Abstract The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg–Landau equation with a general m:n saturable nonlinearity (i.e I m / ( 1 + Γ I ) n , where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple ( m , n ), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

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