Transient evolution of passive mode locking

We present the first deterministic theory of the transient evolution of passive mode locking which gives a closed form expression for the pulse on each transit through the system. The theory is shown to be applicable to both CW and pulsed mode-locked laser systems. Included are studies of the buildup from noise, the mode-locking threshold, the subsequent evolution of the mode-locked pulse, the steady State operating point of CW systems, and the stability of the steady state. Simple criteria are established which enable the design of passively mode-locked systems to generate pulses of prespecified width and amplitude.