Nonlinear diffuse reflection and transmission of radiative energy by a layer of finite thickness |
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| Authors: | H V Pikichian |
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| Institution: | 1.V. A. Ambartsumyan Byurakan Astrophysical Observatory,Byurakan,Armenia |
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| Abstract: | 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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