23 research outputs found
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 is a broad distribution with a large
maximum at/near mid-waveguide, depending universally (for given ) on the
ratio of the length of the disorder segment to the localization length,
. 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 close to 1, which decays faster the lower
is . Evidence is given of the self-averaging nature of the random
quantity . Higher-order moments of the intensity are
also shown.Comment: 9 pages, 9 figure