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.
The method of numerical simulation was used to study the effective lifetime of the excited level of the resonance transition in sodium and lithium vapour. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved with the equation of radiation transfer. The Biberman–Holstein escape factor was calculated as a function of the optical thickness of vapour for different geometries of the luminescing gas and different models of the frequency redistribution functions. The dependence of the escape factor on the optical thickness investigated experimentally by Romberg and Kunze (J. Quant. Spectrosc. Radiat. Transfer. 1988 39 99) is discussed.
This study carries out an experimental investigation of the radiative decay kinetics of the resonance states of sodium atoms excited by dye laser radiation. The effective radiative decay rates of the resonance states as a function of vapor temperature, primary and impurity gas presssure, and the radius of the cylindrical volume containing the vapor were obtained by computer processing ofthe experimental curves using a kinetic decay model.-The radiative decay rate calculated in the Holstein approximation is compared to the measured values. The mechanisms of optical excitation of metallic vapors in resonance radiation trapping conditions have been investigated theoretically to a sufficient degree.lr At the same time there have been few experimental studies devoted to this problem. The decay kinetics of the atomic resonance states in the vapors of alkali metals have largely been studied for a planar radiating layer,2-6 where the nonideal geometry of the radiating volume made it necessary to introduce a fitting parameter to compare the experimental results to theory. The radiative decay kinetics of the populations of the resonance 3P states of atomic Na under conditions of axial laser excitation of a cylindrical shell are investigated in the present paper for the first time; this made it possible to carry out a comparison to theory without introducing variable parameters, since in this case exact analytic expressions are known for the effective lifetimes. It should also be emphasized that cylindrically configured cells are most commonly used in experimental research and hence these results have a certain interest in such studies. For our analysis we selected a concentration range of normal sodium atoms of 3 X 1013 <;no<;4 X 1015 cm - where selective optical excitation of the fine structure components (FSC) 32Pl/2 and 32P3/2 are accompanied by collisional mixing, which has a substantial effect on the persistence kinetics of the NaD lines. Under these conditions the decay of the directly excited fine structure component is biexponential, while the time dependence of the population of the corresponding level takes the form
We have measured the time-dependent fluorescence of the sodium
D lines following pulsed excitation of one
D line, in the presence of radiation trapping with optical depths
k0L of \ensuremath{\sim}10 to 2000. When collisional coupling of the
3P21 and
3P23 levels and different radiative-escape probabilities for each
D line are taken into account, we obtain excellent agreement with Holstein's theory for the effective radiative decay rates in the Doppler region (${k}_{0}L\ensuremath{\sim}10\ensuremath{-}300$) and in the redistributed Lorentzian region (
k0L>1000). For
k0L between these two regions, we observe an abrupt transition between the two limiting formulas. The buildup rate of the sensitized fluorescence signal also yields a $3{P}_{\frac{3}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}$ excitation transfer cross section in agreement with our previously reported cw measurement. Additionally, we have measured the dependence of the
3P fluorescence on laser power and beam diameter, and we explain the observed approach to saturation. We suggest that the previously reported "anomalous" approaches to saturation may be explained in terms of the laser beam burning through the optically thick vapor. Laser-beam spatial intensity variations and self-focusing also contribute to fluorescence signals that deviate from the usual single-atom saturation behavior.