Generalized binomial distribution in photon statistics

TL;DR

This paper introduces a Generalized Binomial Distribution (GBD) for photon statistics, applicable to arbitrary photon distributions, revealing how photon bunching and quantum effects influence photon spatial distribution.

Contribution

The paper derives a GBD applicable to any photon statistics satisfying convolution equations, unifying classical and quantum photon distribution behaviors.

Findings

GBD reduces to binomial for Poisson statistics

GBD reduces to Polya distribution for Bose-Einstein statistics

Photon bunching resembles quantum interference effects

Abstract

The photon-number distribution between two parts of a given volume is found for an arbitrary photon statistics. This problem is related to the interaction of a light beam with a macroscopic device, for example a diaphragm, that separates the photon flux into two parts with known probabilities. To solve this problem, a Generalized Binomial Distribution (GBD) is derived that is applicable to an arbitrary photon statistics satisfying probability convolution equations. It is shown that if photons obey Poisson statistics then the GBD is reduced to the ordinary binomial distribution, whereas in the 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 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.