Some properties of point processes in statistical optics

Abstract

International audienceThe analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical description does not require the methods of quantum optics. This determination is, however, more difficult than ordinarily admitted and the first aim of this paper is to illustrate this point by using some results of the PP theory. For example, it is well known that the analysis of the photodetection of classical fields exhibits the so-called bunching effect. But this property alone cannot be used to decide the nature of a given optical field. Indeed, we have presented examples of point processes for which a bunching effect appears and yet they cannot be obtained from a classical field. These examples are illustrated by computer simulations. Similarly, it is often admitted that for fields with very low light intensity the bunching or antibunching can be described by using the statistical properties of the distance between successive events of the point process, which simplifies the experimental procedure. We have shown that, while this property is valid for classical PPs, it has no reason to be true for nonclassical PPs, and we have presented some examples of this situation also illustrated by computer simulations

Inversion of the Renewal Density with Dead-time

“…Quantum theory of light detection predicts, for example, that the time instants of photons absorption observed at the output of a photodetector are not in general described by a Poisson process and this can be observed by counting or coincidence experiments (Saleh, 1978, Saleh and Teich, 1981, Picinbono and Bendjaballah, 2010. On the other hand number of PPs observed in particle emission in nuclear physics must theoretically constitute Poisson processes.…”

“…This is especially the case in statistical physics when PPs are analyzed by the means of coincidence systems in which we measure the probability of finding points in two distinct small intervals regardless of the number or points appearing between these intervals. (Saleh, 1978, Saleh and Teich, 1991, Snyder and Miller, 1991, Picinbono and Bendjaballah, 2010. This leads immediately to the inverse problem consisting in deducing p(x) from h(x).…”

Measurements of Some Relaxed Properties of Point Processes

“…Probability density functions of RWT and of lifetime for a renewal PP with triangular lifetime. Points: experiment with simulated data, continuous curve: theory given by (8) and (9).…”

“…Renewal PPs introduce also a large class of models important for the applications. of this field of research can been found in [5], [6] and their use in Quantum Optics is summarized in [7], [8].…”

“…In some applications in Physics or Astronomy direct measurements of some properties of PPs have a direct interpretation. This is for example the case in Statistical Optics where the measurements of the variance of the number of points of the PP measured in some time intervals is a practical mean to make a difference between classical or quantum optical fields [7], [8]. Indeed for the classical fields this variance is necessarily greater than the mean value, which justifies the precise measurements of this mean value and this variance.…”