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Abstract
Soliton buildup dynamics in ultrafast fiber lasers are one of the most significant topics in both the fundamental and industrial fields. In this work, by using the dispersive Fourier transformation technique, the real-time spectral evolution of soliton buildup dynamics were investigated in the all-polarization-maintaining Yb-doped fiber laser, which is mode-locked by nonlinear polarization evolution technique through the cross splicing method. It was experimentally confirmed that the same stable soliton state could be achieved through different soliton starting processes because of the initial random noises. In one case, the maximum pulse energy during the soliton starting process could reach ∼15 times the stable pulse energy, which results in the spectral chaotic state and temporal shift. We also provide another soliton buildup case with the same cavity parameters, which illustrates more moderate evolution. It involves smaller energy variation and no complex transition state. These results would deepen our understanding of soliton buildup dynamics and be beneficial for the applications of ultrafast fiber lasers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As the effective ultrashort pulse sources, passively mode-locked fiber lasers have received much attention due to the great significance in applications of optical communications, spectroscopy, biomedicine and material processing [1,2]. So far, there are several methods to realize the passively mode-locking, such as nonlinear polarization evolution (NPE) [3–5], nonlinear optical loop mirror (NOLM) [6], nonlinear amplifying loop mirror (NALM) [7,8] and real saturable absorber (SA) [9,10]. Among them, the NPE has been widely employed in ultrashort pulse generation due to its advantages in the high damage threshold, ultrafast response time and low intrinsic noise. However, NPE is sensitive to the random birefringence of the fiber induced by the environmental perturbations, which greatly hinders its development in practical applications. Then, the all polarization-maintaining-fiber (PMF) laser with high environmental stability could be an effective solution for industrial applications outside of the laboratory. Intuitively, all PMF lasers could be mode-locked by SA [11], NOLM [12] or NALM [13]. As for all PMF lasers mode-locked by NPE technique, there is a main obstacle, namely the polarization mode dispersion (PMD) mismatching in the PMF with large birefringence. At first, by utilizing a faraday mirror (FM) to exchange the polarization angles of the light along the two orthogonal axes, the PMD effect of PMF could be compensated and the linear cavity mode-locked by NPE was realized [14]. Then in 2016, Wang et al. proposed a cross-splicing method to compensate the PMD in PMF, and a ring PMF laser mode-locked by NPE was also demonstrated. However, some bulk optical components were involved in this case [15]. The first all-fiber ring PMF laser mode-locked by NPE was proposed in 2018. The dechirped pulse duration is ∼150 fs and the pulse energy is 0.85 nJ [16]. Since then, the all PMF laser mode-locked by NPE has attracted much attention in the ultrafast laser community [17–19].
On the other hand, as a topic of fundamental physics, the soliton buildup dynamics illustrate various random and fantastic phenomena. Since 1990s, a series of experimental and theoretical investigations on the starting dynamics of mode-locked lasers have been reported [20–22]. However, only the temporal characteristics could be measured directly in the experiments due to the limitation of fast spectral measurement instruments. Recently, the dispersive Fourier transformation (DFT) technique, as a real-time spectroscopy technique, has been proved to be an effective way to investigate the transient soliton dynamics in mode-locked lasers, such as soliton molecules [23,24], soliton explosion [25,26], and so on. Since 2015, by virtue of the DFT technique, the starting dynamics in mode-locked lasers have been widely investigated [27–41]. It has been demonstrated that different mode-locking methods, dispersion regimes and operating states have different impacts on the soliton buildup dynamics. However, to date, almost all the experimental research on soliton buildup dynamics based on DFT technique are focused on the 1550 nm waveband. No related investigation in Yb-doped fiber lasers (YDFLs) with all normal dispersion regime has been reported. Moreover, in the previous reports, the Er-doped fiber lasers (EDFLs) did not include the spectral filters, which are generally employed in the YDFLs to reshape the pulse and help the soliton formation [42]. Therefore, besides the different dispersion regimes, there is another main difference between EDFLs in previous reports and YDFLs, i.e. the spectral filter. Thus, it is assumed that compared to the corresponding EDFLs, the all normal dispersion and the intracavity filter of the YDFLs might have different influences on the soliton buildup dynamics. Moreover, it is also important for the industrial fields to investigate the soliton buildup dynamics in all-polarization-maintaining YDFL, which generally serves as the seed of high-power laser systems based on chirped pulse amplification (CPA) or master oscillator power amplification (MOPA). If some extremely high peak power waves occurred during the starting or restarting process of the laser seed, it would lead to irreversible damage to the laser devices. So far, most of the experimental reports on soliton buildup dynamics only present single starting process in each laser. However, as we know, the soliton starts from the random noise inside the cavity, which means that the soliton starting processes might be different from one another [35]. Therefore, it would be significant to fully investigate the soliton buildup dynamics for both fundamental and industrial interests.
In this work, we conducted an all-polarization-maintaining YDFL mode-locked by NPE, where the dissipative soliton buildup dynamics was investigated by using the DFT technique. Through gathering statistics of the starting dynamics of the fiber laser, we found that the soliton initiation processes are not uniform since the beginning noises are random. For one soliton buildup process, the ratio of maximum pulse energy to stable pulse energy during the starting process is ∼15, which induces the transient chaotic state and temporal shift. In addition, a more moderate starting process was also provided here, where no complex transition state and much smaller energy oscillation occurred. All these results would further enrich the investigations of soliton buildup dynamics.
2. Experimental setup
The experimental setup of the all-polarization-maintaining YDFL is shown in Fig. 1. A 0.8 m-long Yb-doped fiber (YDF, Nufern PM-YSF-HI-HP) with absorption of 250.0 dB/m at 975 nm serves as the gain medium. The optical chopper is placed after the pump laser diode to initiate/stop the mode-locking operation periodically. A bandpass filter (BPF) with an operating center wavelength of 1064 nm and bandwidth of 5 nm is employed to shape the pulse in the laser cavity. A fiber isolator (ISO) that works only on the slow axis ensures the unidirectional propagation of the laser pulses. To extract the laser pulse with a ratio of 10%, a 10:90 tap coupler is used in the cavity. In addition, a three-PMF-section (Fujikura SM98-PS-U25D-H), whose lengths are 1.2 m, 2.4 m and 1.2 m, is fabricated to compensate for the PMD. Note that the angles among YDF and PMF1, PMF2, PMF3, ISO are 23°, 90°, 90°, 45°, respectively. The beat length of the PMF is 2.4 mm. The total cavity length is ∼9.6 m, corresponding to the fundamental repetition rate of 20.78 MHz. The DFT technique is realized by a 15 km single mode fiber, and the spectral resolution of shot-to-shot spectra after DFT is ∼0.29 nm.
The proposed fiber laser is mode locked with NPE technique, whose mechanism in this all PMF laser is as follows [19]. When the pulse with linear polarization goes through the first cross-splicing point (P1) with an angle of 23°, it will split into two pulses with orthogonally polarizations and different intensities. Due to the two splicing points (P2, P3) with an angle of 90° and the precise length design of the three sections of PMF, the PMD could be completely compensated and the two pulses would be merged into one pulse after the three-PMF-section. Note that here the linear phases of the two pulses are the same because of the full PMD compensation. Since the two pulses possess different intensities, they would achieve different nonlinear phase shifts after the three-PMF-section. If the phase difference between the peaks of the two pulses is a multiple of 2π, the polarization at the peak of the merged pulse will be same with the initial pulse. The splicing angle between the PMF3 and the ISO (P4) is set as 45°, making the angle of the ISO well consistent with the polarization angle at the peak of the merged pulse. Then, the transmission at the pulse peak would be highest, while the other portions of the pulse would have lower transmission due to the different nonlinear phase difference induced by different intensities. Therefore, the saturable absorption could be realized in the proposed fiber laser. Note that the angles of splicing points and the lengths of three sections of PMF should be precisely controlled to realize the optimal saturable absorption [19].
3. Experimental results
Due to the saturable absorption of the NPE technique, the self-started mode-locking operation could be achieved just by increasing the pump power to 170 mW. The laser performance in the mode-locked state is summarized in Fig. 2. The mode-locked spectrum centered at 1063 nm with a 10-dB bandwidth of 14 nm, as shown in Fig. 2(a). The corresponding pulse train is provided in Fig. 2(b). The repetition rate is a fundamental one of 20.78 MHz. To identify the duration of the mode-locked pulse, the autocorrelation trace was measured correspondingly, as shown in Fig. 2(c). The pulse width was calculated to be ∼5.34 ps, if the Gaussian intensity profile was assumed. It indicates that the pulse is highly chirped. Moreover, the radio frequency (RF) spectrum was also recorded, as presented in Fig. 2(d). It shows a signal-to-noise ratio of >50 dB, suggesting that the fiber laser is operating in a stable regime.
Fig. 2. Mode-locking operation. (a) Spectrum; (b) Pulse train; (c) Autocorrelation trace; (d) RF spectrum.
Then we set the pump power as 181 mW, which is a little higher than the threshold of mode-locking operation. By using the chopper to periodically initiate/stop the fiber laser, the transition from CW to mode locking operation could be obtained. The period of the chopper is ∼60 Hz. In our experiments, the buildup time of solitons from the starting time of pump to the stable mode-locking is several ms. It means that the steady state after buildup could also last for several ms until the pump is stopped. Combining the DFT technique and oscilloscope, both the spectral and temporal evolutions of the main soliton buildup dynamics were recorded and illustrated in Fig. 3. Note that the 0 RT here refers to the first pulse of the recorded data, rather than the starting time of pump. The whole buildup dynamics includes four stages: pulse amplification, spectral broadening, transient chaotic state, and stable soliton state. Here, due to the relatively low sampling rate of oscilloscope, some problems might be induced on the experimental data, such as a little pulse shift in Fig. 3(b).
Fig. 3. Dramatic soliton buildup dynamics of 1000 RTs. (a) Shot-to-shot spectra, Inset: Average spectrum of 100 stable solitons; (b) Pulse train; (c) Pulse energy evolution (see Visualization 1).
In order to investigate the soliton buildup more clearly, the expanded view of Fig. 3 is presented in Fig. 4. Figure 4(a) illustrates the shot-to-shot spectra of 720-820 RT. It can be seen that before 772 RT, the pulse experiences the amplification, which is demonstrated by the increasing intensity of the spectrum in Fig. 4(a). Here, due to the low intensity of the pulse at the beginning, in Fig. 4(b) the pulse could not be detected by the oscilloscope until ∼735 RT. After the pulse amplification stage, the increasing pulse peak power initiates the spectral broadening stage (773-781 RT). The spectrum broadens rapidly before reaching its maximum bandwidth at 781 RT, which is ∼1.5 times larger than that in the stable state. It should be noted that the spectral broadening completes within only 8 RTs, which is much shorter than that in other fiber lasers [28–40]. During the spectral broadening process, pulse energy increased rapidly. Similar to Ref. [28], we observed a spectral redshift during the rapid spectral broadening process, which might be related to the reabsorption of the gain medium [43]. From 779 RT of the spectral broadening stage, some irregular fringes appear on the optical spectrum, and then the spectrum explodes in the 780 RT. The spectrum starts to display a chaotic evolution from one RT to the next, as shown in Fig. 4(d). These chaotic fringes would gradually reduce and finally disappear until ∼798 RT, together with the spectral narrowing process. In addition, due to the increased pulse energy, the pulse temporally shifts ∼17 ps from 777 RT to 780 RT correspondingly, which could be seen in Fig. 4(e). After a small oscillation of the pulse position from 782 to 785 RT, the pulse shifts in the opposite direction. The separation between the beginning pulse (777 RT) and final stable pulse (805 RT) is ∼7 ps, while the separation between pulses at 780RT and 805RT is ∼24 ps. It can be seen from Fig. 4(c) that the pulse energy reaches almost ∼15 times the energy of stable soliton (Here, the value of stable pulse energy is set to be 1.), which is much larger than those in other reports [28,30,31,33,36,40,41]. After the pulse energy goes to ∼15 at 780 RT, it experiences a rapid decrease to ∼7 and then a small oscillation to ∼1, which coincides with the spectral narrowing and pulse position oscillation processes. Finally, the laser reaches a steady state at ∼805 RT. Note that some data in Figs. 4(a) and (b) exceeded the oscilloscope screen due to the extra high intensity, as a compromise of capturing low intensity waveform with sufficient dynamic range. Since the pulse energy is calculated by integrating the shot-to-shot spectra, the pulse energies from 775 to 779 RTs are not precise (More details could be observed from the Visualization 1.). However, it could still reflect the results qualitatively that the evolutions during this buildup process are quite dramatic. Here, even extremely high waves were generated during the starting process, they are not belonging to the rogue waves because the starting process is a one-time process rather than a continuous state.
Fig. 4. Expanded view of dramatic soliton buildup dynamics of 100 RTs. (a) Shot-to-shot spectra; (b) Corresponding pulse train; (c) Pulse energy evolution; (d) 5 single-shot spectra with evolving fringes; (e) Pulse position evolution from 765-820 RTs.
Fig. 5. Moderate soliton buildup dynamics. (a) Shot-to-shot spectra of 1000 RTs, Inset: Average spectrum of 100 stable solitons; (b) Pulse train of 1000 RTs; (c) Pulse energy evolution of 1000 RTs; (d) Shot-to-shot spectra of 100 RTs; (e) Pulse train of 100 RTs; (f) Pulse energy evolution of 100 RTs (see Visualization 2).
Actually, by starting the fiber laser many times at the same cavity parameters, we found that each soliton buildup dynamics is not exactly the same, mainly shown as the difference of the maximum pulse energy during soliton buildup process while the final stable pulse energy is almost the same. The most dramatic soliton buildup dynamics recorded in the experiments has been presented in Figs. 3 and 4, where the maximum pulse energy is ∼15 times of the stable pulse energy. Besides that, we observed a much more moderate soliton buildup process, where the maximum pulse energy is only ∼1.5 times the stable pulse energy, much smaller than that in Figs. 3 and 4. The corresponding results are presented in Fig. 5. Similar to Fig. 4, at first the pulse got amplification. Then due to the increased peak power, the spectral broadening stage was started. In this case, the broadest spectrum at 776 RT is much narrower than that in Fig. 3, which is only slightly larger than that of the steady mode-locked state. It is because that the maximum pulse energy here is much lower than Fig. 4, which supports less spectral broadening. Note that the spectral redshift is also observed in this case. After the pulse energy reaches the maximum value of ∼1.5 at 776 RT, it drops to ∼1 quickly within 2 RTs. Therefore, after 778 RT the fiber laser enters the stable soliton state. The average spectrum of the 100 RTs stable single-shot spectra in Fig. 5(a) is similar to that in Fig. 3(a). It verifies that the almost same stable mode-locked state could be achieved through different soliton buildup processes due to the same cavity parameters, which is a typical feature of the dissipative optical system [44]. It should be noted that compared to Fig. 4, no evidently chaotic state and temporal shift were involved in this dynamics. With the relatively concise evolution in both spectral and temporal domains, it could be concluded that this soliton buildup process is a more moderate one. As for the other soliton buildup processes with ratio of the maximum pulse energy to stable one between 1.5 and 15, the spectral broadening, duration of chaotic state and temporal shift would be smaller than that in Figs. 3 and 4 but larger than that in Fig. 5. In addition, it should be noted that the stopping process was not observed in our experiments owing to the trigger method.
4. Discussion
In this work, we provide two typical cases of the soliton buildup dynamics, where the final stable soliton states are almost the same, as well as the stable pulse energy values. The difference mainly lies in the maximum pulse energy ratio to stable pulse energy during the soliton starting process. In fact, by recording the soliton buildup dynamics repeatedly, we found that the ratio of maximum pulse energy to stable pulse energy during the whole process is random. The recorded maximum value of the ratio is ∼15, while the minimum one is ∼1.5. The reason is that the soliton starts from the noise inside the cavity, whose feature of randomness leads to the random starting processes [35]. When the pump power was increased from 181 mW to 201 mW, the pulse energy was also increased from ∼0.18 nJ to ∼0.20 nJ, and the occurrence probability of the soliton starting process with larger ratio of maximum pulse energy to stable pulse energy would also increase. It indicates that the soliton starting process is also related to the intracavity energy. When the ratio of maximum pulse energy to stable pulse energy is ∼15, the chaotic state together with temporal shift occur due to the relatively large pulse energy variation in the starting process. The appearance of the chaotic state is related to the high nonlinear effect induced by the relatively high pulse energy, which would make the pulse break into pieces, just like the soliton explosion [26,41]. However, here no Raman component was observed from the spectra of OSA and after DFT. The variation of nonlinear refractive index induced by large change on the pulse energy could be responsible for the temporal shift. The spectral redshift during the spectral broadening process does not lead to the visible temporal shift, which might be owing to the relatively large pulse duration during this process. As mentioned above, the sudden increase in pulse energy would have fatal damage to the laser devices in the application. On the other hand, since the minimum ratio recorded is only ∼1.5, more moderate and concise evolution happens in the corresponding starting process. Obviously, this kind of soliton starting process is more desirable for the applications. As we know, in the numerical simulations, if the initial signal is set as random noise, the startup processes would not unique [35]. However, if a certain small pulse is set as the initial signal, the starting processes would be uniform. Inspired by numerical simulations, it may be possible to uniform the buildup processes by injecting a certain small signal to start the laser. However, what kind of small signal can force the laser mode locking in an ideal way? It is of great significance to deeply investigate the physical mechanisms of the different soliton starting processes and control it precisely in the future.
Compared to the other researches on soliton buildup dynamics in anomalous and net normal dispersion regimes, the spectral redshifts could be observed in this work. The reason could be contributed to the reabsorption of the gain medium, rather than stimulated Raman scattering, since the small spectral shift of ∼3 nm occurred in both the two cases where the energy evolutions are totally different [43]. The increased pulse energy saturates the gain and then the shift of gain band happened due to the reabsorption. In addition, the temporal shift during the starting process was observed, which is due to the relatively large pulse energy variation. It also demonstrates that the corresponding ratio of maximum pulse energy to stable pulse energy is much larger than those in other works [28,30,31,33,36,40,41]. In this experiment, we observed the relaxation oscillation sometimes, which is a common phenomenon during soliton starting dynamics. However, due to the limitation of oscilloscope, we cannot measure the whole starting process, so we only focus on the main buildup process in this work. However, another common phenomenon, the frequency beating dynamics was not observed in our experiments. Besides that, it takes ∼20 to 30 RTs from spectral broadening to stable soliton state in the two cases, while hundreds to thousands of RTs were recorded in most of the previous reports [28–40].
5. Conclusion
In conclusion, the soliton buildup dynamics was investigated in an all-polarization-maintaining YDFL based on NPE. By using the DFT technique, the spectral and temporal evolution of the soliton buildup dynamics could be recorded. We revealed two typical soliton buildup processes at the same cavity parameters, which are induced by the initial different noises. In one soliton buildup process, due to the large ratio of maximum pulse energy to stable pulse energy, the chaotic fringes and obvious temporal shift appeared during the starting process. Another relatively moderate soliton starting process was demonstrated to be more desirable for high-power laser systems. These results would pave the way for the intensive research on soliton dynamics and provide vital significance for the industrial fields.
Funding
Key-Area Research and Development Program of Guangdong Province (2018B090904003, 2020B090922006); National Natural Science Foundation of China (NSFC) (61805084, 11974006, 11874018, 61875058); Guangdong Basic and Applied Basic Research Foundation (2019A1515010879); Science and Technology Program of Guangzhou (2019050001); Open Fund of the Guangdong Provincial Key Laboratory of Fiber Laser Materials and Applied Techniques (South China University of Technology, 2019-2); Open Fund of State Key Lab of Advanced Communication Systems and Networks, Shanghai Jiao Tong University (2020GZKF010).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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