Abstract
We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation.
Highlights
As far as the influence of dissipative effects such as stimulated Raman scattering can be ignored, light propagation in single-mode optical fibers is well described by the one-dimensional (1D) scalar nonlinear Schrodinger (NLS) equation (see Eq (1) below) [1]
The kinetic approach allows us to derive an analytical expression of evolution of the spectrum, whose damped oscillations have been found in agreement with the numerical simulations of both the NLS and kinetic equations
We have studied the nonlinear evolution of incoherent light waves whose propagation is governed by the integrable 1D scalar NLS Eq (1)
Summary
As far as the influence of dissipative effects such as stimulated Raman scattering can be ignored, light propagation in single-mode optical fibers is well described by the one-dimensional (1D) scalar nonlinear Schrodinger (NLS) equation (see Eq (1) below) [1] This equation is integrable and has a class of special solutions called bright and dark solitons, which are sustained in the anomalous (focusing) and normal (defocusing) dispersion regimes respectively. In particular a general method to derive kinetic equations describing the evolution of the spectral distribution function of solitons has been proposed [6] This method seems promising for future investigations of nonlinear propagation of incoherent optical waves in single mode optical fibers
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