Acoustic cloaking theory

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.