Wave transmission through lossy media in the strong localization regime

The asymptotically exact expressions for all statistical moments of the transmission coefficient are obtained for a 1D disordered lossy system. It is shown that even arbitrary small absorption leads to the spectrum quantization of the Fokker-Planck equation. The quantization reveals itself as the appearance of a new scale: the disorder-induced absorption length. Classical wave propagation in randomly layered are thoroughly studied by the moment. Recent progress in experimental technique has been renewed interest in 1D and quasi-1D systems. Much attention has recently been paid to propagation in disordered structures with dissipation caused by inelastic scattering processes. In the presence of inelastic scattering the coherence is destroyed by phase-breaking processes. There exists also the problem of absorption effect that does not imply any incoherent randomizing in a system. The simplest way to take into account absorption is to bring a complex-valued scattering potential into wave transport problems. The authors examined a model containing both absorption and disorder. This problem coincides with the well-known problem of the theory of classical wave propagation through a randomly layered medium in the presence of a finite absorption, which is of particular interest for many reasons. First, all real media always have absorption due to the finite conductivity. Second, some two- and three-dimensional problems may be mapped onto the 1D Schrodinger equation with effective complex-valued potential. Third, the 1D disordered system is the only model expected to be exactly soluble, where the effect of absorption can be studied rigorously. The first results for the power reflection coefficient from a lossy one-dimensional medium were obtained almost twenty years ago. Nevertheless, up to now there has been no method devised to calculate analytically the statistical moments of transmitted energy through a slab where both scattering and absorption are present