Super-diffusion in optical realizations of Anderson localization

TL;DR

This paper investigates how temporal fluctuations in random optical potentials affect Anderson localization, revealing that such fluctuations can induce super-diffusive transport, often faster than ballistic, with implications for optical experiments.

Contribution

It introduces a spectral decomposition approach to analyze the breakdown of Anderson localization due to time-dependent potentials in optics, highlighting anomalous diffusion behaviors.

Findings

Temporal fluctuations destroy Anderson localization in optical systems.

Spectral analysis links diffusion rates to potential's spectral intensity.

Super-diffusive transport occurs when localization is broken by fluctuations.

Abstract

We discuss the dynamics of particles in one dimension in potentials that are random both in space and in time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is suppressed by random fluctuations in the refractive index. If the refractive index fluctuates along the direction of the paraxial propagation of the beam, the localization is destroyed. We analyze this broken localization, in terms of the spectral decomposition of the potential. When the potential has a discrete spectrum, the spread is controlled by the overlap of Chirikov resonances in phase space. As the number of Fourier components is increased, the resonances merge into a continuum, which is described by a Fokker-Planck equation. We express the diffusion coefficient in terms of the spectral intensity of the potential. For a general class of potentials that are commonly used in optics, the solutions of the Fokker-Planck equation exhibit anomalous diffusion in phase space, implying that when Anderson localization is broken by temporal fluctuations of the potential, the result is transport at a rate similar to a ballistic one or even faster. For a class of potentials which arise in some existing realizations of Anderson localization atypical behavior is found.