Transformation Media in Acoustics with Constant Bulk Modulus or Constant Density Tensor

This work is to present a formulation of cloaking or concentrating device in acoustics in which the transformed material could be either having uniform bulk modulus or having homogeneous density tensor. The transformed material parameters, depending on the mapping of physical and virtual coordinates, are often position-varying and anisotropic. This often adds substantial complexity in practical implementation. Here we present a theoretical algorithm that allows us to design a transformation field that could have either uniform bulk modulus or constant density tensor. For cloaking devices with constant bulk modulus, analytical and numerical results are presented for circular as well as for non-circular cloaking devices. Specifically, elliptical and twin-cloak devices are exemplified. To achieve the effect of constant density tensor, we consider only circular geometry. Devices with cloaking or concentrating effects can be exactly formulated. We note, however, that it seems unlikely at this moment to have a transformation device that has constant bulk modulus and constant density tensor at the same time. Nevertheless, we remark the present results are of still sufficient merit in that the uniform material parameters, in either set of material parameters, indeed greatly simplify the practice in real implementations.