Modeling one-dimensional optical turbulence

Overview & Synopsis

Studying non-linear optics systems is of practical importance because it applies to systems such as optical fibers and liquid crystals but also of theoretical importance because non-linear light exhibit properties very similar to hydrodynamics. Non-linear optics are modeled by an non-integrable equation which contains a rich physics. In this thesis, we explore two aspects of this equation. We first analyse the propagation of localized structures in this system and we conclude that the system tends to a final state which acts as a statistical attractor. We identify this attractor as a bound-state, a localized structure which oscillates in amplitude and in width and which propagates among weakly non-linear waves.We also study the turbulent cascades of this system with the help of an reduced model of the wave kinetics. This reduced model allows us to derive the Kolmogorov-Zakharov spectra of cascading quantities. The Kolmogorov-Zakharov spectrum for the wave-action is found to be non-local and replaced by a no-local prediction. These theoretical predictions are then compared to numerical simulations and show an overall good accordance with numerics, particularly for the non-local spectrum of wave-action. Such numerical simulations show the existence of Incoherent Solitons, which are localized structures propagating with an envelope approximately constant but with propagation of smaller structures inside it. Incoherent Solitons have been found in coexistence with cascade, but for different directions in the Fourier space.