Dynamics of passively mode-locked lasers with saturable absorber and saturable nonlinearity

The dynamics of a model of passively mode-locked laser with saturable absorber, the optical amplifier of which possesses a saturable nonlinearity, is considered with interest in both continuous wave and pulse regimes of operation. The study rests on the laser self-starting picture which assumes that the laser should operate instantly in the pulse regime, when continuous waves become unstable in the system. Within the framework of the modulational-instability analysis, a global map for the laser self-starting conditions is constructed in terms of a two-dimensional complex parameter space, mapped by the real and imaginary parts of the modulation gain over a broad range of values of the modulation frequency. The map suggests that the saturable nonlinearity lowers the threshold value of the input intensity required for laser self-starting, analytical expression for this threshold input field is derived in the particular case of a zero modulation frequency. Treating the system dynamics in the full nonlinear regime using numerical simulations, time series of the laser amplitude and instantaneous phase, as well as of the gain, are obtained and their changes with the variation of the homogeneous gain are examined. It is found that a relatively small value of the equilibrium gain will favor gain decrease, and pulse generation and buildup into either simple-periodic or multi-periodic pulse trains, depending on the magnitude of the saturable nonlinearity coefficient.