Dirac cones at k→= in acoustic crystals and zero refractive index acoustic materials

Abstract

We show that two-dimensional acoustic crystals (ACs) can be designed to exhibit Dirac cone dispersion at $\overrightarrow{k}=0$ . Effective medium theory finds that some of these ACs can have effectively zero reciprocal of bulk modulus 1/${\kappa }_{\mathit{eff}}$ and zero mass density ${\rho }_{\mathit{eff}}$ , and thus zero refractive indices at the Dirac point. Numerical simulations are used to demonstrate various phenomena associated with the zero spatial phase change inside such materials.