Numerical analysis of hybrid mode-locking stability in a Ho-doped fiber laser

We numerically study a hybrid mode-locked holmium-doped fiber laser based on the coupled nonlinear Schrödinger equations, by introducing nonlinear polarization rotation and saturable absorber in a same cavity. Maps of mode-locking states related to the intracavity wave-plates are created to evaluate the stability of mode-locking. Nonlinear polarization rotation imposes negative effect of linear absorption and even reverse saturable absorption to the pulses in the hybrid cavity. Saturable absorber compensates the negative effect from nonlinear polarization rotation, then consequently contributes to the stability of single-pulse mode-locking states. The extension of pulse time duration indicates the dynamic synergy between nonlinear polarization rotation and saturable absorber rather than the static combination mechanism of them.