In the light of the perspective of statistical similarity, we examine the maintenance of the second-order coherence of a light wave on weak scattering from a random medium. Some new and nontrivial results relating to properties of the scattered field which remains the second-order coherence of the incident field are presented. By assuming that the scattered field remains the second-order coherence, we can show that all of higher order correlation functions of Fourier component of the scattering potential can reduce to the like-factorization forms with a series of constant coefficients. These coefficients furnish an efficient and direct way to describe the higher order coherence property of the scattered field. We also show that the combination of the maintenance of second- and fourth-order coherence implies the scattered field coherence to all orders. Finally, the structure feature of the random medium is also discussed when the coherence of the incident field is retained up to 2nth order, in particular, in the case of the second-order coherence. Our theory is an important contribution for understanding of spatially fully coherent scattered fields, and also gives a general and new method to discuss the variation of the coherence of the scattered field.
In the light of the perspective of statistical similarity, we examine the maintenance of the second-order coherence of a light wave on weak scattering from a random medium. Some new and nontrivial results relating to properties of the scattered field which remains the second-order coherence of the incident field are presented. By assuming that the scattered field remains the second-order coherence, we can show that all of higher order correlation functions of Fourier component of the scattering potential can reduce to the like-factorization forms with a series of constant coefficients. These coefficients furnish an efficient and direct way to describe the higher order coherence property of the scattered field. We also show that the combination of the maintenance of second- and fourth-order coherence implies the scattered field coherence to all orders. Finally, the structure feature of the random medium is also discussed when the coherence of the incident field is retained up to 2nth order, in particular, in the case of the second-order coherence. Our theory is an important contribution for understanding of spatially fully coherent scattered fields, and also gives a general and new method to discuss the variation of the coherence of the scattered field.
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.
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.
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.
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.
In this paper, we study the problem of multiple scattering of light from a randomly occupied optical lattice, thereby extending the first-order Born analysis of the previous paper. A full multiple-scattering analysis is essential to a complete understanding of the nature of light propagation inside a medium. Our calculations show that the incident wave, when resonant with the atomic medium, is rapidly extinguished due to multiple scattering. The decay constant depends critically on the incident wavelength, the lattice constant, the average number density of atoms, and their polarizability. Both the Bragg scattering amplitudes and directions are modified as a result of multiple scattering. Because of the random site occupation of an otherwise regular lattice structure, a coherent enhancement of the scattering cross section is also predicted to occur along a discrete set of directions that are related to the strictly backward direction by reciprocal lattice vectors.
The higher-order coherence functions of optical fields involving phase fluctuations have not yet been studied extensively. We discuss here an experiment which can in principle yield the fourth-order coherence function. This experiment is a study of the correlation function of the irradiance fluctuations obtained in some interference experiments. Two kinds of delay are then used: optical delays in the interferometer and electrical delays with suitable variations in the correlator.The results of the experiment are calculated theoretically with a particular statistical model of laser light. The possibility of using a spectrum analyzer instead of a correlator is discussed.