Coherent backscattering and localization in a self-attracting random walk model

Abstract

Intensity propagation of waves in dilute 2D and 3D disordered systems is well described by a random walk path-model. In strongly scattering media, however, this model is not quite correct because of interference effects like coherent backscattering. In this letter, coherent backscattering is taken into account by a modified, self-attracting random walk. Straightforward simulations of this model essentially reproduce the results of current theories on "non-classical" transport behavior, i.e. Anderson localization in 1D and 2D for any amount of disorder and a phase transition from weak to strong localization in 3D. However, in the strongly scattering regime corrections are necessary to account for the finite number of light modes due to their non-vanishing lateral extention. Within our model this correction leads to the observation that strong localization does not take place.

Observation of Anderson localization of light in three dimensions

“…1). As has also been found by simulations [35], in the case of localization the mean square displacement, ͗r 2 ͘, of photons saturates after a characteristic time, such that the effective D becomes proportional to 1 / t. This has been added to the behavior in Eq. (1), where the localization length is determined by the diffusion coefficient at early times and the time scale where the time dependence sets in, loc , i.e.…”