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Statistical properties of light propagation in finite-sized random amplifying layered media are studied by selecting the physical solutions according to a criterion in the framework of the time-independent Maxwell's equation. The criterion is demonstrated to be qualitatively correct. We find that the probability of the physical solution, P, decays exponentially with sample size L. Both P and the statistics of the reflection and the transmission coefficients obey a two-parameter scaling, i.e., Λ ≡ L/ξ o and q ≡ ξ o H g , where ξ o is the localization length in the absence of gain and l g is the gain length. It is also found that, in the limit of large L, the localization length remains unchanged in the presence of gain.

Light amplification and localization in random amplifying layered media: Statistics from physical solutions