Abstract
We propose one-dimensional hierarchical metamaterials (HMMs) that have simultaneously negative mass density and Young’s modulus in the sense of effective properties. Frequency-dependent effective properties of the HMMs are evaluated by using a dynamic homogenization theory. By considering three necessary conditions for dynamic homogenizability, we verify that our proposed HMMs can have physically meaningful double negativity, whereas the conventional periodic structures cannot. In addition, HMMs yield the broader ranges of the frequency and the effective properties for double negativity due to the large number of geometrical parameters. By exploring all the possible effective properties of HMMs, we discuss whether we can design metamaterials with the opposite sign of material properties in nature, ultimately aiming at perfect impedance matching.
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