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Physical Review A

Transport of resonance excitation in Na vapor excited by white light

T. Fujimoto, A. V. Phelps

Published Jan 1, 1982• 6 citations
Publisher

Abstract

Experimental line profiles and integrated intensities for backscattered and forward-scattered resonance radiation using white-light excitation are compared with theory for Na densities between ${10}^{19}$ and ${10}^{22}$ atoms/${\mathrm{m}}^{3}$. Absorption measurements are used to verify linewidth and line-wing asymmetry parameters and Na-vapor densities. The scattered spectral intensities are normalized to the incident flux using calibrated diffusers. Measurements of scattered intensities were also made as ${\mathrm{N}}_{2}$ was added to the Na. The line profiles and integrated intensities were calculated using a model which assumes complete redistribution of the radiation scattered by an atom and takes into account both radiative and nonradiative transport of the resonance excitation. The theory includes the effects of quenching by ${\mathrm{Na}}_{2}$ and by admixed ${\mathrm{N}}_{2}$. With the white-light excitation used in these experiments the radiative transport is found to dominate the nonradiative transport except at wavelengths very near line center. The agreement between experimental and theoretical line profiles is good at high sodium densities (\ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/${\mathrm{m}}^{3}$) where instrumental resolution is not a serious limitation. The agreement between experimental and theoretical integrated intensities is within experimental error for Na densities of (1-10) \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ and (2-5) \ifmmode\times\else\texttimes\fi{} ${10}^{21}$ atoms/${\mathrm{m}}^{3}$. At the intermediate densities the approximately 20% discrepancy may be caused by the incomplete redistribution of radiation in the scattering process.

DOI
10.1103/physreva.25.322

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Experimental line profiles and integrated intensities for backscattered and forward-scattered resonance radiation using white-light excitation are compared with theory for Na densities between 1019{10}^{19}1019 and 1022{10}^{22}1022 atoms/m3{\mathrm{m}}^{3}m3. Absorption measurements are used to verify linewidth and line-wing asymmetry parameters and Na-vapor densities. The scattered spectral intensities are normalized to the incident flux using calibrated diffusers. Measurements of scattered intensities were also made as N2{\mathrm{N}}_{2}N2​ was added to the Na. The line profiles and integrated intensities were calculated using a model which assumes complete redistribution of the radiation scattered by an atom and takes into account both radiative and nonradiative transport of the resonance excitation. The theory includes the effects of quenching by Na2{\mathrm{Na}}_{2}Na2​ and by admixed N2{\mathrm{N}}_{2}N2​. With the white-light excitation used in these experiments the radiative transport is found to dominate the nonradiative transport except at wavelengths very near line center. The agreement between experimental and theoretical line profiles is good at high sodium densities (\ensuremath{\sim} 5 \ifmmode\times\else\texttimes\fi{} 1021{10}^{21}1021 atoms/m3{\mathrm{m}}^{3}m3) where instrumental resolution is not a serious limitation. The agreement between experimental and theoretical integrated intensities is within experimental error for Na densities of (1-10) \ifmmode\times\else\texttimes\fi{} 1019{10}^{19}1019 and (2-5) \ifmmode\times\else\texttimes\fi{} 1021{10}^{21}1021 atoms/m3{\mathrm{m}}^{3}m3. At the intermediate densities the approximately 20% discrepancy may be caused by the incomplete redistribution of radiation in the scattering process.
Measurements are reported which show the effect of nonradiative losses at a gas-window interface on the backscattered fluorescence intensity for Na vapor at frequencies in the vicinity of the resonance lines near 589 nm. The Na 3P12,323{P}_{\frac{1}{2},\frac{3}{2}}3P21​,23​​ states are excited with a low-intensity single-mode tunable dye laser at high Na densities and the frequency integral of the backscattered fluorescence intensity in the D1D1D1 and D2D2D2 lines is measured. As the laser is tuned through resonance, the loss of atomic excitation to the window appears as a sharp decrease in the frequency-integrated fluorescence intensity. For example, at 7\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 atoms ${\mathrm{m}}^{\ensuremath{-}3}$ the fluorescence intensity decreases by a factor of 4 in a frequency interval of 4 GHz. Measured absolute fluorescence intensities versus laser frequency are compared with predictions made using the theory of Hummer and Kunasz which includes both radiative and nonradiative transport processes. The agreement between theory and experiment is remarkably good when one considers that the theory contains only one unknown coefficient, i.e., the reflection coefficient for excited atoms at the windows. In our case the excited atoms are assumed to be completely destroyed at the window.
Sodium vapor, in the density range 1013{10}^{13}1013 to 5 \ifmmode\times\else\texttimes\fi{} 1014{10}^{14}1014 ${\mathrm{cm}}^{\ensuremath{-}3}$, was excited by a cw dye laser, tuned 20-150 GHz from either the D1{D}_{1}D1​ or D2{D}_{2}D2​ resonance line. We observed a three-peak scattered spectrum, consisting of the Rayleigh component at the laser frequency, and the two fluorescence components (direct and sensitized) at the atomic resonance-line frequencies. Corrections to the Rayleigh signals for anisotropy and polarization effects, and to the fluorescence signals for radiation trapping, were made in order to obtain the ratio of the sum of the total intensities of the two fluorescence components to that of the Rayleigh component. This ratio combined with a measurement of the line-wing absorption coefficient yields the sodium density and the DDD-line self-broadening rate coefficients [${k}_{\mathrm{br}}=4.67\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the D2{D}_{2}D2​ line and ${k}_{\mathrm{br}}=3.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the D1{D}_{1}D1​ line]. Asymmetry in the self-broadened line wings due to fine-structure recoupling was observed. The measured intensity ratio of the DDD lines, combined with pulsed measurements of the effective radiative decay rates in the presence of radiation trapping, yields the fine-structure collisional-mixing cross section [$\ensuremath{\sigma}(3{P}_{\frac{3}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}})=172$A˚2{\mathrm{\AA{}}}^{2}A˚2(\ifmmode\pm\else\textpm\fi{}18%)] at $T\ensuremath{\cong}300\ifmmode^\circ\else\textdegree\fi{}$ C. Our results are compared to other experiments and to theory.
We have experimentally studied the nonradiative transport of excitation in a dense [N[N[N=(0.3-2.5)\ifmmode\times\else\texttimes\fi{}${10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}]$ potassium vapor. We show that in such a high-density vapor the diffusive nonradiative transport of excitation via ``hopping'' of excitation in dipole-dipole collisions between excited- and ground-state atoms is dominant over the radiative transport through photons. The nonradiative transport mechanism becomes visible in the fluorescence-excitation spectrum signal as a sharp dip close to the resonance frequency. The appearance of the dip, its shape, width, and density dependence can all be explained in terms of a simple diffusion model for the nonradiative transport. This yields values for the diffusion coefficient and the resonance-exchange rate coefficient.
The propagation of light in a resonant atomic vapor can a priori be thought of as a multiple scattering process, in which each scattering event redistributes both the direction and the frequency of the photons. Particularly, the frequency redistribution may result in L\'evy flights of photons, directly affecting the transport properties of light in a resonant atomic vapor and turning this propagation into a superdiffusion process. Here, we report on a Monte Carlo simulation developed to study the evolution of the spectrum of the light in a resonant thermal vapor. We observe the gradual change of the spectrum and its convergence towards a regime of complete frequency redistribution as the number of scattering events increases. We also analyze the probability density function of the step length of photons between emissions and reabsorptions in the vapor, which governs the statistics of the light diffusion. We observe two different regimes in the light transport: superdiffusion when the vapor is excited near the line center and normal diffusion for excitation far from the line center. The regime of complete frequency redistribution is not reached for excitation far from resonance even after many absorption and reemission cycles due to correlations between emitted and absorbed frequencies.
The predictions of the incoherent scattering theory of the transport of resonance radiation developed by Holstein and by Biberman are shown to agree with laboratory measurements of the decay constants for the intensity of the mercury 2537 A resonance radiation following a period of optical excitation. Also, the relative importance of the diffusion of resonance atoms and the escape of resonance radiation as mechanisms for the destruction of mercury atoms in the 3P1^{3}P_{1}3P1​ or resonance state are determined from measurements of decay constants as a function of mercury density and cell radius. The experimental results show that diffusion of the resonance atoms is negligible and that the predictions of imprisonment theory are confirmed to within 15%. The experiment sets an upper limit to the diffusion coefficient at unit gas density for atoms in the 3P1^{3}P_{1}3P1​ state of 5\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 340\ifmmode^\circ\else\textdegree\fi{}K, which is consistent with a value of 4\ifmmode\times\else\texttimes\fi{}1016{10}^{16}1016 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ predicted using the frequency of excitation transfer collisions calculated by Holstein. The success of the theories based on completely incoherent scattering of resonance radiation points to the desirability of including this feature in the treatment of those astrophysical problems in which the spectral line shape is determined by Doppler broadening or by collision broadening.
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