Local and average fields inside surface-disordered waveguides: Resonances in the one-dimensional Anderson localization regime

We investigate the one-dimensional propagation of waves in the Anderson localization regime, for a single-mode, surface disordered waveguide. We make use of both an analytical formulation and rigorous numerical simulation calculations. The occurrence of anomalously large transmission coefficients for given realizations and/or frequencies is studied, revealing huge field intensity concentration inside the disordered waveguide. The analytically predicted dependence of the average intensity, being in good agreement with the numerical results for moderately long systems, fails to explain the intensity distribution observed deep in the localized regime. The average contribution to the field intensity from the resonances that are above a threshold transmission coefficient ${T}_{c}$ is a broad distribution with a large maximum at/near mid-waveguide, depending universally (for a given ${T}_{c})$ on the ratio of the length of the disorder segment to the localization length, $L/\ensuremath{\xi}.$ The same universality is observed in the spatial distribution of the intensity inside typical (nonresonant with respect to the transmission coefficient) realizations, presenting a shape similar to that of the total average intensity, but with a faster decay. Evidence is given of the self-averaging nature of the random quantity $\mathrm{ln}[I(x)]/x\ensuremath{\simeq}\ensuremath{-}1/\ensuremath{\xi}.$ Higher-order moments of the intensity are also shown.