Extreme acoustic metamaterial by coiling up space

We show that by coiling up space using curled perforations, a two-dimensional acoustic metamaterial can be constructed to give a frequency dispersive spectrum of extreme constitutive parameters, including double negativity, a density near zero, and a large refractive index. Such an approach has band foldings at the effective medium regime without using local resonating subwavelength structures, while the principle can be easily generalized to three dimensions. Negative refraction with a double negative prism and tunneling with a density-near-zero metamaterial are numerically demonstrated.