  Analyzing the scattering and conversion process between photons and phonons
coupled via radiation pressure in a circular quantum dot on a honeycomb array
of optomechanical cells, we demonstrate the emergence of optomechanical Dirac
physics. Specifically we prove the formation of polaritonic quasi-bound states
inside the dot, and angle-dependent Klein tunneling of light and emission of
sound, depending on the energy of the incident photon, the photon-phonon
interaction strength, and the radius of the dot. We furthermore demonstrate
that forward scattering of light or sound can almost switched off by an
optically tuned Fano resonance; thereby the system may act as an optomechanical
translator in a future photon-phonon based circuitry.
