking
• Isotropic transformation optics: approximate acoustic and quantum cloaking
• Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
• Mechanics of elastic networks
• Nonlinear pre-stress for cloaking from antiplane elastic waves
• On the Limit and Applicability of Dynamic Homogenization
• Transformation cloaking and radial approximations for flexural waves in elastic plates
• Nonsingular two dimensional cloak of arbitrary shape
• Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets
• Acoustic metafluids made from three acoustic fluids
• Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves
• Determining the full transformation relations in the transformation method
• Analytic Materials