  We present a two-dimensional array of nearest-neighbor coupled waveguides
that is the optical analog of a quantum optomechanical system. We show that the
quantum model predicts the appearance of effective column isolation,
diagonal-coupling and other non-trivial couplings in the two-dimensional
photonic lattice under a standard approximation from ion-trap cavity
electrodynamics. We provide an approximate impulse function for the case of
effective column isolation and compare it with exact numerical propagation in
the photonic lattice.
