Time-periodic Klein tunneling through optomechanical Dirac barriers

We study the interconversion between photons and phonons coupled via radiation pressure in artificial Dirac materials realized by a honeycomb array of optomechanical cells. In particular we analyze the chiral tunneling of (photon-phonon) polaritons through an oscillating planar barrier. While a static barrier accommodates constructively interfering optical or mechanical waves leading to photon or phonon transmission, an oscillating barrier allows for inelastic scattering that causes sideband excitations and interference effects which, in turn, may suppress or revive the light-sound interconversion.