Self-Similar Modes of Coherent Diffusion

TL;DR

This paper derives, measures, and demonstrates self-similar solutions of the coherent diffusion equation, revealing novel contraction behaviors and phase dynamics in optical diffusion experiments.

Contribution

It introduces a generalized set of self-similar solutions with nonuniform phase surfaces based on Gaussian modes, and experimentally verifies their diffusion and contraction behaviors.

Findings

Self-similar solutions exhibit algebraic decay with mode order.

Experimental observation of phase and amplitude self-similarity.

Detection of self-similar contraction, contrary to typical diffusion spreading.

Abstract

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical diffraction. In an experiment of light storage in a gas of diffusing atoms, a complex initial condition is imprinted, and its diffusion dynamics is monitored. The self-similarity of both the amplitude and the phase pattern is demonstrated, and an algebraic decay associated with the mode order is measured. Notably, as opposed to a regular diffusion spreading, a self-similar contraction of a special subset of the solutions is predicted and observed.