Real-time observation of phase transition of bifurcation evolution in mode-locked lasers

By using the dispersive temporal holography technology, we observe the real-time dynamics of period-doubling bifurcation evolution in an ultrafast fiber laser. The pulse properties including the phase, polarization state, chirp, pulse width, and pulse energy are fully bifurcated, which embody the bifurcation induced "phase transition." There are two types of bifurcation in the laser buildup: one to many bifurcation towards the chaos and the multiple bifurcated pulses back to the stationary state along the reversed trajectory. Both of them can be explained by the rule of the same phase transition. We conclude and illustrate the differences and connections to another common pulsation, the Hopf bifurcation. The findings can promote an understanding of the bifurcations in ultrafast lasers, and are beneficial for an improvement of laser stability.