The major results for the linear problem of diffuse reflection and transmission of radiation by a layer of finite thickness are carried over to the nonlinear case by successive application of Ambartsumyan’s approach for a one dimensional anisotropic medium. Formulas are given for nonlinear addition of layers which can be used to construct recurrence calculation procedures for uniform, periodic, and arbitrary stratified media. A complete set of differential equations for invariant imbedding is derived with the aid of these formulas. These equations are used to obtain a system of total invariance equations, which, in turn, offer the possibility of reducing the nonlinear problem of diffuse reflection and transmission during irradiation of a layer from both sides to the simpler problem of illuminating this medium from only one side, with the thickness of the layer remaining only as a fixed parameter. Finally, it is shown that the results obtained for the single frequency case (two-level atom) remain valid in the polychromatic case (multilevel atom), which is important for interpreting astrophysical data.
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Translated from Astrofizika, Vol. 53, No. 2, pp. 285–299 (May 2010).
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Pikichian, H.V. Nonlinear diffuse reflection and transmission of radiative energy by a layer of finite thickness. Astrophysics 53, 251–267 (2010). https://doi.org/10.1007/s10511-010-9116-y
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DOI: https://doi.org/10.1007/s10511-010-9116-y