  Recent progress in optomechanical systems may soon allow the realization of
optomechanical arrays, i.e. periodic arrangements of interacting optical and
vibrational modes. We show that photons and phonons on a honeycomb lattice will
produce an optically tunable Dirac-type band structure. Transport in such a
system can exhibit transmission through an optically created barrier, similar
to Klein tunneling, but with interconversion between light and sound. In
addition, edge states at the sample boundaries are dispersive and enable
controlled propagation of photon-phonon polaritons.
