Abstract
A two-stream analysis is applied to determine the generation threshold of a random gain medium in three cases of practical interest, namely a plane layer of finite width, a plane layer backed by a passive scattering layer and a plane layer with reflecting boundaries. Asymmetric and imperfect scattering are included in the analysis, while the non-uniform-gain case is treated by means of the transformed albedo equation du/dτ = a(τ)-b(τ)sin 2u where u = arctan R and a(τ), b(τ) are functions of optical depth. The two-stream model is validated by comparison with transport theory and provides simple analytical solutions to practical problems with an error generally less than 10%.
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