Analysis of equivalent anisotropy arising from dual isotropic layers of acoustic media

The equivalence between a single mass-anisotropic layer and two isotropic layers is analyzed by studying two systems: one consists of an anisotropic layer sandwiched between two arbitrarily chosen isotropic media; and the other consists of two isotropic layers, of a total thickness equal to that of the anisotropic layer, sandwiched between the same pair of isotropic media. The equivalence is established by matching the transmission and reflection coefficients of the two systems for an arbitrarily chosen incident angle. The first-order equivalence leads to exactly the same set of relations as often quoted in the literature. However, it was concluded that a full second-order equivalence is not possible unless the incident is normal to the surface, or the materials are isotropic. One of the requirements for the second-order equivalence is that the two isotropic layers must have their impedances matched. Together with the first order equivalence requirements, this gives a complete set of conditions for determining all the materials properties of the two isotropic layers. On the other hand, the unattainable full second-order equivalence can be alleviated by a proper placement of layers: by placing the heavier layer adjacent to the medium of greater acoustic impedance. Numerical examples show that this remedy in fact is more important than following the partial requirement for the second order equivalence when the equivalent isotropic layers are used in acoustic cloaking applications.