Photon number distributions of output fields from a beam splitter

We examined the photon statistics of the output light field of a lossless symmetric beam splitter when a n-photon occupation number state and an arbitrary light field are present on the two input ports of the beam splitter. We showed that both the wave-like nature and the particle-like nature of light are contributed to the photon number distribution by investigation of the difference photon number probability at the output port.