Backscattering and localization of high-frequency waves in a one-dimensional random medium

Abstract
Total reflection of waves by a one-dimensional random medium is superficially inconsistent with the decoupling of forward and backward propagating waves in the WKB limit (when no real turning points are present). Actually, complex turning points yield exponentially small reflection terms; in the random case, their cumulative effect over large distances can be evaluated using Fokker–Planck techniques, and total reflection is recovered. We also calculate the localization length as a function of wavenumber and strength of the random fluctuations.