Weak Langmuir turbulence in disordered multimode optical fibers

TL;DR

This paper develops a simplified kinetic model for weak Langmuir turbulence in disordered multimode optical fibers, revealing new nonlinear mode couplings and collective incoherent soliton states, validated by numerical simulations.

Contribution

It derives a scalar kinetic equation from the multimode NLS equation that captures weak Langmuir turbulence phenomena in disordered fibers, including novel nonlinear effects.

Findings

Identification of a new nonlinear coupling due to the Raman effect.

Discovery of collective incoherent soliton states with synchronized spectral oscillations.

Validation of the kinetic model through numerical simulations showing quantitative agreement.

Abstract

We consider the propagation of temporally incoherent waves in multimode optical fibers (MMFs) in the framework of the multimode nonlinear Schr\"odinger (NLS) equation accounting for the impact of the natural structural disorder that affects light propagation in standard MMFs (random mode coupling and polarization fluctuations). By averaging the dynamics over the fast disordered fluctuations, we derive a Manakov equation from the multimode NLS equation, which reveals that the Raman effect introduces a previously unrecognized nonlinear coupling among the modes. Applying the wave turbulence theory on the Manakov equation, we derive a very simple scalar kinetic equation describing the evolution of the multimode incoherent waves. The structure of the kinetic equation is analogous to that developed in plasma physics to describe weak Langmuir turbulence. The extreme simplicity of the derived kinetic equation provides physical insight into the multimode incoherent wave dynamics. It reveals the existence of different collective behaviors where all modes self-consistently form a multimode spectral incoherent soliton state. Such an incoherent soliton can exhibit a discrete behavior characterized by collective synchronized spectral oscillations in frequency space. The theory is validated by accurate numerical simulations: The simulations of the generalized multimode NLS equation are found in quantitative agreement with those of the derived scalar kinetic equation without using adjustable parameters.