Transformation acoustics with bulk media composed of polarized sources

Active acoustic metamaterials consisting of paired sensor-driver unit cells offer a promising path towards the practical realization of exciting transformation acoustics devices. The design of these cells is founded in a microscopic acoustic model that describes materials as collections of subwavelength polarized sources which respond to the local conditions of pressure and particle velocity. The current ability to express the polarizabilities that characterize these sources in terms of the effective macroscopic acoustic properties is limited to only a few simple cases and is not applicable to inhomogeneous bulk media of arbitrary geometries. Here, we address this challenge and derive general closed-form expressions relating the bulk modulus to the monopole polarizability and the mass density tensor to the dipole polarizability. Furthermore, we use these expressions to adapt transformation acoustics to the microscopic model. We demonstrate the accuracy of our approach by comparing the fields scattered by several devices, including cylindrical cloaks with steep property gradients and anisotropy, with the fields scattered by the devices' realizations with polarized sources.