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Physical Review Letters

Coupling of Spatial and Temporal Coherence in Depolarized Double Scattering

Dae M. Kim, J.G. Gallagher, C. D. Armeniades

Published Sep 26, 1977• 5 citations
Publisher

Abstract

Measurements of strongly density-dependent Rayleigh linewidth of depolarized doubly scattered light are presented. A new theory based on the coupling between spatial and temporal parts of coherence is proposed to explain our data. In addition, it is shown experimentally that successive application of Van Hove space-time correlation formulation to double scattering is not valid in general.

DOI
10.1103/physrevlett.39.804

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Measurements of strongly density-dependent Rayleigh linewidth of depolarized doubly scattered light are presented. A new theory based on the coupling between spatial and temporal parts of coherence is proposed to explain our data. In addition, it is shown experimentally that successive application of Van Hove space-time correlation formulation to double scattering is not valid in general.
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We present the first calculation of coherent backscattering with inelastic scattering by saturated atoms. We consider the scattering of a quasi-monochromatic laser pulse by two distant atoms in free space. By restricting ourselves to scattering of two photons, we employ a perturbative approach, valid up to second order in the incident laser intensity. The backscattering enhancement factor is found to be smaller than two (after excluding single scattering), indicating a loss of coherence between the doubly scattered light emitted by both atoms. Since the undetected photon carries information about the path of the detected photon, the coherence loss can be explained by a which-path argument, in analogy with a double-slit experiment.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
We report on the effects of dense optical systems on the static and dynamic properties of laser light. The measurements of the angular irradiance distribution as a function of the optical density and the size of the scattering centers confirm previous measurements performed by Woodward. Our study of the scattered irradiance correlation function indicates that, in the presence of multiple scattering, the relaxation time may be significantly smaller than that predicted on the basis of the single-particle Brownian model. Furthermore, the angular dependence of the irradiance relaxation time deviates from the usual proportionality to the inverse square of the momentum transfer. We discuss a number of tests that have been performed to minimize the possibility that some of our conclusions could be affected in part by particle aggregation, surface charges, and depolarization of the scattered light.
We present scattering from many-body systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the scattering amplitude as a space-time integral over the scattering sample for an incident wave characterized by its correlation function, which results from the shaping of the wave field by the apparatus. Instrument resolution effects, seen as due to the loss of correlation caused by the path differences in the different arms of the instrument, are automatically included and analytic forms of the resolution function for different instruments are obtained. Each element of the apparatus is associated with a correlation length (or time). These correlation lengths, determined by the dimensions of the apparatus, are generally much smaller than these dimensions and larger than the wavelength. As is well known, these are the conditions for the validity of geometrical optics so that the conventional treatment, where the scattering is calculated by the van Hove plane-wave approach and the trajectories through the instrument are treated classically, is usually valid. In the present approach analytic expressions for the correlation functions are obtained. The intersection of the moving correlation volumes (those regions where the correlation functions are significant) associated with the different elements of the apparatus determines the maximum correlation lengths (times) that can be observed in a sample, and hence, the momentum (energy) resolution of the measurement. This geometrical picture of moving correlation volumes derived by our technique shows how the interaction of the scatterer with the wave field shaped by the apparatus proceeds in space and time. Matching of the correlation volumes so as to maximize the intersection region yields a transparent, graphical method of instrument design.