  We investigate the single-photon transport in a single-mode optical fiber
coupled to an optomechanical system in the single-photon strong-coupling
regime. The single-photon transmission amplitude is analytically obtained with
a real-space approach and the effects of thermal noises are studied via
master-equation simulations. The results provide an explicit understanding of
optomechanical interaction and offer a useful guide for manipulating single
photons in optomechanical systems. Based on the theoretical framework, we
further propose a scheme to generate the mechanical NOON states with arbitrary
phonon numbers by measuring the sideband photons. The probability for
generating the NOON state with five phonons is over 0.15.
