Three-dimensional fractal structure with double negative and density-near-zero properties on a subwavelength scale

We constructed a three-dimensional fractal acoustic metamaterial using the combination of zigzag channels and Menger fractal structures that had high structural symmetry and could extend into 3D space easily. Reflection and transmission coefficients were numerically calculated and experimentally measured, and the results matched well with each other. Using the finite element method and the S-parameter retrieval method, the band structures, the equivalent frequency surface and the effective parameters of the acoustic metamaterial were calculated. The results showed that the 3D acoustic metamaterial had double negative property in the normalized frequency range of 0.205–0.269 and density-near-zero property in the normalized frequency vicinity of 0.356. A plate lens model and a quarter-bending model were constructed to demonstrate the double negative property and the density-near-zero property of the acoustic metamaterial, respectively. These results showed that the 3D acoustic metamaterial could achieve excellent acoustic properties and would be promising to construct the 3D double negative structure and control acoustic waves on a subwavelength scale within a single unit.