Soliton Lattice and Gas in Passive Fiber-Ring Resonators

Abstract

We consider multisoliton patterns in the model of a synchronously pumped fiber-loop resonator. An essential difference of this system from its long-line counterpart is that, due to the finite length, dynamical regimes may be observed that would be unstable in the infinitely long line. For the case when the effective instability gain, produced by competition of the modulational instability (MI) of the flat background and losses, is small, we have consistently derived a special form of the complex Ginzburg-Landau equation for a perturbation above the continuous wave (cw) background. It predicts bound states of pulses with a uniquely determined ratio of the pulse width to the separation between them. Direct numerical simulations have produced regular soliton lattices at small values of the feeding pulse power, and irregular patterns at larger powers. Evidence for a phase transition between the lattice and gas phases in the model is found numerically. At low power, the width-to-sep aration ratio as found numerically proves to be quite close to the analytically predicted value. We also compare our results with recently published experimental observations of MI-stimulated formation of a pulse array in a mode-locked fiber laser.