Real time revealing relaxation dynamics of ultrafast mode-locked lasers

Single-shot measurement of ultrashort time with a dispersive temporal interferometer (DTI) paves the way for exploring intracavity dynamics in ultrafast lasers. Here, we report observations of pulse evolution dynamics after mode-locking buildup in ultrafast lasers. We observe the roundtrip time and phase evolution of the mode-locked pulses after buildup, and we unveil that the pulse experiences three different stages before stabilization, i.e., the soliton breathing stage, the relaxation oscillation stage, and the long-term relaxation stage. We find that the gain depletion effect makes the pulse move forward but does not shift its phase, and it can be distinguished by a DTI from the refractive index change. With this, the dynamics of the three stages is analyzed. Moreover, it is unveiled that the gain relaxation dynamics can intensively affect a laser's stability. These results provide additional perspectives on the intracavity dynamics of mode-locked lasers and of complex nonlinear systems, and they can help to improve the laser stability, which may impact laser design, ultrafast diagnostics, and nonlinear optics.