The master equations of mode-locking

Summary form only given. The theory of active mode-locking was first formulated by Kuizenga and Siegman. The master equation of passive mode-locking with a fast saturable absorber was set up by Haus. For a while, the subsequent master equation describing mode-locking with a slow saturable absorber held sway, since ultrashort pulses ran into the relaxation rate of the saturable absorber. Mode-locking by artificial saturable absorbers, such as KLM (Kerr Lens Modelocking) and Additive Pulse Modelocking (AFM) is well described by the master equation with a fast saturable absorber, complemented by self-phase modulation as done by Martinez et al.