Effective Transport Equations and Enhanced Backscattering in Random Waveguides

In this paper we derive a general system of transport equations for the moments of reflected and transmitted mode amplitudes in a randomly perturbed waveguide, in a regime where backscattering is significant. The derivation is based on a limit theorem for the system of coupled differential equations for the mode amplitudes, in the limit where the amplitude of the random fluctuations of the medium is small, the correlation lengths in the transverse and longitudinal directions are of the same order of the wavelength, and the waveguide is long. Using this system we derive several results in specific regimes, including the enhanced backscattering phenomenon for the reflected wave: when an incoming monochromatic wave with a specific incidence angle is present, the mean reflected power has a local maximum in the backward direction twice as large as the mean reflected power in the other directions.