Theory of passively mode-locked lasers including self-phase modulation and group-velocity dispersion

Closed-form analytical solutions are obtained for a passively mode-locked laser for the case in which self-phase modulation and group-velocity dispersion, in addition to the more conventional mechanisms of saturable absorption and gain, shape the laser pulses. Provided that the self-phase modulation and group-velocity dispersion are related in a manner similar to that which causes soliton formation in optical fibers, this additional pulse shaping can reduce the pulse duration below the limit otherwise set by the laser bandwidth.