Computational analysis of sub-wavelength scatterers exhibiting electro-momentum coupling

The macroscopic response of acoustic metamaterials with sub-wavelength asymmetry may be described by the so-called Willis constitutive relations, which include coupling between the acoustic pressure and momentum density. One method to describe the behavior of acoustically-small, Willis material building-blocks is via a polarizability matrix relating the monopole and dipole scattering moments to the local pressure and velocity fields, providing a metric for the design of microscale structures leading to macroscopically observable Willis coupling. Additionally, heterogeneous, piezoelectric media with sub-wavelength asymmetry have been shown to exhibit coupling between momentum density and electric fields, a material response known as electro-momentum coupling. Recent studies have generalized the polarizability concept to include coupling between acoustic and electromagnetic fields for theoretical point scatterers in two and three dimensions, and derived analytical bounds based on conservation of energy. In this work, we computationally study the coupled, acousto-electromagnetic polarizability of heterogeneous, piezoelectric scatterers and assess the practicability of achieving electro-momentum coupling in physically realizable geometries. Numerical results are obtained using a custom finite element approach, which includes the fully electrodynamic nature of the system and accounts for large differences in the characteristic wavelengths of the acoustic and electromagnetic fields. [This work was supported by DARPA.]