Physical constraints on lossy acoustic metamaterials with complex effective properties

Abstract

Recent theoretical and experimental work on acoustic metamaterials (AMM) has demonstrated materials that demonstrate many properties, such as negative modulus and density, beyond what is capable using conventional materials. In most cases, AMM are assumed to be passive and causal with frequency dependent losses accounted for via complex modulus and density. Despite the maturity of AMM research, literature concerning the physical constraints on the complex effective constitutive properties for passive, causal AMM is very limited. This work presents the physical limits for the real and imaginary effective dynamic mass density and dynamic compressibility via recourse to restrictions placed on the AMM by conservation of energy, passivity, and causality. We further note that constitutive properties are determined from the effective wavenumber and impedance extracted from simulation or experiment. Although care is normally taken to guarantee that passivity holds for the wavenumber and impedance, assumptions implicit in various homogenization schemes can result in constitutive properties that do not satisfy passivity and causality. This work will therefore also discuss implications on AMM homogenization and extraction of properties due to constraints based on the foundational concepts of conservation of energy, passivity, and causality. [This work was supported by the Office of Naval Research.]