COHERENTLY AMPLIFYING RANDOM MEDIUM - STATISTICS OF SUPER-REFLECTION

Light-wave propagation in a randomly scattering but uniformly and cohe rently amplifying optical medium is analysed for the statistics of the coefficient of reflection r(l) that may now exceed unity, hence super -reflection. Uniform coherent amplification is introduced phenomenolog ically through a constant negative imaginary part added to the otherwi se real dielectric constant of the medium, assumed random. The probabi lity density p (r, I) for the reflection coefficient, calculated in a random phase approximation, tends to an asymptotic form p(r, infinity) having a long tail with divergent mean (r) in the limit of weak disor der but with the sample length I (measured in units of the localizatio n length in the absence of gain) much greater than 1. This super-refle ction is attributed to a synergetic effect of localization and coheren t amplification, as distinct from the classically diffusive path-lengt h prolongation. Our treatment is based on the invariant-imbedding meth od for the one-channel (single-mode) case, and is in the spirit of the scattering approach to wave transport as pioneered by Landauer. Gener alization to the multichannel case is pointed out. Relevance to random lasers, and some recent results for a sub-meanfree path sample are al so briefly discussed. (C) 1998 Academic Press Limited.