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Non-conventional Anderson localization in a matched quarter stack with metamaterials | E.J.Torres-Herrera
; F.M.Izrailev
; N.M.Makarov
; | Date: |
3 Mar 2013 | Abstract: | We study the problem of non-conventional Anderson localization emerging in
bilayer periodic-on-average structures with alternating layers of materials
with positive and negative refraction indices $n_a$ and $n_b$. Main attention
is paid to the model of the so-called quarter stack with perfectly matched
layers (the same unperturbed by disorder impedances, $Z_a=Z_b$, and optical
path lengths, $n_ad_a=|n_b| d_b$, with $d_a$, $d_b$ being the thicknesses of
basic layers). As was recently numerically discovered, in such structures with
weak fluctuations of refractive indices (compositional disorder) the
localization length $L_{loc}$ is enormously large in comparison with the
conventional localization occurring in the structures with positive refraction
indices only. In this paper we develop a new approach which allows us to derive
the expression for $L_{loc}$ for weak disorder and any wave frequency $omega$.
In the limit $omega
ightarrow 0$ one gets a quite specific dependence,
$L^{-1}_{loc}proptosigma^4omega^8$ which is obtained within the fourth order
of perturbation theory. We also analyze the interplay between two types of
disorder, when in addition to the fluctuations of $n_a$, $n_b$ the thicknesses
$d_a$, $d_b$ slightly fluctuate as well (positional disorder). We show how the
conventional localization recovers with an addition of positional disorder. | Source: | arXiv, 1303.0521 | Services: | Forum | Review | PDF | Favorites |
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