Transition from diffusive to localized regimes in surface corrugated waveguides

Exact calculations of transmission and reflection coefficients in surface r andomly corrugated waveguides are presented. The elastic scattering of diff use light or other classical waves from a rough surface induces a diffusive transport along the waveguide axis. As the length of the corrugated part o f the waveguide increases, a transition from the diffiusive to the localize d regime is observed. This involves an analogy with election conduction in nanowires, and hence, a concept analogous to that of "resistance" can be in troduced. An oscillatory behavior of different transport properties (elasti c mean free path, localization length, enhanced backscattering,...) versus the wavelength is predicted. An analysis of the transmission coefficients ( transmitted speckle) shows that as the length of the corrugated part of the waveguide increases there is a strong preference to forward coupling throu gh the lowest mode. This marks a clear anisotropy in the forward propagatio n which is absent in tile case of volume disorder. The statistics of reflec tion coefficients is analyzed, first using random matrix theory (RMT) to an alytically deduce the probability densities in the localization regime, aft erwards exact numerical calculations of the coupling to backward modes in s urface corrugated waveguides will he put forward for comparison. We show th at the reflected speckle distributions are independent of the transport reg ime, at variance with the regime transition found in the transmission case. Despite the strong anisotropy, the analysis of the probability distributio ns of both transmitted and reflected waves confirms the distributions predi cted by Random Matrix Theory for volume disorder.