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Journal of Experimental and Theoretical Physics

The effect of spatial dispersion and boundaries of a medium on resonance radiation transfer

A. N. Starostin, M. A. Chesnokov

Published Jan 1, 2002• 1 citation
Publisher

Abstract

An integral equation is derived for the spectral density of excited atoms using optically dense bounded dispersion media as an example. It is found that the inclusion of the thermal motion of atoms and of the effects due to the existence of a boundary brings about a nonlocal correlation between the concentration of excited particles and the intensity of electromagnetic field in the medium. It is demonstrated that, when the spatial dispersion of permittivity and the boundary effects are disregarded, the obtained result transforms to the well-known Biberman-Holstein equation. The problem on the spectral intensity of radiation of a heated half-space is also investigated.

DOI
10.1134/1.1448608

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An integral equation is derived for the spectral density of excited atoms using optically dense bounded dispersion media as an example. It is found that the inclusion of the thermal motion of atoms and of the effects due to the existence of a boundary brings about a nonlocal correlation between the concentration of excited particles and the intensity of electromagnetic field in the medium. It is demonstrated that, when the spatial dispersion of permittivity and the boundary effects are disregarded, the obtained result transforms to the well-known Biberman-Holstein equation. The problem on the spectral intensity of radiation of a heated half-space is also investigated.
Based on the already-developed general theory (I.M. Sokolov, D.V. Kupriyanov, and M.D. Havey, JETP 112 (2), 246 (2011)), we have studied the spatial distribution of excited atoms and of the atomic polarization that a weak monochromatic field creates in a dense ultracold atomic medium. We show that, in the case of a homogeneous random spatial distribution of atoms, the amplitude of atomic polarization averaged over spatial configurations decreases outside boundary regions according to an exponential law, while its phase linearly increases. Based on this, we have numerically determined the extinction coefficient and the light wavelength in the medium, as well as its dielectric permittivity. The dispersion of the permittivity at different concentrations has been studied. We show that, for dense clouds, the real part of the dielectric permittivity acquires negative values in a certain frequency range. Based on the calculation of the spatial distribution of excited atoms, we have analyzed the character of the transfer and trapping of quasi-resonant radiation in atomic clouds of differing density.
This work is devoted to generalization of the semi-classical theory of interaction of broadband laser radiation with the atomic gas at the room temperature in the cell in the case of the closed excitation contour. The atomic density matrix equations and spectrum and correlations transport equations have been derived for excitation by fluctuating field with Gaussian statistics. It is shown that the spatial oscillations of radiation intensity and atomic density matrix can be excited. It was found that such medium can serve as a filter of incoherent part of the radiation.
Scattering of resonance radiation in a dense two-level medium is considered with allowance for the local field effects. The system is studied in the framework of the mean-field approximation for a modified hierarchy of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices of an ensemble of atoms and modes of a quantized electromagnetic field. The local field correction is consistently derived from the initial Hamiltonian of the system. The problem of scattering of a short rectangular pulse from a quasi-point sample is considered numerically and theoretically. The possibility of a multimode spectrum of scattered radiation with frequencies multiple of the Rabi frequency and with other intermediate frequencies is demonstrated. The relative intensities of spectral lines are determined.
Starting from the quantized version of Maxwell's equations for the electromagnetic field in an arbitrary linear Kramers-Kronig dielectric, the Heisenberg equations of motion for a two-level atom resonantly coupled to the radiation field in the presence of dispersive and absorbing dielectric bodies are derived. The theory is applied to the problem of spontaneous decay of excited atoms in absorbing media. The decay rate is calculated for the (Glauber-Lewenstein) real-cavity model, and a comparison with the recently studied (Clausius-Mosotti) virtual-cavity model [S. Scheel, L. Kn\"oll, D.-G. Welsch, and S. M. Barnett, Phys. Rev. A 60, 1590 (1999)] is given. It is shown that owing to nonradiative decay associated with absorption, the rate of spontaneous decay sensitively depends on the cavity radius, particularly when the atomic transition frequency approaches an absorption band of the medium. Only when the effect of absorption is fully disregarded, is the familiar local-field correction factor recovered.
The coherent radiation of N atoms that are excited by an external field is studied close to a resonant transition. The resonant atoms are uniformly distributed over a sphere and the external field is a pulse that propagates in a fixed direction. The linear classical continuum theory is used for the above configuration. Exact expressions are obtained for the polarization, for the fields everywhere in space, and for the energy radiated and absorbed by the resonant atoms. Two equivalent methods for the derivation of the exact expression of the polarization are given, i.e., either by solving Maxwell’s equations and boundary conditions, or by solving an integral equation inside the sample. The equivalence of the two methods, in the general case of an arbitrary external field, has been proved elsewhere. Approximate expressions are also obtained for the physical quantities mentioned above in the extreme cases of a dilute and a dense resonant sample with radius much smaller than the radiation wavelength. Inside the dense small sample the polarization depends on position, and this space dependence is expressed in terms of spherical Bessel functions and vector spherical harmonics. It is shown that outside the dense small sample, a broadening of the original resonant line and a shift of the resonance frequency occur in the radiation spectrum of the atoms.