GENERALIZED BINOMIAL DISTRIBUTION IN PHOTON STATISTICS
Aleksey Ilyin · 2016
Photon-number distribution among two parts of a given vol-ume is found in case of an arbitrary photon statistics. This problem is related to the interaction of light beam with a macroscopic device, for example a diaphragm, that sepa-rates the photon flux into two parts with known probabili-ties. To solve this problem, a Generalized Binomial Distribu-tion (GBD) is derived that is applicable to an arbitrary pho-ton statistics satisfying probability convolution equations. It is shown that if photons obey the Poisson statistics then the GBD is reduced to the ordinary binomial distribution whereas in case of Bose-Einstein statistics the GBD is reduced to the Polya distribution. In this case, the photon spatial distribution depends on the phase-space volume occupied by the photons. This result involves a photon bunching effect, or such collective behavior of photons that sharply differs from the behavior of classical particles. It is shown that the photon bunching effect looks similar to the quantum interference effect.