Photon Statistics and Coherence in Light Beams

Abstract

It was the thesis of Toynbee that great religions arise by the encounter of two great civilizations. The Graeco-Roman civilization meeting the Syrian civilization is supposed to have produced Christianity. Be that as it may, we know for certain that meeting of two disciplines of thought or even two subdisciplines in the same categories produce fascinating results. One such very fruitful encounter is the application of stochastic theory of point processes to the theory of interference in light beams. A new element was injected into this field, by the wellknown Brown and Twiss experiment¹ which opened up a new chapter on “photon statistics and coherence” in optics. A semiclassical study of these coherence properties and the statistics of the ejected electrons has been carried out by Glauber, Sudarshan, and others² using P- representations or quasi-probability distributions. These are density matrix descriptions obtained by a knowledge of the coherent state formulation of the photon fields. Mandel³ adopted a simpler procedure of obtaining the first few moments of the number of photoelectrons ejected in time internal [0, T], by taking the correlations in intensity of the photon beam at different times. They all found that the first few moments coincided with those of the Bose distribution for the number of photolectrons emitted by thermal light. However, a general method can be adopted to find the probability distribution of photoelectrons if one knows all orders of correlations in intensity existing in the incident beam.