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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Nonlinear radiation trapping in an atomic vapor excited by a strong laser pulse

Nikolai N. Bezuglov, Andrey N. Klyucharev, A. F. Molisch, M. Allegrini, F. Fuso, T. Stacewicz

Published Mar 1, 1997• 17 citations

Abstract

We investigate radiation trapping in an atomic vapor which has been excited by a strong short laser pulse. Since the saturation of the vapor by the pulse leads to a decrease in the effective absorption coefficient, the radiation trapping becomes nonlinear. We derive approximate analytical expressions for the excited-state density in the directly excited region, the fluorescence-excited region, and the density averaged over the whole cell. Starting out from fairly simple approximate expressions based on a prescribed distribution of excited atoms, we then develop physically motivated correction factors that drastically improve the accuracy. All these expressions are given for three important cell geometries: the plane-parallel slab, the infinite cylinder, and the sphere. We compare our results to accurate numerical solutions, and find agreement within 5--10%. We then derive the decay time of the emergent radiation, and find that it can be smaller than the natural lifetime of the excited atoms, in agreement with recent experimental results obtained for sodium vapors.

DOI: 10.1103/physreve.55.3333

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Physical Review A•Apr 1, 1996•15 citations

We investigate radiation trapping in an atomic vapor which has been excited by a strong short laser pulse. Since the saturation of the vapor by the pulse leads to a decrease in the effective absorption coefficient, the radiation trapping becomes nonlinear. We derive approximate analytical expressions for the excited-state density in the directly excited region, the fluorescence-excited region, and the density averaged over the whole cell. Starting out from fairly simple approximate expressions based on a prescribed distribution of excited atoms, we then develop physically motivated correction factors that drastically improve the accuracy. All these expressions are given for three important cell geometries: the plane-parallel slab, the infinite cylinder, and the sphere. We compare our results to accurate numerical solutions, and find agreement within 5--10%. We then derive the decay time of the emergent radiation, and find that it can be smaller than the natural lifetime of the excited atoms, in agreement with recent experimental results obtained for sodium vapors.

We present experiments of a laser with variable pulse energy and beam width saturating sodium vapor near the

{D}_{1}

-line transition. At high optical depth and in a buffer gas atmosphere of argon, the effect of nonlinear radiation trapping is shown to drastically change the spatial distribution and temporal evolution of the excited-state population and of the fluorescence light trapped by the nonlinear medium. Besides observing the transient behavior of the fluorescence light, a pump-probe beam experiment enables us to gain a tomographic view inside the atomic vapor. Nitrogen as a buffer gas is used to compare with the situation where radiation trapping effects are negligible. Finally, numerical simulations based upon equations of radiative transfer for a two-level atomic system elucidate the role of nonlinear radiation trapping and support given interpretations of the experiments.

We analyze nonlinear radiation imprisonment (RI) effects in an optically thick vapor in different temperature regimes. An analytical approach is proposed to treat nonlinear decay problems. Special attention is paid to vapor samples having curvilinear geometries (cylinder, sphere) and being excited by a strong laser pulse. We derive a number of new formulas for different radiative trapping factors as functions of opacity and propose a general approach for RI evaluation allowing us to deal with samples both at room and low, or very low, temperatures, such as those customarily achieved in magneto-optical trap (MOT) experiments. As a result, we predict a ``subnatural'' decay of radiation escaping from cold vapors, which can be envisioned as the basis for a sensitive and reliable MOT diagnostic tool.

In three-level atoms where one level is the ground state and one is a metastable state, even low-intensity resonance radiation can lead to bleaching. This effect causes the radiation trapping to become nonlinear and thus greatly complicates the simulation of such a system. We set up equations to model an optically excited three-level atomic vapor in a two- or three-dimensional cylindrical cell; the model includes the effects of radiation trapping, particle diffusion, and quenching. We then develop a fast and efficient approximate method for the solution of these equations. Results are compared to Monte Carlo simulations; agreement within 15% is achieved.

The effect of imprisonment of radiation in sodium vapor on the measured lifetime of the

3 ^{2}P

states has been investigated in an experiment in which the atoms in the vapor were excited with 10-nsec pulses of resonance radiation and the elapsed times between the exciting and the fluorescent pulses were recorded using a time-to-amplitude converter and kicksorter. At vapor densities below

{10}^{10}

atoms/

{\mathrm{cm}}^{3}

, where there is no multiple scattering, the measured lifetime reaches a constant value of (1.63\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec, equal to the natural lifetime of the

3 ^{2}P

states. In the density range

{10}^{9}

-

{10}^{13}

atoms/

{\mathrm{cm}}^{3}

, the variation of the effective lifetime with the vapor density is in good agreement with the predictions of Milne's theory of radiation trapping; agreement with Holstein's theory is observed only in the range

{10}^{12}

-

{10}^{13}

atoms/

{\mathrm{cm}}^{3}

. The results of a subsidiary Hanle experiment show that a multiply scattered photon of sodium resonance fluorescence loses its original polarization and that, at high sodium vapor pressure, coherence is not preserved.

We describe the influence of radiation trapping on the spatial distribution of the excited-state population in sodium vapor, interacting with a linearly polarized Gaussian laser beam. Counterintuitively the excitation volume experiences a strong spatial shrinking at high optical depth. The interpretation of this nonlocal effect is based on the numerical solution of the stationary Holstein equation, which takes into account the full frequency dependence of the reabsorption probability within the process of diffusion of radiation. The calculations performed are in good qualitative agreement with the spatial effects observed experimentally. \textcopyright{} 1996 The American Physical Society.