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Time interval statistics of the Brillouin spectrum

Singh, Manmohan

Published Jun 15, 1990• 0 citations
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Abstract

Based on the unique analytic form of the one-fold generating-function very recently given by the present author in [3], we provide in this paper a complete and an exact anaysis of the time-interval-statistics of the Brillouin spectrum with its central Rayleigh line. We also distinguish the time-interval-distributions for the present Brillouin triplet from the time-interval-distributions for the pure Brillouin spectrum (a doublet) given in Ref. [4]. As in Ref. [4], we establish here too the invalidity of the earlier numerical-results due to Blake and Barakat [5] for the present Brillouin triplet, as they violate even the well known equation (32) for the time-interval-distribution for the conditional photocount

DOI
10.5169/seals-116229

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Based on the unique analytic form of the one-fold generating-function very recently given by the present author in [3], we provide in this paper a complete and an exact anaysis of the time-interval-statistics of the Brillouin spectrum with its central Rayleigh line. We also distinguish the time-interval-distributions for the present Brillouin triplet from the time-interval-distributions for the pure Brillouin spectrum (a doublet) given in Ref. [4]. As in Ref. [4], we establish here too the invalidity of the earlier numerical-results due to Blake and Barakat [5] for the present Brillouin triplet, as they violate even the well known equation (32) for the time-interval-distribution for the conditional photocount
The statistical characteristics of a stationary gaussian field endowed with Brillouin spectrum are studied. A closed-form expression for the exact one-fold generating function (g.f.) corresponding to the arbitrary count rates and the sample times is derived. The time-interval distribution of the photon counting statistics is extracted from the g.f. without resort to any approximate procedures. Comparison with the earlier results obtained by use of the approximate methods shows that the error in such approximations is considerable.
Two-fold photoelectron counting statistics are studied for quasimonochromatic light of arbitrary spectral profile. A numerical scheme is developed for the evaluation of the double generating function from which the joint probabilities, the photoelectron correlation function, and the clipped photoelectron correlation function can be evaluated. The time need not be short compared to the coherence time as in previous studies. Numerical results are presented for the photoelectron correlation function and for the clipped correlation function for the spectrum which would be observed in a Brillouin scattering experiment.
There has been considerable interest in recent years in the statistical properties of optical frequency electromagnetic fields. Of particular interest is the study of photon bunching and the probability density for waiting time between adjacent photocounts. In this paper we derive an expression for the probability density of the time interval distribution as well as some other quantities of interest in photon bunching for the case where the incident radiation is comprised of superposed coherent and chaotic radiation of arbitrary spectral shapes. Calculations show that the key parameters are the average number of chaotic counts per coherence time and the ratio of the strengths of coherent and chaotic parts (signal-to-noise ratio).
Extending the concept of the time-dependent physical spectrum introduced by Eberly and Wodkiewicz (1977) the authors present a formula for the n-fold time-resolved correlation spectrum depending on n time and n frequency arguments. The corresponding measuring device consists of n coupled photodetectors with frequency resolving equipment in front of each. As an application the authors consider the resonance fluorescence radiation of a two-level atom irradiated monochromatically. Under certain conditions the authors derive a simple expression for the n-fold detection probability of photons at time t i (i=1, . . ., n) with frequencies belonging to the central peak or to one of the sidebands of the fluorescence triplet.