Anisotropy of localized states in an anisotropic disordered medium

TL;DR

This paper investigates how anisotropy affects Anderson localization of scalar waves in disordered media, revealing that moderate anisotropy influences mode shapes and lifetimes without altering critical transition properties.

Contribution

It demonstrates that anisotropy modifies the spatial shape and lifetime of localized modes while leaving the localization transition characteristics unchanged.

Findings

Localized modes are anisotropic in shape.

Modes with longer lifetimes are more anisotropic.

Critical exponents are unaffected by moderate anisotropy.

Abstract

We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the localization transition are found to be unaffected by the anisotropy provided that the determinant of the anisotropy tensor is kept equal to one upon introducing the anisotropy. Localized modes have anisotropic spatial shapes although their anisotropy is weaker than the one expected from purely geometric considerations. The modes with the longest lifetimes are found to be the most anisotropic and their anisotropy increases with the size of the disordered medium.