Abstract
Keywords
1. Introduction
Solitons in fiber lasers, a consequence of balanced intra-cavity nonlinearity and dispersion, have attracted much attention owing to their unique features of preserving their temporal and spectral shapes over propagation distances and to the wide application scope, ranging from optical communications to laser metrology and material processing[
Worthy of note is that many of these investigations emphasized the build-up stage of a mode-locked laser, where unpredicted soliton complexes thrive, and their dynamics have proven informative to the understanding of the soliton formation and interactions[
In this paper, we investigated the build-up dynamics of a self-started soliton fiber laser with TS-DFT. We found a variety of short-lived pulsing states formed before the laser entered a steady soliton state. This is different from previous demonstrations where RO, beating dynamics, and Q-switching (or Q-ML) were involved in the build-up stage of an ML laser[
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2. Experimental Setup
Our experimental setup is shown in Fig. 1. The output of a soliton fiber laser was investigated. The fiber cavity contained a semiconductor saturable absorber mirror (SESAM), a piece of 0.8-m-long erbium-doped fiber (Er80-4/125-HD-PM, Liekki), and 1.2 m of polarization-maintaining fiber (PMF, dispersion of at 1550 nm). The net intra-cavity dispersion was estimated to be at 1550 nm. More details regarding the fiber laser can be found in Ref. [20]. Fundamentally, the laser produced soliton pulses at a repetition rate of 100 MHz, corresponding to a cavity round-trip time of 10 ns, when the laser pump power was set to ∼100 mW. Although the laser could emit harmonically mode-locked (HML) solitons at higher pump power[
Figure 1.Experimental setup. AOM, acoustic-optic modulator; LD, laser diode; EDF, erbium-doped fiber; OC, optical coupler; WDM/OI, wave division multiplexer and optical isolator; SMF, single-mode fiber; FPD, fast photo-detector; SESAM, semiconductor saturable absorber mirror; OSA, optical spectrum analyzer.
3. Results and Discussion
A portion of the data recorded in a TS-DFT measurement of 9.5 ms, corresponding to 0.95 million round trips, is shown in Fig. 2, presenting the formation and evolution of mode-locked fiber solitons. The spectra measured by TS-DFT (red) and the static spectrometer (black curve on a linear scale and green on a log plot) were consistent, as indicated in the inset of Fig. 2(a). Also, the typical Kelly sidebands were recognized for the soliton laser. The relation between the wavelength and the temporal spacing on the fast time scale was measured to be 5.5 nm/ns. Note that the spectral validation was carried out for a stationary ML state. Interestingly, unlike most demonstrated cases where noise and Q-ML occupied the stage prior to a stable ML state[
Figure 2.(a) A time sequence recorded in a TS-DFT measurement. A build-up regime for the fiber laser is displayed. (b) Zoom-in picture of the regime prior to a stable ML state. Spectra measured by TS-DFT (single-shot) and OSA are displayed in inset of (a) and the OSA data are also plotted in log scale (green) for showing the Kelly sidebands. The states labeled as A, B, and C are presented in Figs.
A transient pulsation state lasting 28 µs (or 2800 round trips) is displayed in Fig. 3(a). In order to investigate the spectral dynamics, the TS-DFT data were rearranged into a two-dimensional (2D) map in Fig. 3(b) with consecutive round-trip numbers on the axis and cavity round-trip time or fast time (i.e., 10 ns) on the axis. Note that the corresponding wavelengths were not labeled in the 2D map, since the absolute values of the wavelength were unclear for the fast-changing, short-lived ML state.
Figure 3.(a) Time-domain sequence of a transient ML state and (b) the corresponding TS-DFT results displayed in a 2D map. (c) Zoom-in of (b) showing the spectral dynamics of the evolving pulses. (d) The field autocorrelation traces calculated with the Fourier transform of each TS-DFT spectrum in (b).
Like a steady ML state[
The observed multi-pulse interactions (i.e., repulsion, attraction, and collision) in Fig. 3 were indeed a consequence of the balance between dispersion and nonlinearity[
We also noticed that a whole decaying process might last a few µs or even longer, which was close to the recovery time of the gain. Hence, it was possible that the fiber laser was recovered from gain depletion before a pulsing state vanished completely. As a result, instead of annihilation, a new round of evolution might be initialized at the end of a decaying process. For instance, the decaying of a giant pulse in the middle of Fig. 4(a) led to formation of multiple pulses followed by another evolution process (from the to the round trip).
Figure 4.(a) Time-domain trace and (b) real-time spectral evolution measured with TS-DFT for a transient ML state. The y axis from 0 to 10 ns corresponds to a spectral scale from longer to shorter wavelengths. Note that for the transient states, the absolute values of wavelengths were not determined.
As evidenced by the spectral dynamics in Fig. 4(b), a spectral shift was noticed as a dislocation of the two evolving traces before and after the appearance of the giant pulse. In fact, due to the spectral dependency of intra-cavity loss, the decaying process was spectrally uneven. For instance, in our experiment, the long-wavelength components decayed much slower than the short wavelength ones, as shown in Fig. 4(b). Consequently, the former was more likely to survive from gain depletion and recovery, which also explained the red shift for the spectral evolution in Fig. 4(b).
Figure 5 shows another transient ML state in Fig. 2. Compared to the states in Figs. 3 and 4, the difference could be readily identified from the recorded time-domain trace in Fig. 5(a), where a train of relatively stable, low-intensity pulses were presented. Also, as indicated in the corresponding 2D spectral map [Fig. 5(b)], after RO and beating dynamics, two largely separated pulses were formed, each as a victor of multi-pulse competitions evidenced by the spectral interference patterns [corresponding to the round-trip numbers of 300 to 600 in Fig. 5(b)]. An expanded view of the spectral evolution of the two pulses is displayed in Fig. 5(c), together with a three-dimensional plot in Fig. 5(d). We noticed that the two evolving pulses were spectrally broadened while remaining separated, forming a short-lived bound state of pulses. In the end, one of the pulses led to a giant pulse, which terminated the ML due to gain depletion, and the other simply disappeared [shown in Fig. 5(b)] as a result of multi-pulse competition and energy balance[
Figure 5.(a) Recorded time-domain trace and (b) corresponding TS-DFT data for a different transient state. (c) An expanded view for the evolving solitons and (d) a three-dimensional image showing the spectral dynamics of the solitons.
Furthermore, statistical analysis in Fig. 6(a) showed that the probability of occurrence for the transient ML states in Fig. 5 was 25%, defined by the event number of transient states normalized to the total one before the laser entered a stable ML regime. Comparatively, the probability for the case in Fig. 3 was about 10%. The results indicated that our laser tended to produce stably separated multiple pulses (like those in Fig. 5 or HML pulses in Ref. [20]). Also, when the pump power was further decreased by ∼10%, nearly to the threshold of fundamental ML, only Q-switched bursts [each lasting less than 5 µs, as depicted in Fig. 6(b)] could be observed in the build-up stage. Such Q-switched lasing dynamics were similar to those in Ref. [9]. We believed that for our fiber laser, the excess pump power resulted in the transient and unstable ML states before the laser reached a point where intra-cavity energy, dispersion, and nonlinearity were balanced properly, and, consequently, a steady ML state could be achieved.
Figure 6.(a) Probability of occurrence for two typical transient ML states observed with different pump powers, which correspond to the results presented in Figs.
Our experimental observations showed that an unusual transient regime occurred before the build-up of a stable ML state in a fiber laser. The unambiguous presence of various transient ML states in this regime was revealed for the first time, to the best of our knowledge, which may enrich the existing dynamics during the development of the mode-locked pulses. Also, these behaviors might stimulate further theoretical analysis and numerical simulations to investigate the underlying mechanisms.
4. Conclusion
In conclusion, we observed a string of ML states with short life time varying from a few to nearly a hundred µs. Various lasing dynamics, including multi-pulse formation, interaction, and decaying evolution, were found in these transient states, all of which happened before a fiber laser reached a steady ML state. Furthermore, we found that redundant pump power or excess intra-cavity energy might be responsible for the emergence of these short-lived pulsing states. We believe these findings could be valuable for further studies of transient behaviors of mode-locked fiber lasers.
References
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