Acoustic crystals with Dirac-like cone dispersion mapped to effective zero-index acoustic materials

Different two-dimensional (2D) acoustic crystals are investigated and the conditions under which these acoustic crystals can be mapped to effective zero-index materials are discussed. Acoustic crystals with Dirac-like points can only be mapped to effective zero-index materials when all three of the following conditions are met simultaneously: (i) the Dirac-like point is formed by monopole and dipole moments, (ii) the Dirac-like point is at a low enough frequency, and (iii) in the extended states above the Dirac-like point frequency, there is only one propagating band. The difference between the optical and acoustic regime is the change in the refractive index near the Dirac point frequency.