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The self-starting dynamics of a model for passively mode-locked lasers withsaturable absorber, in which the optical amplifier has a saturablenonlinearity, is examined. The basic assumption is that the laser will operatein the mode-locked regime when the continuous-wave regime becomes unstable.Within the framework of the modulational-instability analysis, a global map forthe laser self-starting criteria is constructed. According to this map, thesaturable nonlinearity enhances the input-field intensity required for laserself-starting. Analytical expression of the zero modulation-frequency regime ofthis threshold input field is derived, which turns out to be valid in thenormal as well as in the anomalous dispersion regime, where evidence ofself-starting is also given.

Effect of saturable nonlinearity on cw stability in passively mode-locked lasers with fast saturable absorbers