Critical behavior of a passively mode-locked laser: rational harmonic mode locking

The critical behavior of passive mode locking has been demonstrated in a figure-eight fiber laser that performs rational harmonic mode locking (RHML). On both the repetition rate and the pulse amplitude distribution, the observed pulse trains near the threshold exhibit the same regulations as the rational harmonic mode-locked ones. The theory also shows that there should be a middle status of RHML before achieving normal mode locking. It is important to note that the results provide what we believe to be the first confirmed attempt to address a fundamental question: how does a laser become mode locking with an increase of pump power?