Self-Similar Modes of Coherent Diffusion

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.

10 pages, 5 figures

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• Phase gradient protection of stored spatially multimode perfect optical vortex beams in a diffused rubidium vapor
• Shape-preserving diffusion of a high-order mode
• Structured beams invariant to coherent diffusion
• Diffusion Effects in Gradient Echo Memory
• Anomalous transport in periodic photonic chains with designed loss
• Continuous generation of delayed light