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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 9, 2014

Generalized binomial distribution in photon statistics

Aleksey Ilyin
From the journal Open Physics


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.


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Received: 2014-4-24
Accepted: 2014-8-22
Published Online: 2014-10-9
Published in Print: 2015-1-1

© 2015 Aleksey Ilyin

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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