Effect of evanescent channels on position-dependent diffusion in disordered waveguides

Wave interference leads to deviations from the diffusive description of wave propagation through a random medium. This is a manifestation of an onset of Anderson localization – a paradigm in mesoscopic physics [1–3]. Self-consistent theory (SCT) of localization [4,5] accounts for the wave interference effects by renormalizing (reducing) the diffusion coefficient. In an experiment, one deals with samples of finite size. In such an open system, the SCT predicts [6–9] that the diffusion coefficient becomes position dependent. This is because the wave can escape through a boundary and hence reduce interference corrections. Localization in finite media can be studied in quasi-one-dimension (quasi-1D) where the transition from diffusion to localization occurs with an increase in the system length [10]. A wire for an electronic system or a random waveguide as an optical counterpart are examples of quasi-1D systems. Position dependence of the diffusion coefficient has been demonstrated [11,12] in ab-initio numerical simulations of wave transport in a disordered waveguide. Details of the microscopical disorder become evident in the near-field [13,14] and play an important role in the transport of the electromagnetic waves in random media [15]. The evanescent fields are an inseparable part of the quasi-modes of the open random media considered in transport geometry. In optical systems considered here, quasi-modes [16] are used to explain the effect of coherent random lasing [17–20]. Fluctuations of the local density of states [21–23] and the related spatial intensity correlations [24,25] carry information about near-fields; thus they are sensitive to the microscopical details of the disorder and are not universal. The position-dependent diffusion coefficient is defined as the ratio between local statistically averaged flux and the gradient of energy density. Because both of the latter two parameters should be smooth on the scales less than transport mean free path, the position