Hierarchical metamaterial with simultaneously negative mass density and Young's modulus

Abstract

In this study, we propose one-dimensional hierarchical metamaterials (HMMs) that have simultaneously negative mass density and Young’s modulus from the perspective of effective medium. Frequency-dependent effective properties of HMMs are derived by using a dynamic homogenization theory and the double negative properties are obtained at the second optical branch. Since the frequency range of the double negativity for hierarchical structures is significantly lower than the one for periodic structures without structural hierarchy, it satisfies three necessary conditions such that dynamic homogenization is physically sound. By exploring all the possible double negativities of HMMs, we check whether we can design metamaterials with opposite sign of mechanical properties in nature, ultimately aiming at the perfect transmission of wave energy.