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Abstract
Rapid progress in real-time measurement technology has uncovered varieties of transient pulse dynamics. Here, we report the vector nature of noise-like pulse (NLP) in a passive fiber laser based on the nonlinear optical loop mirror (NOLM) as the polarization independent saturable absorber. After achieving the basic operation regime of NLP, various types of vector pulses, namely, the polarization locked noise-like vector pulse (PLNLVP), the group velocity locked noise-like vector pulse (GVLNLVP), and the transitional state of combined characteristics of GVLNLVP and polarization rotation noise-like vector pulse (PRNLVP) are also obtained in the cavity. Besides, by utilizing the Dispersive Fourier transform (DFT) technique, the spectral evolution and the energy vibration of pulsating PLNLVP, GVLNLVP, and the transitional state of combined characteristics of GVLNLVP and PRNLVP are also analyzed in real time. Particularly, the coexisting pulsation vector state of NLP and soliton is also captured. All these findings will help to complement our understanding of noise-like vector pulses (NLVPs) in a fiber laser.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
During the past several decades, passively mode-locking fiber lasers have aroused great attention because of their stability, compactness, and ease of use [1–4]. Furthermore, passively mode-locked fiber lasers can also provide an excellent platform for exploring a variety of intriguing soliton dynamics [5–7]. Governed by the Ginzburg-Landau equation [8,9], the composite balance among the gain, loss, nonlinearity, and dispersion can bring some interesting phenomena like conventional soliton [10], dissipative solitons [11], vector soliton [12], noise-like pulse (NLP) [13–17], etc. In particular, varieties of complex behaviors in these pulses may be revealed, such as the stationary, pulsating, and chaotic manners [18].
In general, NLP is the packet consisting of loads of short sub-pulses with random pulse intensities and amplitudes. Characterized by its features like smooth and wide optical spectrum, the NLP can be used in supercontinuum generation [19–24]. In addition, the NLP can exhibit complex nonlinear transient dynamics under certain parameter conditions, which is a challenge to record by using traditional measurement method. Recently, the dispersive Fourier transform (DFT) technique, as a novel real-time measurement method, was first used to unveil the real-time spectral information of NLP [25]. Afterward, Wang et al. reported that each of the loosely bound solitons in the NLP operation is consisting of chaotic pulses with random intensities [26]. Moreover, Wang et al. investigated the transient evolutions of different vector NLP in real time [27]. Although many characteristics of NLP have been extensively reported, some novel characteristics of NLP are still waiting to be explored in the time domain and frequency domain. Thus, it is necessary to continue exploring the features of NLP.
Given that the birefringence introduced by external pressure and twists in single mode fiber (SMF), the vector pulses typically comprising two orthogonally polarized components can propagate in the fiber laser [28,29]. Thus, different group velocities and phases are generally generated in the two orthogonally polarized modes when the pulse propagates in SMF. Among them, the difference in group velocities will causes the pulse to widen or even break, while the difference in phase velocities leads to the variation of the polarization state. Up to now, various types of vector solitons can be observed based on polarization insensitive devices, such as the polarization rotation vector soliton (PRVS) and polarization locked vector soliton (PLVS) under weak intracavity birefringence, and the group velocity locked vector soliton (GVLVS) under the condition of stronger intracavity birefringence [30–34]. Particularly, the two polarization components of PLVS can further couple as a vector soliton by compensating their phase velocity shift through the cross-phase modulation (XPM) and self-phase modulation induced nonlinear phase shift [35]. In the PRVS, the pulse intensity of two orthogonally polarized components can periodically vary in fiber laser in cavity roundtrip time [36]. Being different from the PRVS and PLVS, the typical formation process of GVLVS is that the two components are coupled as a unit by shifting their central wavelengths to compensate for group velocity difference [37]. In recent years, although many vector pulses have been investigated extensively, there is still a rare report on noise-like vector pulses (NLVPs). Particularly, to the best of our knowledge, the pulsating NLVPs have not been sufficiently explored yet. Therefore, it is interesting to explore the real-time dynamics of NLVPs in a fiber laser with a nonlinear optical loop mirror (NOLM).
Indeed, the NLVPs can exhibit rich transient dynamics from a fiber laser with a NOLM. In this paper, the basic NLP operation can be obtained by changing the intracavity parameters. By utilizing the DFT, the transient dynamics evolutions of the stationary and pulsating NLVPs in different forms can be visualized, including group velocity locked noise-like vector pulse (GVLNLVP), polarization locked noise-like vector pulse (PLNLVP), as well as the transitional state of combined characteristics of GVLNLVP and polarization rotation noise-like vector pulse (PRNLVP). Additionally, the coexisting state vector nature of conventional soliton and NLP is also unfolded for the first time. We also discuss the influence of the intracavity birefringence on the NLVPs. This investigation will contribute to further understanding the mechanism of NLVPs and enrich the vector pulse framework towards transient dynamics.
2. Experimental setup
Figure 1 illustrates the experimental setup of our proposed fiber laser. In order to realize the mode-locking operation, a 30:70 optical coupler (OC1) is utilized to connect the unidirectional ring (UR) and NOLM, which can provide different nonlinear phase shift. The UR consists of a 10:90 OC2, a polarization controller (PC1), a piece of 4 m erbium-doped fiber (EDF), and a polarization-independent isolator (PI-ISO). Among them, the EDF is served as the gain medium, which is pumped by a 980 nm laser diode (LD) via a 980/1550 nm wavelength division multiplexer (WDM). The PC1 is utilized to tune the cavity birefringence and polarization state. The PI-ISO is applied to guarantee unidirectional propagation. The OC2 with 10% port is utilized as the output of the laser for the detection of various instruments. The NOLM is comprised of a PC2 and a segment of 70 m SMF, the SMF provides adequate nonlinear phase shift difference between the two optical pulses propagating in opposite directions. The whole cavity length is ∼ 86.3 m, consisting of 4 m EDF with group-velocity dispersion (GVD) of −18.5 ps/(nm•km) and 82.3 m SMF with GVD of 17 ps/(nm•km). Thus, the net dispersion is around −1.69 ps2, which indicates that the fiber laser operates under a large anomalous dispersion regime. In addition, to resolve the NLVPs, a polarization beam splitter (PBS) is connected with an external PC to separate the two orthogonally polarized components. The pulse trains are recorded by using a 4 GHz digital oscilloscope (Keysight, MSOS404A). A radio-frequency (RF) analyzer (Unit, UTS2020) and an optical spectrum analyzer (OSA) (Anritsu, MS9740A) are utilized to monitor the stability of the pulse and measure the spectrum of the laser, respectively. To monitor the real-time spectral evolution of the NLVPs, a 30 km SMF is as a dispersive element to realize DFT technique. The spectral resolution is around 0.49 nm in our case.
3. Results and discussion
3.1 Mode-locking operation on NLP regime
By adjusting cavity polarization settings, different mode-locked operations like solitons or NLP can be achieved in the fiber laser, respectively. As presented in Fig. 2, the fundamental NLP can be obtained when the pump power is set to 355.5 mW. Figure 2(a) presents the optical spectrum measured by the OSA, which displays a broad and smooth dual-wavelength spectral shape. The corresponding pulse train is illustrated in Fig. 2(b). One can see that the interval of two adjacent pulses is about 420 ns, matching well with the length of the cavity. In addition, the corresponding autocorrelation trace is plotted in Fig. 2(c). A narrow (∼2.18 ps) coherence peak rides on a broad pedestal, which is consistent with the characteristics of NLP operation in the laser cavity. The shot-to-shot spectrum is recorded by means of the DFT method, where substantial fluctuations can be seen on the real-time spectrum, as illustrated in Fig. 2(d). Meanwhile, the inset in Fig. 2(d) presents the averaged spectrum over 1000 roundtrips after DFT.
Fig. 2. Basic NLP operation. (a) Output spectrum; (b) Corresponding pulse train; (c) Autocorrelation trace; (d) Shot-to-shot spectrum (Inset: the corresponding averaged spectrum after DFT).
3.2 Characteristics of stationary NLVPs
Since the laser cavity has no polarization-sensitive components, the dynamics of NLVPs can be investigated in our experiment. After a precise adjustment of PCs, the NLVPs can be obtained, as can be observed from Fig. 3. Figure 3(a) presents the OSA spectra without and with PBS. Among them, the total spectrum is denoted by red curve, then the blue and green curves denote the horizontal and vertical components after the PBS, respectively. It is obvious that two components have similar spectral profiles and same central wavelengths. Figure 3(b)-3(d) show the corresponding pulse trains of the total and two components, they possess same pulse-to-pulse interval and uniform intensity. Considering the spectral and temporal features, we can suggest that these two components conform to the typical characteristic of PLNLVP. To gain insight into the characteristics of PLNLVP, the real-time spectral information is captured by using the DFT system. In the NLP operation regime, shot-to-shot spectral profiles over 1000 roundtrips are exhibited, where no obvious variations of the spectral profiles are observed, as illustrated in Fig. 3(e)-3(g). The insets of Fig. 3(e)-3(g) display the corresponding averaged linear spectra of DFT.
Fig. 3. Stationary PLNLVP operation. (a) Polarization resolved spectra; (b)-(d) Total and polarization resolved pulse trains; (e)-(g) Total and polarization resolved shot-to-shot spectra (Inset: the corresponding averaged spectra after DFT).
For the different birefringence distributions in the laser cavity, the coupling between two orthogonally polarized components of the vector pulse has a great influence on its physical properties, which may lead to various types of NLVPs. In order to further explore other NLVPs, we change the pump power and orientation of the PCs, which then alter the transmittance of the NOLM as well as the overall effective laser gain. The spectral profile is changed as shown in Fig. 4(a). Different from the optical spectrum aforementioned, the single-wavelength NLP is obtained. From Fig. 4(a), the total spectrum centers at 1593.8 nm, while the two orthogonally polarized components locate at 1591.4 nm and 1596.1 nm, respectively. Particularly, we notice that the two polarization components possess a 4.7 nm wavelength difference. This wavelength shift features of the two polarized components, in this case, is similar to that of GVLVS. According to the formation mechanism of GVLVS, we can know the two orthogonal polarization modes of the NLP need to compensate for linear-birefringence-induced polarization dispersion by shifting their central wavelengths. Particularly, the XPM effect plays an important role in its formation. The intensity of the total pulse train is uniform, while the two components reflect the obvious polarization rotation characteristic of PRNLVP, as presented in Fig. 4(b)-4(d). Since the pulse intensities along the two components periodically alter between higher and lower value in the time domain, we suspect that the spectral features in the frequency domain will also correspondingly undergoes a periodic change. In Fig. 4(e)-4(g), by using DFT technology, the spectral profiles and peak intensity periodically changed in two orthogonally polarized components can be clearly observed. For better clarity, the single-shot spectra of 1000 cavity roundtrips are also provided, as demonstrated in Fig. 4(h)-4(j). It is worth noting that, the NLVPs possess obvious wavelength difference (4.7 nm) and polarization rotation features. Thus, we consider this NLVPs are a transitional state between GVLNLVP and PRNLVP, namely, GVL-PRNLVP.
Fig. 4. Stationary GVL-PRNLVP operation. (a) polarization resolved spectra; (b)-(d) Total and polarization resolved pulse trains; (e)-(g) Total and polarization resolved pulse trains after DFT process; (h)-(j) Total and polarization resolved shot-to-shot spectra (Inset: the corresponding averaged spectra after DFT).
3.3 Characteristics of pulsating NLVPs
As an interesting nonlinear phenomenon, pulsation widely occurs in versatile fields. It is noted that the pulsating NLVPs are also observed in our experiment by further carefully adjusting the intracavity PCs. The OSA spectra without PBS and with PBS are displayed in Fig. 5(a). Different from the GVL-PRNLVP, the two components exhibit similar spectral profiles and same central wavelength. This means that the wavelength difference between them is zero. Figure 5(b)-5(d) display the long-term pulse trains of total and two orthogonally polarized components without DFT. We can clearly see that the pulse intensities appear recurrent evolution. The pulsation periods of the total and two polarization components are identical (35.7 µs). The corresponding RF spectrum has several sidebands with a 28 kHz offset, which is consistent with the pulsating period, as shown in Fig. 5(e). To further study the evolution of the pulsating NLVPs, the DFT technique is introduced to illustrate the shot-to-shot spectra, as shown in Fig. 5(f)-5(h), respectively. Different from OSA spectra, we can observe a periodic stretch and compression of the pulse. These results indicate that the pulsating PLNLVP has been formed. Additionally, the inset of Fig. 5(f)-5(h) display the periodic energy evolution, which is formed by integrating the DFT spectrum intensity in each roundtrip. Obviously, the pulse energy here undergoes a slow increase followed by a rapid decay in each oscillating period. One can see that the oscillating energy and spectral bandwidth breathing vary periodically with an identical period. It is worth noting that long wavelength components pulsate more significantly than short wavelength components of NLVPs from the real-time spectra evolution.
Fig. 5. Pulsating PLNLVP operation. (a) Polarization resolved spectra; (b)-(d) Total and polarization resolved pulse trains; (e) RF spectrum; (f)-(h) Total and polarization resolved shot-to- shot spectra (Inset: the energy variations).
Moreover, further changing the polarization of the cavity, another pulsating NLVPs are obtained. The spectral profiles of the total and two components are similar to each other, while the wavelength shift is up to 4 nm, as shown in Fig. 6(a). The pulse trains in a larger time scale in Fig. 6(b)-6(d) have the same pulsation period. Therefore, we deem that this NLVPs are pulsating GVLNLVP. To obtain more insight into the spectral evolution, shot-to-shot spectra are presented in Fig. 6(e)-6(g), respectively. The energy variations also are respectively illustrated in the inset of Fig. 6(e)-6(g). Remarkably, the pulse energy varies almost sinusoidally. In particular, this spectral profiles and energy oscillation are similar to Fig. 5(f)-5(h), which display periodically.
Fig. 6. Pulsating GVLNLVP operation. (a) Polarization resolved spectra; (b)-(d) Total and polarization resolved pulse trains; (e)-(g) Total and polarization resolved shot-to-shot spectra (Inset: the energy variations).
The third pulsating NLVPs can be obtained by further proper adjustment of the PCs. Figure 7(a) presents the corresponding spectra before and after PBS. The wavelength shift is 3 nm, and the spectral feature is similar to the GVLNLVP mentioned above. From Fig. 7(b)-7(d), the pulse trains display obvious polarization rotation characteristics, i.e., the asynchronous modulation behaviors of the two polarized modes. That indicates PRNLVP has been formed. Therefore, the pulsating NLVPs can simultaneously show the features of the GVLNLVP and PRNLVP, which is also named a transitional state between GVLNLVP and PRNLVP. In order to demonstrate the real-time spectral evolution, shot-to-shot spectra with identical periods are respectively provided, as shown in Fig. 7(e)-7(g). Particularly, the spectral profiles and energy of the two orthogonal polarization components display obvious asynchronous evolution. It is worth mentioning that Liu et al. investigated the trapping characteristics of PRVS in a fiber laser [37], whose polarized components all exhibit asynchronous during the temporal and spectral domain. Here evolution dynamics are completely similar to previous works. In contrast to conventional PRVS, the superposition of the polarization rotation and intensity modulation result such asynchronous behaviors.
Fig. 7. Pulsating GVL-PRNLVP operation. (a) Polarization resolved spectra; (b)-(d) Total and polarization resolved pulse trains; (e)-(g) Total and polarization resolved shot-to-shot spectra (Inset: the energy variations).
3.4 Characteristics of coexisting mode-locked pulsating NLVPs
Again, by further slightly adjusting the PCs, a distinct coexisting mode-locked pulsating NLVPs state can be obtained in our experiment. As presented in Fig. 8(a), the spectral components include soliton and NLP. The two orthogonal polarization components of NLVPs have a 2.8 nm wavelength shift. In particular, we note that the central wavelengths of soliton always locate at 1573.6 nm from the inset of Fig. 8(a). Meanwhile, extra sharp peak-dip characteristic is visibly observed on the polarization-resolved spectra, implying that between the two orthogonally polarized components exist the energy exchange [38]. Extra peak-dip structure and the same central wavelengths are notable features of PLVS. In this coexisting mode locking, the solitons display the features of PLVS, while the NLP shows the characteristics of GVLNLVP. Figure 8(b) presents the corresponding pulse train of total without PBS. Multiple solitons possess a uniform low intensity and are randomly distributed in the whole laser cavity. The pulse interval of NLP is 420 ns. Figure 8(c) shows the RF spectrum with two symmetric side peaks around the main peak, which has a 130 kHz frequency difference, indicating that pulse train exists intensity modulation. The pulsation period of NLP is about 7.6 µs, as shown in Fig. 8(d). On the contrary, the soliton intensities are all no obvious fluctuations. To gain more information about the novel behavior, we also provide the real-time dynamics in the temporal and spectral domain, as exhibited in Fig. 8(e) and 8(f). From Fig. 8(e), we can see that the spectrum and the total energy display obviously periodic oscillations. As illustrated in Fig. 8(f), the NLP pulsates in fiber laser, while the multiple solitons keep uniform amplitude intensity. Figure 9(a) and 9(b) present the pulse trains of two components, which exhibit obvious polarization rotation characteristics. To further reveal the spectral evolution, Fig. 9(c) and 9(d) depict the shot-to-shot spectra after PBS, respectively. We can observe the two components have asynchronous spectra modulation behaviors. Moreover, it is found that the pulsation and polarization-evolution have identical period. The pulse energy and polarization orientation of the pulsating NLVP return back to their own original value every ∼18 cavity roundtrips. In particular, the coexisting pulsating NLVPs simultaneously possess the features of GVLNLVP and PRNLVP. Similarly, we consider it is the transitional coexisting mode-locked state of GVL-PRNLVP.
Fig. 8. Coexisting mode-locked pulsating GVL-PRNLVP operation. (a) Polarization resolved spectra; (b) Short-term pulse train of total; (c) RF spectrum; (d) Long-term pulse train of total; (e) Total shot-to-shot spectrum (Inset: the energy variations); (f) Total shot-to-shot temporal pulse evolution without DFT.
Fig. 9. Coexisting mode-locked pulsating GVL-PRNLVP operation. (a) and (b) Polarization resolved pulse trains; (c) and (d) Polarization resolved shot-to-shot spectra (Inset: the energy variations).
Another coexisting pulsating NLVPs can be also obtained by further slightly adjusting the PCs. The spectral profiles of the total and two polarization components are similar to each other and have almost the same central wavelengths, as illustrated in Fig. 10(a). Meanwhile, the solitons spectra also center all at 1573.6 nm and display extra peak-dip structure. As displayed in Fig. 10(b)-10(d), the long-term pulse trains of total and two orthogonally polarized components have identical pulsation periods. It is found that both the pulsating NLVPs and soliton agree well with the features of PLNLVP and PLVS, respectively. Thus, we deem that the coexisting mode-locked pulsating PLNLVP is also obtained in our experiment. Then we employ the DFT again to measure the spectral information of the total and two orthogonally polarized components over 200 consecutive roundtrips as presented in Fig. 10 (e)-10(g). Both spectra and energy periodically evolve along roundtrips. Interestingly, the solitons always exhibit the features of PLVS compared with NLP in this coexisting mode-locked condition.
Fig. 10. Coexisting mode-locked pulsating PLNLVP operation. (a) Polarization resolved spectra; (b)-(d) Total and polarization resolved pulse trains; (e)-(g) Total and polarization resolved shot-to-shot spectra (Inset: the energy variations).
It should be mentioned that the DFT technique is universally applicable when the transform-limited pulses before being measured by the DFT method are shorter than ∼20 ps. As for nanosecond pulse such as dissipative soliton resonance (DSR), the DFT technique is unviable for real-time spectral observation. However, NLPs are not temporally coherent but consist of many shorter pulses that allow the envelope to be stretched by ∼30 km SMF. By virtue of DFT, the pulse undergoes significant modifications in the temporal profile and mimics the spectrum waveform. Therefore, the vector features of the NLPs are investigated by DFT technology in the experiment.
Generally, the birefringence of fiber laser provides an important role in the vector nature, and the associated optical spectrum and pulse train can show different features based on different birefringence conditions. When the interaction between two orthogonally polarized components of the NLP in different ways, various types of NLVPs can be formed. In a relatively low birefringence, the PLVS and PRVS generally easy to be formed, while the GVLVS is usually formed in a large cavity birefringence. In particular, the extra peak-dip sideband of spectra is one notable feature of PLVS in the vector soliton regime [39]. Nevertheless, in our experiment, it presents inconspicuous on the spectra of NLVPs. We deem that this result should be related to a low coherence degree of the NLP regime. In our experiment, the transitions between these pulsating NLVPs states may take place with a proper cavity birefringence. Besides, by altering the PCs, the pulsating NLVPs having some features of combining the GVLNLVP with PRNLVP are observed, and the central wavelength shift of 3 nm is larger than the one in pulsating PLNLVP (0 nm) but smaller than that in pulsating GVLNLVP (4 nm). This means that the birefringence of this case is stronger than pulsating PLNLVP but weaker than pulsating GVLNLVP. Moreover, with further adjustment of the PCs, we can observe other kinds of NLVPs in our experiment. The coexisting pulsating NLVPs are also obtained for the first time. Especially, the soliton component always possesses the features of PLVS in the coexisting mode locking operation. Besides, the features of the GVLNLVP and PRNLVP can be simultaneously displayed in this particular state. As we know, the transitional state between GVLNLVP and PRNLVP has yet been no report on its mechanism. Thus, it is necessary to explore this completely unclear mechanism. Then a question would naturally arise as to how the polarization-state evolution of the transitional state between GVLNLVP and PRNLVP could be revealed. Actually, the numerical simulations are helpful to verify experimental results in fiber lasers. Unfortunately, due to the complicated coupling in this state, the simulations to reproduce the experimental results are still challenging. Overall, the mergence between pulsating and vectorial nature can provide an intriguing scenario towards the transient ultrafast dynamics of coexisting modes.
4. Conclusion
In summary, we investigate the characteristics of the NLVPs based on the NOLM. By virtue of DFT, it is found in real time that spectra evolutions and polarization dynamics of NLVPs. Various types of NLVPs, both stationary and pulsating NLVPs, as well as the transitional state between GVLNLVP and PRNLVP, are observed with the adjustment of the PCs. Additionally, the NLVPs of coexisting mode locking also have been investigated in our experiment. Particularly, this state can similarly display the transition features of GVL-PRNLVP. Further investigation of these observed NLVPs is needed to explain the forming mechanism, which is related to our next work. Our findings can enrich the research framework towards pulsating NLVPs.
Funding
Natural Science Project of Huaibei Normal University (2023ZK043); Innovation Fund for Postgraduates of Huaibei Normal University (CX2023040); Joint Training Demonstration Base for Graduate Students of Anhui Province (2022lhpysfjd046); Key Natural Science Research Project for Colleges and Universities of Anhui Province (2022AH050399); Natural Science Foundation of Anhui Province (2008085MF211); National Natural Science Foundation of China (41875040).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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