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Optica Acta International Journal of Optics

Some Recent Research on Coherence and Fluctuations of Light

Published Oct 1, 1966• 9 citations
Publisher

Abstract

A review is presented of various investigations on coherence and fluctuations of light which have been carried out within the last few years. In particular some of the research carried out at the University of Rochester and related investigations undertaken elsewhere are described. This research is mainly concerned with the following topics: classical and quantum description of higher order coherence effects, photon correlation and coincidence experiments, stellar correlation interferometry, photon bunching, and the determination of the statistical properties of light from photoelectric counting experiments.

DOI
10.1080/713817998

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Abstract : The report summarizes researches concerned with theoretical studies of coherence effects in electromagnetic fields, with special reference to the electromangetic range of the spectrum. Various properties of fluctuating fields were investigated and second and higher order coherence effects were analyzed. Relation between the classical and quantum theory of coherence was also considered. A degree of coherence of arbitrary order was introduced which has some advantages over that introduced earlier by other authors. Further, diagonal coherent state representation of quantum operators was studied. Some related investigations in statistical mechanics, and in diffraction theory of the electromagnetic field were also carried out. (Author)

•Sep 1, 1967•0 citations
A review is presented of various investigations on coherence and fluctuations of light which have been carried out within the last few years. In particular some of the research carried out at the University of Rochester and related investigations undertaken elsewhere are described. This research is mainly concerned with the following topics: classical and quantum description of higher order coherence effects, photon correlation and coincidence experiments, stellar correlation interferometry, photon bunching, and the determination of the statistical properties of light from photoelectric counting experiments.
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.
During the last week of June 1960, a three-day conference on the coherence properties of electromagnetic radiation was held on the campus of the University of Rochester. Sponsored by the US Air Force, the University of Rochester, and the Optical Society of America, the purpose of the conference was to bring together optical and atomic physicists from this country and abroad to discuss problems of common interest dealing with the question of coherence throughout the electromagnetic spectrum. To a large extent motivation was supplied by a number of controversial and surprising developments in widely separated branches of physics within the last decade. Certainly much of the attention paid to questions of coherence after so many years of its having lain dormant is due in no small measure to the now famous Brown-Twiss experiment (1955) on the correlation in fluctuations of the output currents of two photoelectric detectors exposed to mutually coherent fields of light. The controversy that followed demonstrated clearly the lack of understanding of the statistical properties inherent in the emission, propagation, and detection of radiation. Whether or not one chose to explain the correlation as a natural tendency for bosons to clump or a natural interference effect among Fourier components in the finite spectral width of every natural source (or both) seemed at first to be a question of taste.
Introduction We will now study the properties of fluctuating electromagnetic fields, paying attention mainly to the optical region of the electromagnetic spectrum. It seems hardly necessary to stress that every electromagnetic field found in nature has some fluctuations associated with it. Even though these fluctuations are, as a rule, much too rapid to be observed directly, one can deduce their existence from suitable experiments that provide information about correlations between the fluctuations at two or more space-time points. The simplest manifestations of correlations in optical fields are the well-known interference effects that arise when two light beams that originate from the same source are superposed. With the availability of modern light detectors and electronic circuitry of very short resolving time, other types of correlations in optical fields began to be studied in more recent times. These investigations, as well as the development of lasers and other novel types of light sources, led to a systematic classification of optical correlation phenomena and the complete statistical description of optical fields. The area of optics concerned with such questions is now generally known as optical coherence theory . The first investigations of coherence phenomena are due to Verdet (1865, 1869) and von Laue (1907a, b). Some early investigations of Stokes (1852) and Michelson (1890, 1891a, b, c, 1892, 1920) although not explicitly mentioning coherence – because this concept is of a much later origin – have also contributed to the clarification and development of this subject.
Introduction In the preceding chapters we have been largely concerned with the simplest coherence effects of optical fields, namely those which depend on the correlation of the field variable at two space-time points ( r 1 , t 1 ) and ( r 2 , t 2 ). As we have seen, these effects include the most elementary coherence phenomena involving interference, diffraction and radiation from fluctuating sources. In this chapter we present an extension of the theory to cover more complicated situations, which have to be described by correlations of higher order, i.e. by correlations of the field variables at more than two space-time points or the expectation values involving various powers and products of the field variables. Situations of this kind have become of considerable importance since the development of the laser and of nonlinear optics. The basic difference between the statistical properties of thermal light and laser light can, in fact, only be understood by going beyond the elementary second-order correlation theory. Many of the higher-order coherence phenomena are most clearly manifest in the photoelectric detection process, which can only be adequately described by the quantum theory of detection or by taking into account the quantum features of the field, both of which will be studied in the succeeding chapters. However, because the field is still described classically in the semi-classical theory of light detection, and also because the classical field description provides a natural stepping stone to the quantum description of field correlations, we will now discuss the general description of field correlations of all orders on the basis of the classical theory of the fluctuating wavefield.
Abstract A theoretical analysis is given of the correlation to be expected between the fluctuations in the outputs of two photoelectric detectors when these detectors are illuminated with partially coherent light. It is shown how this correlation depends upon the parameters of the equipment and upon the geometry of the experiment. The correlation may be detected either by linear multiplication of the fluctuations in the two outputs or by a coincidence counter which counts the simultaneous arrival of photons at the detectors. The theory is given for both these techniques and it is shown that they are closely equivalent. A laboratory test is described in which two photomultipliers were illuminated with partially coherent light and the correlation between the fluctuations in their outputs measured as a function of the degree of coherence. The results of this experiment are compared with the theory and it is shown that they agree within the limits of accuracy of the test; it is concluded that if there is any systematic error in the theory it is unlikely to exceed a few parts per cent.
Abstract : The report summarizes researches concerned with theoretical studies of coherence effects in electromagnetic fields, with special reference to the electromangetic range of the spectrum. Various properties of fluctuating fields were investigated and second and higher order coherence effects were analyzed. Relation between the classical and quantum theory of coherence was also considered. A degree of coherence of arbitrary order was introduced which has some advantages over that introduced earlier by other authors. Further, diagonal coherent state representation of quantum operators was studied. Some related investigations in statistical mechanics, and in diffraction theory of the electromagnetic field were also carried out. (Author)