Polarizability of electro-momentum coupled scatterers

Abstract

The macroscopic response of acoustic metamaterials with sub-wavelength asymmetry is described with coupled constitutive relations for the acoustic pressure and momentum density. This coupling leads to momentum that is dependent on the strain rate and pressure that depends on the local acceleration. The coupled constitutive form has become known as the Willis form because they were first predicted by John Willis [Wave Motion, 3(1), 1–11 (1981)]. The subwavelength behavior of the Willis material building-blocks can be described by a polarizability matrix relating the monopole and dipole scattering moments to the local pressure and velocities fields when off-diagonal terms are non-zero [Phys. Rev. B. 96(10), 104303 (2017)], providing a metric for the design of microscale structures leading to macroscopically observable Willis coupling. More recently, Pernas-Solomon and Shmuel showed that heterogeneous piezoelectric media with subwavelength asymmetry can lead to coupling between pressure, momentum density, and electric displacement fields, a material response known as electro-momentum coupling [J. Mech. Phys. Solids, 34, 103770 (2020)]. This work will present a polarizability description of electro-momentum coupled scatterers and the means to calculate the polarizabilities that couple local pressure, velocity, and electric fields with the aim of creating metamaterials for acoustic sensing. [Work supported by DARPA.]