Hysteresis phenomena in passively mode-locked fibre laser with nonlinear polarization rotation

This paper investigates theoretically an ytterbium-doped fibre laser passively mode-locked through nonlinear polarization rotation. The setup consists in a unidirectional cavity with a polarizer placed between a quarter wave plate and a set of a half wave and a quarter wave plates. The model takes into account the optical Kerr nonlinearity, the group velocity dispersion (GVD) and the saturated gain together with the spectral gain filtering. It includes also the orientation of the phase plates. The model reduces to two equations: one algebraic equation associated to the effect of the optical Kerr effect and of the phase plates and a differential equation for the gain and the GVD. The results are in good agreement with the main features exhibited by mode-locked fibre lasers. Bistability between the mode-locked and the continuous regimes is obtained as experimentally reported.