Wave localization in anisotropic random media

Abstract

As a phenomenon generic to waves in random media, localization has many general features common to both quantum particles, e.g., electrons, and classical waves, e.g., electromagnetic and elastic waves. One such aspect is that all waves localize in two- or one-dimensional systems with an arbitrary amount of randomness, and that in three dimensions a wave localizes only in certain energy regimes that are separated from the delocalized regimes by so-called mobility edges. In this paper, the results of recent work on the anisotropic dimensional crossover behavior for wave localization are described. Starting from a randomly layered medium, some scattering centers were introduced, i.e., inhomogeneities, into each of the layers in a controlled manner. These inhomogeneities cause the wave to scatter out of the layering direction. When the strength and the density of the scattering inhomogeneities become equal to the randomness encountered in propagating from layer to layer, then the system becomes an isotropic, 3-D random medium. Therefore, in increasing the scattering strength and density of the scatterers there is essentially a “cross over” from one-dimensional randomness, where all waves are localized, to isotropic three-dimensional randomness, where there can be mobility edges. What is found is that there is a critical anisotropy below which the system behaves as 1 D and above which the system behaves as 3 D. In other words, the transition is achieved in a discontinuous manner. The talk will emphasize the underlying physics of the localization and its anisotropic critical transition.