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Australian Journal of Physics

Diffuse Reflection and Transmission by Uniform Noncoherently Scattering Media

RBT Black

Published Jun 1, 1967• 1 citation
Publisher

Abstract

Diffusely reflected and transmitted spectral line profiles are calculated for uniform noncoherently scattering media onto which radiation of frequency near that of a resonance line of the medium is incident. Profiles are calculated for incident light that is either collimated or unifQrmly diffused and that is either monochromatic, or of uniform frequency distribution, or contains an absorption line centred on the resonance line under discussion. Spectral lines generated by uniformly excited media are also calculated.

DOI
10.1071/ph670271

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Diffusely reflected and transmitted spectral line profiles are calculated for uniform noncoherently scattering media onto which radiation of frequency near that of a resonance line of the medium is incident. Profiles are calculated for incident light that is either collimated or unifQrmly diffused and that is either monochromatic, or of uniform frequency distribution, or contains an absorption line centred on the resonance line under discussion. Spectral lines generated by uniformly excited media are also calculated.
The coherent, radiative excitation modes of a resonant medium lend a resonant character to the amplitudes for reflection and transmission of light. For a plane wave incident upon a slab-shaped medium of two-level atoms, the reflection and transmission coefficients exhibit sharp peaks and dips as a function of the detuning of the wave from the central atomic resonance frequency. The locations and widths of these resonant features for a normally incident plane wave correspond to the imaginary and real parts, respectively, of the radiative decay constants of the coherent excitation modes of the medium discussed in the preceding paper [Phys. Rev. A 61, 063814 (2000)]. For the case of oblique incidence, generalizations of the modes discussed in the preceding paper are required. The richly detailed, resonant frequency dependence of the reflected and transmitted intensities is shown to depend significantly on the angle of incidence and the polarization of the incident light.
Scattering of polychromatic light by a medium whose dielectric susceptibility is a random function of position is considered within the accuracy of the first Born approximation. It is shown, in particular, that if the two-point spatial correlation function of the dielectric susceptibility has Gaussian form and the spectrum of the incident light has a Gaussian profile, the spectrum of the scattered light may be shifted toward the shorter or the longer wavelengths, depending on the angle of scattering. The results are analogous to those derived recently in connection with radiation from partially coherent sources [ Nature (London)326, 363 ( 1987)].
The scattering of radiation in the presence of collisions can be described quantum-mechanically in terms of essentially two processes. The first may be thought of as an absorption to the excited state followed subsequently (after propagating in the excited state) by emission. This gives rise to radiation redistributed about the transition frequency. The effects of m-degeneracy are particularly interesting for this first process. As an example a case is considered in which the incident frequency is in the quasi-static line wing, while the scattered frequency is close to the line center. It is found that under these circumstances the dominant contribution from this process in the scattered spectrum is obtained for an absorption of the incident frequency taking place during a strong (close) collision and reemission of the scattered frequency when the atom is essentially unperturbed
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.