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.
 W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1-2 (John Wiley & Sons, New York-Chichester- Brisbane-Toronto, 1970)Search in Google Scholar
 R.L. Graham, D.E. Knuth, O.Patashnik, Concrete Mathematics: A Foundation for Computer Science, Second Edition (Addison- Wesley Publishing Company, Inc., 1989)10.1063/1.4822863Search in Google Scholar
 M.O. Scully, M. Suhail Zubairy, Quantumoptics (Cambridge University Press, Cambridge, 2001)Search in Google Scholar
 R. Glauber, Lecture #17, In C. DeWitt (Ed.), Quantum Optics and Electronics (Gordon and Breach, Science Publishers, New York- London-Paris, 1965)Search in Google Scholar
© 2015 Aleksey Ilyin
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.