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

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/l_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.