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Physical Review A

Generalizations of Gaussian Optical Fields

B. Picinbono, M. Rousseau

Published Mar 1, 1970• 48 citations
Publisher

Abstract

Stationary Gaussian optical fields are also often called thermal fields because they are generated by natural or thermal sources. By using the amplitude of the field, we show that thermal fields are only a particular case of the more general class of Gaussian fields. Such nonthermal Gaussian fields can be obtained experimentally, and we calculate some properties, concerning particularly the effect of Hanbury Brown and Twiss, photocounting, and coincidence experiments. We show that the thermal fields are the less chaotic or incoherent Gaussian fields. Finally, we introduce pseudo-Gaussian fields which appear in some experiments of diffusion with laser light. They are non-Gaussian fields, but their intensity has the same properties as that of a Gaussian field.

DOI
10.1103/physreva.1.635

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Stationary Gaussian optical fields are also often called thermal fields because they are generated by natural or thermal sources. By using the amplitude of the field, we show that thermal fields are only a particular case of the more general class of Gaussian fields. Such nonthermal Gaussian fields can be obtained experimentally, and we calculate some properties, concerning particularly the effect of Hanbury Brown and Twiss, photocounting, and coincidence experiments. We show that the thermal fields are the less chaotic or incoherent Gaussian fields. Finally, we introduce pseudo-Gaussian fields which appear in some experiments of diffusion with laser light. They are non-Gaussian fields, but their intensity has the same properties as that of a Gaussian field.
This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams.
We establish classically the probability distribution (P-distribution) for the complex amplitudes of multimodal and unimodal optical fields belonging to the class of generalized Gaussian fields recently introduced. From this result follows immediately the unique P-representation for this class of fields. However, all the generalized Gaussian fields, except the chaotic field, are not fully stationary. To each of them we can associate a stationary equivalent field which possesses the same intensity. We give the P-representation of this stationary equivalent field in the monomode case.
An account is given of optical coherence theory as it existed in the 1950's when, essentially, only thermal sources and slow detectors were available and it sufficed to characterize the coherence and polarization properties of an electromagnetic field by second-order correlation functions. The necessity for a more sophisticated specification of the coherence properties of fields, involving the use of higher-order correlation functions, first hinted at by the Hanbury-Brown-Twiss experiments and emphasized by the advent of the laser, is then introduced. Both classical and quantum mechanical treatments are discussed, each leading, in almost all cases of practical interest, to similar results. It is seen that the development of fast detectors enabled the higher-order correlation functions to be measured using photon counting techniques and an account of experimental work verifying the complete theory using such techniques is given. The review concludes with a discussion of some developments in associated areas whose origin lies in the resurgence of interest in coherence theory during the last decade.
Results were recently reported on statistical properties of phase-modulated laser light. A detailed analysis is presented here of random-phase modulation. In particular it is shown that there are two kinds of such modulation: modulation by phase fluctuations, in which the instantaneous phase is a stationary stochastic process, and modulation by phase diffusion in which the phase is a diffusion process with an always increasing variance. In the case of a Gaussian modulation we show that the optical fields in the two preceding cases are very different, and we calculate their coherence functions. This difference can be detected by an interference experiment, but more easily by photon coincidence or intensity-correlation experiments on a beat between a reference beam and the modulated beams. We present a theoretical analysis of such experiments in the two cases of modulation.
A simulation technique is described and utilized to generate superposed coherent and chaotic (thermal) radiation of arbitrary spectral shape. The statistical properties of a simulated radiation field with a Lorentzian spectral density is investigated with a photoelectron counting experiment. The experimental photocount distribution and normalized mth-order factorial moments are compared to theory and verify that the simulated radiation field, an appropriately modulated laser beam, has the expected statistical properties. The concept described indicates that one may, in principle, generate a thermal source of comparable intensity to that of a laser, arbitrary spectral shape, and bandwidth.