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Contemporary Physics

Light scattering

P. R. Berman

Published Sep 1, 2008• 7 citations
Publisher

Abstract

Light scattering of monochromatic radiation by atoms and dilute vapours is reviewed. The relative contributions of incoherent and coherent scattering are calculated for weak incident fields. It is shown that, to lowest order in the intensity of the driving field, there can be several inelastic components in the scattered spectrum. The positions and widths of these components are related to light shifts and optical pumping of the atoms in the field. The complications that one encounters in scattering by two atoms, moving atoms, and atomic ensembles are discussed in qualitative terms.

DOI
10.1080/00107510802551572

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Light scattering of monochromatic radiation by atoms and dilute vapours is reviewed. The relative contributions of incoherent and coherent scattering are calculated for weak incident fields. It is shown that, to lowest order in the intensity of the driving field, there can be several inelastic components in the scattered spectrum. The positions and widths of these components are related to light shifts and optical pumping of the atoms in the field. The complications that one encounters in scattering by two atoms, moving atoms, and atomic ensembles are discussed in qualitative terms.
The semi-classical method for calculating the observable properties of light scattered from an optically thin atomic vapour is placed in the context of the well known input-output relations for random signals transmitted through a linear system. The autocorrelation of the scattered field amplitude, the statistic from which the mean intensity spectral density and intensity fluctuations may be deduced, is expressed in terms of the autocorrelation of the incident optical field and the autocorrelation of the scattering system; these latter are quantities that can be readily measured or calculated. An appendix contains a classical and a semi-classical calculation of the scattering system autocorrelation function for a vapour of atoms optically excited from a J=0 level under the conditions of a level crossing experiment. In the course of this calculation the relationship between the matrix element of the electric dipole moment operator and the corresponding classical quantity is carefully examined.
Resonant scattering (redistribution) of weak monochromatic light by atoms in the presence of collisions has been considered by Omont et al., who allowed for the broadening of both upper and lower levels of the transition. Mollow (who also has considered this problem for intense radiation) has shown that their results are applicable only if collisional repopulation of the levels (in contrast to collisional depopulation) is ignored. We here consider in detail the effect of repopulation. It leads, in the weak-field limit, to a true-coherent component ($\ensuremath{\delta}$-function spectrum) at the driving frequency, as well as a component at this frequency whose width is essentially the inelastic collisional rate of the lower state. An additional redistributed component due to repopulation of the upper level is also obtained.
Cooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of ‘single-photon superradiance’, or cooperative scattering in the linear-optics regime, can also be explained by ‘standard optics’, i.e. using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohm’s law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility.
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incident fields. The implications of our findings for the observation of photon antibunching are also discussed.
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.
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.