A passively mode-locked fiber laser is theoretically investigated. The mode locking is achieved using the nonlinear polarization technique. We consider the practical case of the ytterbium-doped fiber laser operating in the normal dispersion regime. The effect of the phase plates is explicitly taken into account. The resulting model reduces to one iterative equation for the optical Kerr nonlinearity, the phase plates and the polarizer, and one partial differential equation for the gain and the dispersion. Numerical simulations allow us to describe several features observed in passively mode-locked fiber lasers such as bistability between the mode lock and the continuous regime, multiple pulse behavior, hysteresis phenomena. The dynamics of the number of pulses as a function of the pumping power is also reported. Pump power hysteresis is demonstrated.

Experiments with erbium-doped fiber lasers demonstrate cw, sinusoidal, and self-pulsing operation. The obtained regimes depend on three control parameters: ion-pair concentration, photon lifetime, and pumping rate. We present a theoretical model which describes the active medium as a mixture of isolated ions and ion pairs. Starting with the adapted laser rate equations we show that the description of the dynamical behavior of this system can be reduced to only four first-order coupled equations. A linear stability analysis demonstrates the existence of self-pulsing for a finite range of pumping rates. At both ends of this range Hopf bifurcations occur: one located near the first laser threshold and the other at a higher pumping ratio, whose position is closely related to the pair concentration. Results of numerical calculations are in good qualitative agreement with our experimental data.

The dynamics of a fiber ring laser mode locked by nonlinear polarization rotation is reduced to a quintic complex Ginzburg-Landau (CGLQ) equation. The coefficients of the equation are explicitly given as functions of the physical parameters of the laser, especially the orientation of the phase plates. Then known results about analytic solutions, stability of pulselike solutions, and bound states of the CGLQ equation are examined from the point of view of their dependence with regard to the physical parameters.

We report passive mode locking of a soliton erbium-doped double-clad fiber laser operating at the 322nd harmonic of the fundamental cavity frequency. Repetition rates up to $3\mathrm{GHz}$ have been obtained with pulses of $1\mathrm{ps}$ duration and $18\mathrm{pJ}$ of energy. The supermode suppression at the 322nd harmonic is better than $25\mathrm{dB}$. In addition, the transition dynamics from a bunched state of pulses to stable harmonic mode locking is presented, revealing a very long time scale.

We give a detailed theoretical analysis of spontaneous periodic pattern formation in fiber lasers. The pattern consists of a bound state of hundreds of pulses in a ring fiber laser passively mode locked by nonlinear rotation of the polarization. The phenomenon is described theoretically using a multiscale approach to the gain dynamics: the fast evolution of a small excess of gain is responsible for the stabilization of a periodic pattern, while the slow evolution of the mean value of gain explains the finite length of the quasiperiodic soliton train. The resulting model is well adapted to experimental observations in a Er:Yb-doped double-clad fiber laser.