Analysis on femtosecond pulses generated by passively mode-locked lasers with higher-order effects

A theoretical model for passively mode-locked lasers is presented, in which the higher-order effects, such as third-order dispersion, nonlinear dispersion, and self-frequency shift arising from stimulated Raman scattering, and a fast as well as a slow saburable absorber responses are taken into account. An exact soliton-like solution is obtained under a definite parameter conditions and its stability is also analyzed numerically under small perturbations in amplitude, chirp and white noise. The results indicate that the pulses can be stable under a finite perturbation and become identical to the exact solution after a distance of evolution. In addition, we have also found that a quite arbitrary initial Gaussian pulse can converge to the exact solution after a distance of evolution.