Retrieval method for the bianisotropic polarizability tensor of Willis acoustic scatterers

TL;DR

This paper introduces a new method to accurately determine the polarizability tensor of Willis acoustic scatterers using limited scattering data, facilitating better understanding and design of these complex materials.

Contribution

It presents an explicit retrieval method for the polarizability tensor of Willis acoustic scatterers based on scattering amplitudes and matrix formalisms, which was not previously available.

Findings

The method successfully retrieves tensor components from simulated scattering data.

Numerical examples validate the effectiveness of the retrieval approach.

Applicable to both one- and two-dimensional configurations.

Abstract

Acoustic materials displaying coupling between pressure and momentum are known as Willis materials. The simplest Willis materials are comprised of sub-wavelength scatterers that couple monopoles to dipoles and {\it vice versa}, with the interaction defined by a polarizability tensor. We propose a method for retrieving the polarizability tensor for sub-wavelength Willis acoustic scatterers using a finite set of scattering amplitudes. We relate the polarizability tensor to standard T-matrix and S-matrix scattering formalisms. This leads to an explicit method for retrieving the components of the polarizability tensor in terms of a small set of scattered pressure data in the near- or far-field. Numerical examples demonstrate the retrieval method for one and two dimensional configurations.