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Journal of the Optical Society of America B

Coherence properties of nonstationary polychromatic light sources

M. Bertolotti, Aldo Ferrari, Leonid Sereda

Published Feb 1, 1995• 54 citations
Publisher

Abstract

We discuss the relation between the coherence of light from nonstationary sources in the space–time domain and the coherence of the monochromatic components of the light. For this purpose we use Loéve’s theory of harmonizable stochastic processes, particularly the spectral representation of a nonstationary stochastic process and the relation between its correlation function and the two-frequency spectral function as a measure of coherence of the monochromatic components of the source.

DOI
10.1364/josab.12.000341

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We discuss the relation between the coherence of light from nonstationary sources in the space–time domain and the coherence of the monochromatic components of the light. For this purpose we use Loéve’s theory of harmonizable stochastic processes, particularly the spectral representation of a nonstationary stochastic process and the relation between its correlation function and the two-frequency spectral function as a measure of coherence of the monochromatic components of the source.
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The concept of cross-spectral purity of light, established by Mandel for stationary optical fields, is extended to nonstationary fields. Separability conditions that ensure the cross-spectral purity of nonstationary light are derived in the space-frequency and space-time domains. It is also shown that the property of cross-spectral purity is not strictly preserved on propagation of fields with any appreciable spectral bandwidth. Further, we introduce a method for generating cross-spectrally pure (stationary and nonstationary) fields from spatially incoherent light sources by means of achromatic Fourier-transform systems.
This paper presents a review of research, both theoretical and experimental, concerning the influence of coherence properties of fluctuating light sources and of correlation properties of scattering media on the spectra of radiated and scattered fields. Much of this research followed a discovery made in 1986, that the spectrum of light may change on propagation, even in free space. More than 100 papers on this topic have been published to date and many of them are reviewed, or at least mentioned, in this article. After an introduction and a summary of some of the main mathematical results relating to second-order coherence theory of statistically stationary optical fields, spectral changes that may take place on superposing fields produced by two partially correlated sources are discussed. Spectral effects in fields produced by two-dimensional secondary sources and by three-dimensional primary sources are then considered. The section which follows describes spectral changes that may arise when polychromatic light is scattered on media whose physical properties vary randomly either in space and/or in time. A review is also presented of recent research, which has revealed that under certain circumstances the changes in the spectrum of light scattered on random media may imitate the Doppler effect, even though the source, the medium and the observer are all at rest with respect to one another. In the final section a brief review is given of a new emerging technique sometimes called spatial-coherence spectroscopy. It is based on the discovery that it is possible, under certain circumstances, to determine field correlations from spectral measurements.
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