Mobility Edge in Aperiodic Kronig-Penney Potentials with Correlated Disorder: Perturbative Approach

It is shown that a non-periodic Kronig-Penney model exhibits mobility edges if the positions of the scatterers are correlated at long distances. An analytical expression for the energy-dependent localization length is derived for weak disorder in terms of the real-space correlators defining the structural disorder in these systems. We also present an algorithm to construct a non-periodic but correlated sequence exhibiting desired mobility edges. This result could be used to construct window filters in electronic, acoustic, or photonic non-periodic structures.Comment: RevTex, 4 pages including 2 Postscript figure

Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder

We present first analytical results on transport properties of many-mode waveguides with rough surfaces having long-range correlations. We show that propagation of waves through such waveguides reveals a quite unexpected phenomena of a complete transparency for a subset of propagating modes. These modes do not interact with each other and effectively can be described by the theory of 1D transport with correlated disorder. We also found that with a proper choice of model parameters one can arrange a perfect transparency of waveguides inside a given window of energy of incoming waves. The results may be important in view of experimental realizations of a selective transport in application to both waveguides and electron/optic nanodevices.Comment: RevTex, 4 pages, no figures, few references are adde

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 s-like 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 given $T_{c}$) on the ratio of the length of the disorder segment to the localization length, $L/\xi$. The same universality is observed in the spatial distribution of the intensity inside typical (non-resonant with respect to the transmission coefficient) realizations, presenting a s-like shape similar to that of the total average intensity for $T_{c}$ close to 1, which decays faster the lower is $T_{c}$. Evidence is given of the self-averaging nature of the random quantity $\log[I(x)]/x\simeq -1/\xi$. Higher-order moments of the intensity are also shown.Comment: 9 pages, 9 figure