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Physical Review A

Effects of finite laser coherence in quasielastic multiple scattering

Tommaso Bellini, Matthew A. Glaser, Noel A. Clark, Vittorio Degiorgio

Published Oct 1, 1991• 39 citations
Publisher

Abstract

We have studied the amplitude and temporal correlations of intensity fluctuations of multiply scattered light transmitted through a colloidal suspension. When the coherence length ${\mathit{l}}_{\mathit{c}}$ of the incident light becomes comparable to the width of the probability distribution of photon-path lengths, both the amplitude and dynamics of intensity fluctuations become functions of ${\mathit{l}}_{\mathit{c}}$. In this article we present a simple theory that relates these coherence effects to the photon path-length distribution P(L). We have tested this theory using P(L) calculated from computer simulations and from the diffusion approximation, and find that our theory qualitatively accounts for the observed dependences on coherence length. Our results indicate when the effects of finite laser coherence must be taken into account in quasielastic multiple scattering. In the few-scattering regime of quasielastic multiple scattering, we find that the intensity autocorrelation function generally has a stretched-exponential form, and we discuss the origin of this behavior.

DOI
10.1103/physreva.44.5215

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We have studied the amplitude and temporal correlations of intensity fluctuations of multiply scattered light transmitted through a colloidal suspension. When the coherence length lc{\mathit{l}}_{\mathit{c}}lc​ of the incident light becomes comparable to the width of the probability distribution of photon-path lengths, both the amplitude and dynamics of intensity fluctuations become functions of lc{\mathit{l}}_{\mathit{c}}lc​. In this article we present a simple theory that relates these coherence effects to the photon path-length distribution P(L). We have tested this theory using P(L) calculated from computer simulations and from the diffusion approximation, and find that our theory qualitatively accounts for the observed dependences on coherence length. Our results indicate when the effects of finite laser coherence must be taken into account in quasielastic multiple scattering. In the few-scattering regime of quasielastic multiple scattering, we find that the intensity autocorrelation function generally has a stretched-exponential form, and we discuss the origin of this behavior.
We find experimentally that in the forward direction the length scale of quasiballistic photons dominates the dynamic intensity-intensity correlation function of light multiply scattered from randomly diffusing spheres. This implies a breakdown of the photon-diffusion approximation, which is characterized by a single length, the transport mean free path. We suggest why this breakdown occurs, introduce phenomenologically a dynamic correlation length as an additional length scale, and with this extension reconcile the theory with experiment.
The concentration dependence of the statistical properties of light scattered by a monodisperse sphere suspension has been studied. Theoretical predictions for photon-counting distributions, obtained by supposing the scattered field is a superposition of coherent signal S and noise excitation N, agree well with the experimental results, thus providing an alternative method to obtain quantitative information on the influence of multiple scattering on measurements. Moreover, the autocorrelation function is deformed from an exponential law to a stretched-exponential law, as expected, and the experimental results show that the parameter dw{\mathit{d}}_{\mathit{w}}dw​, quantifying the exponential stretching, and the ratio S/N exhibit a similar dependence on the level of multiple scattering.
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.
The authors present a weak light field, scattering theoretical description of the intensity autocorrelation function for the scattered light from a many-atom (molecule) system. The theory considers both resonant and near-resonant scattering for atoms with many sublevels in both the ground and electronically excited states, and it incorporates the effects of the finite coherence time of the incident radiation. The theory is derived using incident two-photon wave packets with spatial dispersion among the target atoms. Purely anti-bunching contributions arise from single-atom-two-photon scattering and from successive two-atom-two-photon scattering events. However, there are interleaved two-atom-two-photon scattering processes which provide purely bunching contributions since both atoms may be scattering at the same time. Path length differences in the successive two-atom scatterings can also induce some bunching character to the correlation function. The dependence of the risetime and decay of the intensity correlation function upon the atomic excited state lifetimes and the coherence time of the incident light emphasises the correlation between photons which have been coherently and/or incoherently scattered.
The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys. Rev. Lett. 98, 083601 (2007)], we analyze how static speckle-intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.