Rogue waves formation from Eckhaus modulation instabilities in optical fiber cavities
Laboratoire de Physique des Lasers, Atomes et Molécules
Modulation instabilities are very common in nonlinear physical systems including nonlinear optics, plasma physic and hydrodynamics. They lead to the spontaneous formation of periodic solutions that can be stable or experience secondary instabilities resulting in complex regular states or spatiotemporal chaotic ones. Here we report on the dynamics of dissipative periodic solutions in a coherently driven passive optical fiber cavity. We mainly address their dynamics in a strongly nonlinear regime that exhibits Eckhaus secondary instabilities where stable propagating dissipative wave-trains are generated with a definite frequency and a constant group velocity. Their stability range is enlarged in the presence of the third-order dispersion, which determines completely their group velocity. An increasing in the injected pump value leads to transitions from periodic wave trains to chaotic regimes with a continuous spectrum and the appearance of rogue waves in the form of abnormal high amplitudes. We have characterized this transition and determined the transition curves from regular to chaotic regimes where supercontinuum and rogue waves may occur.