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

TL;DR

This paper investigates how classical waves become localized in weakly scattering two-dimensional media with anisotropic disorder, revealing that localization depends on wavelength, direction, and disorder anisotropy.

Contribution

It introduces a perturbative path-integral method to analyze wave localization in anisotropic 2D media, highlighting the effects of wavelength and disorder anisotropy on localization behavior.

Findings

Long-wavelength waves are always localized regardless of direction.

Localization length is isotropic in the long-wavelength limit.

At shorter wavelengths, localization depends on the direction relative to the disorder anisotropy.

Abstract

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.