We analyze the line shape and width of atomic coherent-population-trapping (CPT) resonances excited by laser beams with different transverse intensity profiles. A dramatic difference in the resonance line shape is found when comparing a beam with a ``steplike'' profile to a beam with a Gaussian profile. In particular, for nonuniform profiles, a non-Lorentzian functional form is given that is more appropriate for describing the nonlinear resonance line shape than is a conventional Lorentzian. Our analysis is supported by measurements of CPT line shapes in a thermal vapor of
85Rb.Absorption profiles of cesium resonance lines at 8521 and 8944 \AA{} have been measured for the wavelength range from 0.5 to 30 \AA{} from the line centers using a tungsten ribbon light source, cell lengths
L from 0.31 to 6.1 cm, and Cs densities
N from 2 \ifmmode\times\else\texttimes\fi{}
1014 to 2 \ifmmode\times\else\texttimes\fi{}
1016 ${\mathrm{cm}}^{\ensuremath{-}3}$. The wavelength dependence of the absorption coefficients are consistent with a Lorentzian form and values of $\frac{\ensuremath{\gamma}f}{N}=1.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ and 0.30 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$
cm3 ${\mathrm{sec}}^{\ensuremath{-}1}$ are obtained for 8521 and 8944 \AA{} lines. Here $\ensuremath{\gamma}$ is the collisional (or Lorentzian) half-width and
f is the oscillator strength. The values of $\frac{\ensuremath{\gamma}f}{N}$ deduced from total fractional absorption data agree with those determined from the line profiles. Our results agree well (to within 15%) with those of Gregory and with theory, but disagree with more recent data. A source of error in some previous determinations of half-widths is the fact that even when the calculated absorption is very large, the measured transmission at the line center is significant; about 3.5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ compared to \ensuremath{\sim} ${10}^{\ensuremath{-}100,000}$ predicted from our measurements in the wings of the lines for $N=1.14\ifmmode\times\else\texttimes\fi{}{10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and
L=5.9 cm. This effect is shown to result from transmission through the monochromator at wavelengths in the far wings of the instrument function.
We have studied trapping of resonance radiation under conditions of moderate to low line-center optical depths in sodium-argon mixtures. We report measured effective radiative decay rates, which are compared with predictions of the Post [Phys. Rev. A 33, 2003 (1986)] and the Milne [J. Lond. Math. Soc. 1, 40 (1926)] theories of radiation trapping. These theories are expected to be valid for spectral lines with low to moderate line-center optical depths, where the commonly used Holstein [Phys. Rev. 72, 1212 (1947); 83, 1159 (1951)] theory of radiation trapping is expected to break down. The experiment was performed under conditions in which the trapping was dominated by either the Doppler-broadened Gaussian or by the impact-broadened Lorentzian line-shape function. The measured effective radiative decay rates agree well with those predicted by the Milne and Post theories over the range of low to moderate optical depth.
Population and alignment relaxation for the Doppler broadening case in the infinite plane parallel geometry has been studied in the range of the optical thickness at the line center between ${10}^{\mathrm{\ensuremath{-}}3}$ and
102. The obtained population and alignment relaxation rates are compared with analytical estimates. The validity of two approximations used in the estimates, i.e., the complete frequency redistribution of absorbed and successively emitted photons and the pure-parabolic distribution of excited atoms, is discussed. Also studied is the mixing of the population and the alignment, which is due to the spatial anisotropy of the geometry. This mixing leads to the self-alignment effect, which develops at a sufficiently late time after excitation. A separate simulation with the alignment effect omitted has revealed that, at a large optical thickness, the population relaxation rate agrees with the result with the alignment effect included. It is therefore concluded that the previous estimate on the influence of the self-alignment to the population relaxation rate is too large. The velocity distribution of the excited atoms in the direction perpendicular to the planes shows an effectively lower (higher) temperature at the center (boundary) than the base temperature (\ensuremath{\approxeq}5%) under the self-alignment condition.
An eigenvalue problem for decay modes of resonance radiation proposed by Holstein is solved by a variational method and some higher decay modes are obtained by rigorous calculations of matrix elements when enclosure geometry is an infinite slab and the line-shape is due to Doppler broadening. Holstein's intergo-differential equation is extended to include the effect of external radiation and the contributions of higher modes to output radiation are calculated after stationary external radiation irradiated perpendicularly to one of the surfaces of the slab is abruptly cut off. This result is not consistent with the strange experimental results for mercury 2537 Å radiation obtained by Mochizuki and Fowler–advancement of the relative phase of the output radiation when the intensity of external radiation is modulated sinusoidally–and it is concluded that the reason for their results should be found in some unknown mechanisms.
The resonance fluorescence of a crystalline solid consisting of two-level atoms is studied. The method of Heitler and Ma (1949) is used to solve the equations. From the calculated result, it is found that the probability of emission of photons is discrete in angular and in wavelength distributions. The emission line in the incident direction is identical in shape with the absorption line. While there is no actual trapping of radiation, the effect of photon-trapping manifests itself in both the emission and the absorption spectra.