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Physical Review Letters

Field correlations within a fluctuating homogeneous medium

H. M. Nussenzveig, J. T. Foley, K. Kim, E. Wolf

Published Jan 19, 1987• 16 citations
Publisher

Abstract

The general form of the field correlations within a fluctuating homogeneous medium is determined in terms of the corresponding source correlations. Under very general conditions, the degree of spectral coherence has a universal form, independent of the source, if the fluctuations are isotropic. It they are anisotropic, the degree of coherence at separations that are large compared with the wavelength directly yields the generalized dynamical structure factor of the medium.

DOI
10.1103/physrevlett.58.218

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The general form of the field correlations within a fluctuating homogeneous medium is determined in terms of the corresponding source correlations. Under very general conditions, the degree of spectral coherence has a universal form, independent of the source, if the fluctuations are isotropic. It they are anisotropic, the degree of coherence at separations that are large compared with the wavelength directly yields the generalized dynamical structure factor of the medium.
We investigate the behavior of the spectral degree of coherence of fluctuating scalar wave fields generated by statistically homogeneous and isotropic sources within absorbing media. In the limit of negligible losses, the degree of coherence is shown to be of a known universal form (sinc function), whereas in the limit of infinite losses it is shown to asymptotically approach the degree of coherence of the source. The intermediate cases are studied for fields produced by sources with Gaussian and sinc-type coherence functions. These studies show that the concept of negligible losses is meaningful only when defined with respect to specific source distribution statistics, and that even for arbitrarily small nonzero losses, the coherence length of the field can be arbitrarily short.
A theory is developed, valid within the accuracy of the first-order Born approximation, of the scattering of electromagnetic fields that applies under much more general conditions than do the current theories. The incident field is assumed to be statistically homogeneous and stationary, of arbitrary state of coherence, of arbitrary state of polarization, and to have arbitrary spectrum. The medium is assumed to be linear and spatially and temporally random, with the randomness being characterized by an ensemble that is statistically homogeneous, isotropic, and stationary. The analysis is not restricted to scattering from a medium in thermal equilibrium and applies in both off-resonance and near-resonance regions of the medium.
The first-order coherence condition is derived in terms of correlations between different field modes. Fluctuations of the electromagnetic field are shown to play an important role in the concept of coherence. The coherent states are shown to be the only ones which reduce these fluctuations to their minimum value. For the case of a field in which the different field modes are independent, the degree of first-order coherence and the visibility of interference fringes are shown to be specified completely by these fluctuations. Measurements of this visibility yield information on the statistical properties of radiation fields. For squeezed states, this visibility is expressed as a function of squeezed parameters. Moreover, the difference between generalized coherent states becomes manifest in measurements of this visibility.
Statistical correlations of the light emitted by a partially coherent source can produce frequency shifts in the spectrum observed in the far field if the correlation function of the emitted radiation does not satisfy a certain scaling law. A Fourier achromat is used to generate a secondary source in which the degree of spectral coherence is independent of wavelength; i.e., it violates the scaling law. The spectrum detected in the far zone of the secondary source is, in general, found to be displaced in frequency and distorted relative to the spectrum measured at the secondary source. The displacement can be toward the higher frequencies or the lower frequencies depending on the direction of observation.
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.