Some personal reflections on acoustic metamaterials

Abstract

This article is concerned with waves in n-component composites with random microgeometry. Such composites have been contemplated for decades but more recently have acquired prominence through the development of the so-called metamaterials. The account is a personal one and traces the development of variational formulations and the recognition of unconventional couplings in effective constitutive relations. It then addresses the inadequacy of treatments which consider only mean waves, beyond the “homogenization” or long-wavelength limit. The variational formulation can be employed to find approximations to the solution in all realizations, as well as for the mean waves. This has been illustrated by solving explicitly a problem of transmission and reflection at the interface between a composite and a homogeneous material. The solution has been published already, for the mean waves. A new development is the deduction of mean energy fluxes, which conform to conservation of energy. A striking phenomenon, beyond the reach of homogenization theory, is that a substantial fraction of the incident energy is reflected incoherently as frequency tends to zero, even when the homogeneous half-space and composite are acoustically matched.