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.

Figure 1

Capturing the interaction of different pulses with DTI.

Figure 2

Time shift due to gain depletion. (a) Scheme of the gain depletion across an amplified soliton. (b) Scheme of the gain depletion at different roundtrips. (c) Time separation of signal pulse and reference pulse as a function of gain depletion. The inset plots the two pulses. (d) Time interferogram evolution at different gain depletion.

Figure 3

Experimental setup. The left part is the fiber laser, while the right part is the real-time detection system. WDM: wavelength division multiplexer; OC, optical coupler; EF, extra fibers. The total length of EFs is equal to the cavity length, so the DTI captures the interference of two pulses from adjacent roundtrips. A detailed setup of DTI in shown in Fig. S3.

Figure 4

Soliton breathing stage of mode-locked laser. (a) Time interferogram evolution measured through DTI. (b) Pulse intensity (upper), roundtrip time (middle), and relative phase (lower) evolutions. (c) Relation of $\delta T_r$ and $\phi$ in 1000 roundtrips after mode-locking buildup. The radius (angle) corresponds to $\delta T_r$ ($\phi$). $R=\delta T_r-C$, with $C$ a constant. (d) $\phi$ as a function of intensity for 300–340 roundtrips. Their relation over 900 roundtrips is displayed in Fig. S5 [43].

Figure 5

Relaxation oscillation in 7 ms after mode-locking buildup. (a) Single-shot time interferogram evolution, which is captured using the ultrasegmentation method with 1 μs holdoff time. Therefore, the adjacent interferograms have an interval of 1 μs. A total of 7000 interferograms are presented in (a), which lasts 7 ms. (b) Pulse intensity, time separation, and relative phase. (c) Relation of $\delta T_r$ and $\phi$. The scatters are the experimental data, and the black line is a theoretical line of Eq. (3). (d) $\phi$ as a function of intensity. The black line is the fitting of the scatters.

Figure 6

Relaxation in 7 s after mode-locking buildup. (a) Time interferogram evolution over 7 s. The time interval of adjacent interferograms is 1 ms. (b) Spectrum evolution. (c) Pulse intensity, time separation, and relative phase evolutions. The olive line in the middle is calculated by the blue line ($\phi$) in the lower part through Eq. (2). The red dashed line in the lower part is the exponential fitting. (d) Relation of $\delta T_r$ and $\phi$. The black line is the fitting of scatters with Eq. (2).