Negative refraction realized by band folding effect in resonator-based acoustic metamaterials

We show in the paper that a two-dimensional acoustic metamaterial with isotropic negative refraction band at subwavelength scale can be constructed simply by arranging only one kind of Helmholtz resonators into honeycomb-like lattice. To understand the phenomenon, the mechanism for double negative metamaterial is investigated. We point out that double negative metamaterials can be obtained only when the phase accumulating over their constructive unit cell becomes greater than π but smaller than 2π. Based on the understanding, we attribute the negative refraction phenomenon in our suggested structure as a result of the band folding effect.