Models for passively mode-locked fiber lasers

We give a review of theoretical approaches we have recently developed for the description of passively mode-locked fiber lasers. Mode-locking is assumed to be obtained with nonlinear polarization rotation. The first approach takes the form of a cubic Ginzburg-Landau equation where the coefficients take into account the orientation of the phase plates. A fully analytical study can be performed. The second model includes gain saturation allowing to investigate multiple pulse behaviour and multistability phenomena. Under some approximations this model reduces to a complex quintic Ginzburg-Landau equation. Passive harmonic mode-locking can also be obtained with a suitable adaptation of the model.