Phase-plane analysis of passively mode-locked dye lasers

A simplified model is presented of passively mode-locked dye lasers with self-phase modulation and group-velocity dispersion. The model treats pulse width and chirp as dynamical variables and follows their evolution in a pulse-width-chirp phase plane as they approach steady state. The model allows the separate dynamical effects of pulse shortening, pulse broadening, chirp buildup, and chirp decay to be examined in detail.