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Physical Review

Resonance Absorption of Sunlight in Twilight Layers

THOMAS M. DONAHUE, Robert J. Resnick

Published Jun 15, 1955• 13 citations
Publisher

Abstract

Solar radiation must pass at least once through the absorbing layer to reach the twilight zone of a layer of atoms scattering resonance radiation. The attenuation of the solar beam is calculated for resonance absorption and the resulting scattered intensity compared with the transparent layer model intensity for the same thickness of material. It is shown that in the case of sodium, the reduction in intensity for layers thicker than ${10}^{9}$ atoms/${\mathrm{cm}}^{2}$ is too serious to permit the deduction of layer thickness from a simple theory which neglects imprisonment of resonance radiation.

DOI
10.1103/physrev.98.1622

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Solar radiation must pass at least once through the absorbing layer to reach the twilight zone of a layer of atoms scattering resonance radiation. The attenuation of the solar beam is calculated for resonance absorption and the resulting scattered intensity compared with the transparent layer model intensity for the same thickness of material. It is shown that in the case of sodium, the reduction in intensity for layers thicker than 109{10}^{9}109 atoms/cm2{\mathrm{cm}}^{2}cm2 is too serious to permit the deduction of layer thickness from a simple theory which neglects imprisonment of resonance radiation.
The features of resonance fluorescence and absorption of resonance laser radiation in atomic vapors in a superthin cell with thickness L of the order of a wavelength lambda are investigated theoretically. Taking into account the Fabry-Perot interference effect, it is found that the dependence of the fluorescence and absorption spectra on the ratio L/lambda is substantially different. Coherent spectral narrowing - the Dicke effect - when L=(2n+1)lambda/2 and broadening of the spectral line when L = n lambda (n is a whole number) are observed in the absorption spectra. This effect is absent in the spector of resonance fluorescence in extended media. It is also shown that the processes of saturation and optical pumping significantly alter the spectral line shape as the laser intensity increases; in particular, additional sub-Doppler dips appear at the frequency of the atomic transitions. Calculated curves are given for the D2 lines of ^85Rb atoms. © 2004 Optical Society of America
The absorption of the resonance radiation (2536A) of mercury was studied by dividing the radiation from a resonance lamp into two parts, each part going into a separate photo-electric cell. An absorption cell containing mercury vapor whose pressure could be controlled by cooling a side tube was placed in the path of one beam. The ratio of the amount of light passing into each beam could be varied by a mechanical device. From the setting of the mechanical device, giving a balance between the two photo-electric currents, the absorption of the mercury vapor could be inferred. The absorption per atom was calculated and found to decrease rapidly as the total amount of absorbing vapor was increased, thus showing that the resonance radiation is not homogeneous. The maximum atomic absorption coefficient was 11\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$, which indicates that an atom can stop the radiation which falls upon an area one hundred times larger than its cross sectional area.
Resonant light diffraction by an atomic beam of sodium has been uncovered by careful measurements of the spatial dependence of the absorption. Recently developed modulation techniques made such measurements possible. Both on-resonance and off-resonance excitations as well as the influence of intense fields have been studied. The observed spatial behavior is in good agreement with a preliminary calculation based on the interference between the field scattered by the atoms and the excitation field.
The description of the self-imprisonment of resonance radiation in gases or solids and of the density distribution of excited species depends upon a transmission coefficient $T(\ensuremath{\rho})$, the probability that a quantum of emitted radiation will traverse a thickness $\ensuremath{\rho}$ of material. This coefficient is shown to be given by the rapidly convergent series $T(\ensuremath{\rho})=\ensuremath{\Sigma}{n}^{}\frac{{(\ensuremath{-}{k}_{0}\ensuremath{\rho})}^{n}}{n!{(n+1)}^{\frac{1}{2}}}$, where k0{k}_{0}k0​ is a constant characteristic of the excited species and of the temperature. The above expression is used to give the first accurate discussion of resonance radiation confined between infinite parallel planes, and of radiation inside a sphere over a wide range of ${k}_{0}\ensuremath{\rho}$ values.
The phenomena which take place during the time of propagation of a monochromatic pulse of a resonance radiation through optically dense on the transition frequency medium containing resonance absorbing centers are considered. Due to the action of the pulse of the resonance radiation the saturation of absorption in the layer of the medium takes place. As a result the absorption decreases in the layer and the radiation penetrates into the next layer. Thus translucent region continuously moves deeper into the medium and the process is wavelike.When the density of the initial photon flux is constant and the distribution of absorbing centers is homogeneous the absorption coefficient and the photon density in the depth of the media depends only on the variable $t\phantom{\rule{0.15em}{0ex}}\ensuremath{-}\phantom{\rule{0.15em}{0ex}}x/v$. The velocity of translucency wave v may be by several orders of magnitude less than the velocity of light. The mechanism of the saturation can be various. The small value of the loss of photons in the transluced region of the medium is the necessary condition for the rise of translucent waves. The condition of realization of translucent wave is fulfilled for a large number of condensed states having intense absorption lines. These conditions are the most favourable in the case of presence of methastable levels between the levels 1 and 2 (type-ruby system). The effect of the translucent waves is general for various ranges of spectrum of electromagnetic radiation and may be realized in astrophysical scale.
In Chapter 3, we move to a semiclassical treatment (quantum theory) of light absorption and scattering, specifically from atoms. We start with a description of how lidar measures Doppler shift, and the fundamental difference between the measurement when the laser is in resonance with an atomic transition (resonant) and when it is not (nonresonant). We follow with a treatment of quantum polarizability and the resulting absorption cross section, leading to the differential resonance scattering cross section and its contrast with the classical result. After quantum polarizability, we demonstrate the radiation pattern of coherently excited atoms. This takes us to an interpretation of the Hanle Effect. Following these descriptions of the phenomena that impact resonance lidar, we extend our understanding by closing the chapter with an overview of the rudimentary physics of sodium laser guide stars.