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Spectroscopy Letters

A Fast Computer-Simulation Method for Generating Values of n(2) in Intensity Fluctuation Spectroscopy

J. C. Abad, M. Á. Rebolledo

Published Jan 1, 1981• 8 citations
Publisher

Abstract

In this paper we present a fast method of simulation of the normalized second factorial moment n(2)(T) of the photon-counting distribution obtained in an intensity fluctuation spectroscopy experiment, in order to test the confidence with which one can derive information from such measurements.
DOI
10.1080/00387018108062569

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A level-crossing detection method is presented and developed based on measurement of the normalized second factorial moment n((2))(T) of the photon-counting distribution of the resultant fluorescence. Expression n((2))(T) is obtained, and the errors expected in the determination of signal width and crossing field are theoretically studied. The validity of the approximations performed to establish the theoretical model is proved by an experiment with a square-wave periodically modulated light beam.
A photon counting method is adapted to spectroscopy in very low intensity, as it is useful for data acquisition. There are two Poissonian lights which cannot be discriminated by this method. One is coherent light, and the other is Gaussian-Lorentzian light with infinite spectral linewidth. In this experiment, Gaussian-Lorentzian light with finite spectral linewidth was superposed on each Poissonian light, and the difference of the two radiation mechanisms was determined by profiles of the second-order factorial moment of the photon counting distribution.
Two techniques are described for obtaining information about the intensity correlation function of an optical field, from measurements of photoelectric counting distributions. The first method is based on double differentiation of the second factorial moment with respect to the counting time. It requires very accurate data, but is shown to be quite feasible, and yields the intensity-correlation function explicitly. The second procedure is less sensitive to inaccuracies and allows the correlation time and certain other parameters to be determined from the factorial moments. In addition, it yields some information about the general form of the correlation function, but no explicit function. The procedures are illustrated and compared by application to photoelectric counting measurements of a laser far below the threshold of oscillation.
It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of n photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photocounting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.