Dirac cones with zero refractive indices in phoxonic crystals.

In this paper, simultaneous zero refractive indices (ZRIs) for both sound and light are realized on the basis of a 2D triangular lattice phoxonic crystal (PxC) with C symmetry. For the phononic mode, accidental phononic Dirac degeneracy at the center of Brillouin zone (BZ) occurs at a relatively high frequency which leads to the failure of the efficient medium theory; hence, it is no longer applicable to the realization of acoustic ZRI. We thus turn to a low-frequency phononic Dirac cone located at K point, the corner of the BZ, which shows in-phase pressure field oscillations in expanded unit cells. Using zone folding, we further reveal the cause for the characteristic of acoustic ZRI. For the photonic mode, a low-frequency photonic Dirac-like cone can be achieved by adjusting the geometric parameter due to the high contrast permittivity between scatterers and the matrix. When the phononic and photonic low-frequency Dirac dispersions coexist, the PxC can be mapped into a zero-index material for both sound and light at the same time. The new mechanism for simultaneously controlling sound and light helps to achieve acousto-optic synchronous cloaking and unidirectional transmission, which are numerically demonstrated.