Reciprocity, passivity, and causality in fully coupled acousto-electrodynamic media

Abstract

Multiple-scattering homogenization procedures in acoustics and electromagnetics have shown that subwavelength asymmetries and lattice effects in metamaterials give rise to bianisotropy, the tensorial coupling of two constitutive relations. Asymmetric piezoelectric scatters in the quasi-electrostatic regime have recently been shown to couple the electric field to the bianisotropic elastodynamic relations, yielding an additional, emergent property termed electro-momentum coupling. To facilitate the study of scatterers responsible for electro-momentum coupling, Wallen et al. [Proc. Mtgs. Acoust. 46, 065002 (2022)] and Lee et al. [J. Appl. Phys. 132, 125108 (2022)] abandoned the quasi-electrostatic approximation in favor of a simultaneously acoustic and electrodynamic scatterer. We previously used a multiple-scattering homogenization procedure to show that a collection of such scatterers gives rise to constitutive relations that fully couple acoustics and electrodynamics. Now, we derive bounds on these fully coupled relations due to reciprocity, passivity, and causality. These results recover known bianisotropic and piezoelectric bounds and reveal that the imaginary parts of the additional electro-momentum and magneto-momentum coupling coefficients vanish in lossless, reciprocal, and passive media. The bounds also verify that the constitutive relations derived by our homogenization procedure satisfy reciprocity, passivity, and causality. [Work supported by DARPA and ARL:UT McKinney Fellowship in Acoustics.]