Localization of Classical Waves in Weakly Scattering Two-Dimensional Media with Anisotropic Disorder

We study the localization of classical waves in weakly scattering 2D systems with anisotropic disorder. The analysis is based on a perturbative path-integral technique combined with a spectral filtering that accounts for the first-order Bragg scattering only. It is shown that in the long-wavelength limit the radiation is always localized, and the localization length is independent of the direction of propagation, the latter in contrast to the predictions based on an anisotropic tight-binding model. For shorter wavelengths that are comparable to the correlation scales of the disorder, the transport properties of disordered media are essentially different in the directions along and across the correlation ellipse. There exists a frequency-dependent critical value of the anisotropy parameter, below which waves are localized at all angles of propagation. Above this critical value, the radiation is localized only within some angular sectors centered at the short axis of the correlation ellipse and is extended in other directions.Comment: 10 pages, 5 figure

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

Ueber eine besondere Art monocularer Relief-Anschauung

UEBER EINE BESONDERE ART MONOCULARER RELIEF-ANSCHAUUNG Ueber eine besondere Art monocularer Relief-Anschauung (9) (-

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