Effects of ion pairs on the dynamics of erbium-doped fiber lasers

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.