Radiation diffusion and saturation in optically thick Na vapor

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 $k_{0}L$ of ∼10 to 2000. When collisional coupling of the $3P_{\frac{1}{2}}$ and $3P_{\frac{3}{2}}$ 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 ($k_{0}L\sim 10-300$) and in the redistributed Lorentzian region ($k_{0}L>\mathrm{}1000\mathrm{}$). For $k_{0}L$ 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 $3P_{\frac{3}{2}}\to 3P_{\frac{1}{2}}$ 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.