Stable regimes of pulse generation in fiber rings with modulated dispersion and nonlinear outcoupling

We investigate a model of a fiber-ring laser, which includes nonlinear saturation and dispersion of gain, nonlinearity (saturation) of the splitter which releases outgoing solitons, and smooth modulation of the group-velocity dispersion (GVD) coefficient along the ring. A conclusion is that the gain dispersion (effective spectral filtering), splitting saturation, and GVD modulation are all necessary for stability of a pulse-circulation regime. Finite intervals are identified from which values of the outcoupling saturation parameter Γ and GVD-modulation rate γ must be chosen to secure stable periodic operation of the scheme and hence stable periodic generation of outgoing solitons. In an adjacent interval, period doublings and subsequent transition to a chaotic pulse-circulation regime occurs. If Γ or γ are too small or too large, only a continuous-wave state is generated. In the case when the gain is too strong, the ring resonator switches into a turbulent regime via a cascade of soliton splittings. Robust pulses are found too in the absence of the gain saturation.