Energy exchange in fast optical soliton collisions as a random cascade model

TL;DR

This paper models energy exchange in optical soliton collisions as a random cascade process, revealing multifractal statistical properties and power-law behaviors in soliton amplitude dynamics during propagation.

Contribution

It introduces a novel analogy between optical soliton energy exchange and turbulence cascade models, applying multifractal analysis to characterize soliton amplitude statistics.

Findings

Soliton amplitude dynamics follow multifractal statistics.

Power-law decay of correlation functions and error rates with propagation distance.

Analytical expressions relate exponents to multifractal spectrum.

Abstract

We study the dynamics of a probe soliton propagating in an optical fiber and exchanging energy in fast collisions with a random sequence of pump solitons. The energy exchange is induced by Raman scattering or by cubic nonlinear loss/gain. We show that the equation describing the dynamics of the probe soliton's amplitude has the same form as the equation for the local space average of energy dissipation in random cascade models in turbulence. We characterize the statistics of the probe soliton's amplitude by the \tau_{q} exponents from multifractal theory and by the Cram\'er function S(x). We find that the n-th moment of the two-time correlation function and the bit-error-rate contribution from amplitude decay exhibit power-law behavior as functions of propagation distance, where the exponents can be expressed in terms of \tau_{q} or S(x).