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Open Physics

formerly Central European Journal of Physics

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Volume 13, Issue 1 (Jan 2015)


Generalized binomial distribution in photon statistics

Aleksey Ilyin
  • Corresponding author
  • Moscow Institute for Physics and Technology, Dolgoprudny, Russia
  • Email:
Published Online: 2014-10-09 | DOI: https://doi.org/10.1515/phys-2015-0005


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.

Keywords : Bose-Einstein statistics; Polya distribution; photon bunching; quantum interference

PACS : 42.50.-p; 02.50.-r; 42.50.Fx; 42.50.Ar; 05.30.-d


  • [1] R. Hanbury Brown, R.Q. Twiss, Nature 177, 27 (1956)

  • [2] C.K. Hong, Z.Y. Ou, L. Mandel, Phys. Rev. Lett. 59, 2045 (1987)

  • [3] G. Di Giuseppe et al., Phys. Rev. A 68, 063817 (2003)

  • [4] S.D. Chatterji, Amer. Math. Monthly 70, 958 (1963) [Crossref]

  • [5] W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1-2 (John Wiley & Sons, New York-Chichester- Brisbane-Toronto, 1970)

  • [6] L.Mandel, E.Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995)

  • [7] L. Mandel, Proc. Phys. Soc. (London) 74, 233 (1959) [Crossref]

  • [8] R.L. Graham, D.E. Knuth, O.Patashnik, Concrete Mathematics: A Foundation for Computer Science, Second Edition (Addison- Wesley Publishing Company, Inc., 1989)

  • [9] M.O. Scully, M. Suhail Zubairy, Quantumoptics (Cambridge University Press, Cambridge, 2001)

  • [10] R. Glauber, Lecture #17, In C. DeWitt (Ed.), Quantum Optics and Electronics (Gordon and Breach, Science Publishers, New York- London-Paris, 1965)

  • [11] J. Sperling, W. Vogel, G.S. Agarwal, Phys. Rev. A 85, 023820 (2012) [Crossref]

  • [12] J. Sperling,W. Vogel, G.S. Agarwal, Phys. Rev. Lett. 109, 093601 (2012) [Crossref]

  • [13] T.J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, I.A.Walmsley, Phys. Rev. Lett. 110, 173602 (2013) [Crossref]

About the article

Received: 2014-04-24

Accepted: 2014-08-22

Published Online: 2014-10-09

Published in Print: 2015-01-01

Citation Information: Open Physics, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2015-0005. Export Citation

© 2015 Aleksey Ilyin. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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