Phase Transition Theory of Many-Mode Ordering and Pulse Formation in Lasers

A novel theory for the ordering of many interacting modes in lasers is presented. By exactly solving a Fokker-Planck equation for the distribution of waveforms in the laser in steady state, equivalence of the system to a canonical ensemble is established, where the role of temperature is taken by amplifier noise. Passive mode locking is obtained as a phase transition of the first kind and threshold is calculated, employing mean field theory backed up by a numerical study. For zero noise, compliance with the existing noiseless theory is shown.