  Photon statistics in a weakly driven optomechanical photonic crystal cavity,
with Kerr-type nonlinearity, is analyzed both analytically and numerically.
Single-photon blockade effect is demonstrated via calculations of the
zero-time-delay second-order correlation function $g^{(2)}(0)$. The analytical
results obtained by solving the Schr\"{o}dinger equation are in complete
conformity with the results obtained through numerical solution of the quantum
master equation. The experimental feasibility with state-of-the-art device
parameters is discussed. It is observed that photon blockade could be generated
at the telecommunication wavelength, even at lower values of the nonlinear
susceptibility parameters and in the weak single-photon optomechanical coupling
regime.The system is found to be robust against pure dephasing-induced
decoherences.
