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Abstract
The vector nature of noise-like pulses (NLPs) in a figure-eight erbium-doped fiber laser based on the nonlinear amplifier loop mirror (NALM) configuration is experimentally investigated. After achieving the operation regime of NLPs, both the group velocity locked noise-like vector pulses (GVL-NLVPs) and the polarization locked noise-like vector pulses (PL-NLVPs) are observed in the cavity. By virtue of the dispersive Fourier transform (DFT) technique, their spectral evolution and the energy vibration are measured and analyzed in real time. We also obtain another state of noise-like vector pulses (NLVPs) with combined characteristics of GVL-NLVPs and PL-NLVPs. It is shown that the NLVPs are sensitive to the cavity birefringence. Our results would be beneficial to complement the understanding of vector dynamics of NLPs in ultrafast fiber lasers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In fields of micromachining, optical communication, medicine, and etc., passively mode-locked fiber lasers can be promising light sources to produce ultrashort pulses. Governed by the Ginzburg-Landau equation (GLE), passively mode-locked fiber lasers can generate various solitons depending on a composite balance among the dispersion, nonlinearity, gain and loss [1]. According to the soliton quantization effect [2], conventional solitons cannot endure excessive nonlinearity and may break into multiple solitons under a high pump power. In this operation regime, multiple solitons can interact with each other in the laser, leading to some interesting phenomena like soliton molecules [3,4], bound solitons [5,6], dissipative soliton resonance [7,8] and noise-like pulses (NLPs) [9–11]. Therefore, the passively mode-locked fiber laser can provide an excellent testing ground for exploring the nonlinear dynamics and intrinsic mechanism of these soliton phenomena.
As a ubiquitous operation in the ultrafast laser system, NLP refers to a wave packet comprising of chaotic sub-pulses with random intensity, repeating itself at a fundamental or harmonic repetition rate. NLP was first discovered based on an erbium-doped fiber laser, in which the spectrum was broadened to 44 nm [12]. Afterwards, the real-time spectral evolution of NLP showing large fluctuations was first revealed by the dispersion Fourier transform (DFT) technique [13]. The formation mechanism and the influence factors of NLPs are investigated by various groups as well. Tang et al. attributed the bunched NLP emission to the combination of the soliton collapse and cavity positive feedback [14]. Zhao et al. reported that the broadening of the NLP spectrum was originated from the strong four-wave-mixing (FWM) and soliton self-frequency shift effects in the fiber laser [9]. The influence of intra-cavity nonlinearity on the generation and evolution of NLPs was also investigated in figure-of-eight fiber lasers [15]. Characterized by the ultrabroad and smooth output spectrum exceeding the gain bandwidth, the NLPs can show impressive performance in super-continuum generation [16–21]. Besides, the accompanying high energy and excellent tolerance of large nonlinearity make them a good candidate for participation in many applications like industrial processing and medicine [22–25].
Owing to the birefringence introduced by imperfect drawing and unavoidable external pressure, the single mode fibers (SMFs) can support the propagation of two orthogonal polarization components [26,27]. Vector solitons (VSs) can be generated in fiber lasers with suitable birefringence. With weak intracavity birefringence, polarization locked VSs (PLVSs) can be generated [28,29]. The two orthogonally polarized components, based on the compensation of their phase velocity shift through the self-phase modulation (SPM) and cross-phase modulation (XPM) induced nonlinear phase shift, can couple as a single vector soliton [30]. Moreover, a PLVS can further stabilize itself with dynamic adjustment through the coherent energy exchange [30]. Under the condition of stronger intracavity birefringence, there will be large group velocity shift between the two orthogonally polarized components. By shifting their central wavelengths to compensate the group velocity difference, the two components can be trapped together and co-propagate as a non-dispersion unit [31–33], which is the typical formation process of the group velocity locked VSs (GVLVSs) [34]. Researches on vector solitons have been carried out in fiber lasers mode-locked by graphene since no polarization sensitive component is involved in the cavity [35,36]. Without polarization discrimination devices in the cavity, mode-locked fiber lasers based on the nonlinear amplifying loop mirror (NALM) is also a suitable platform to investigate the vector feature of NLPs [37]. Moreover, the NALM loops possess two polarization controllers, which enables convenient adjustment of the vector soliton operation [38]. Although the vector nature of NLPs has been reported, their unique vector characteristics in real time have not been explored yet. Considering the importance and complexity of NLPs, it will be necessary to further investigate the real-time formation process and physical mechanism of noise-like vector pulses.
In this paper, we report on the experimental studies of the noise-like vector pulses in an erbium-doped figure-eight fiber laser. With proper adjustment of the cavity polarization state, we successfully observed both group velocity locked noise-like vector pulses (GVL-NLVPs) and polarization locked noise-like vector pulses (PL-NLVPs). Moreover, another type of noise-like vector pulses (NLVPs) combining the features of both GVL-NLVPs and PL-NLVPs is also obtained. By virtue of the DFT technique, the real-time spectra and energy evolutions of vector NLPs in different forms have been visualized. The influence of the cavity birefringence on the vector NLPs operation is also discussed.
2. Experimental setup
The experimental schematic of the figure-eight fiber laser is shown in Fig. 1, which is mode-locked by the NALM. The NALM loop on the left part is comprised of a polarization controller (PC1), a piece of 1-m-long erbium-doped fiber (EDF, Liekki Er80-8/125) as the gain medium and a pump/laser signal wavelength division multiplexer (WDM) to introduce the pump light from a single-mode fiber pigtailed 976-nm laser diode (LD). The main loop on the right part consists of another polarization controller (PC2), a polarization-independent isolator (PI-ISO) to guarantee the unidirectional operation and an output coupler (OC) to extract 30% of the laser output. The EDF has a group-velocity dispersion (GVD) parameter of −20 ps2/km at 1550 nm, and the device pigtail (∼10.1 m in total) is the single mode fiber with a GVD parameter of −23 ps2/km at 1550 nm. Thus, the overall cavity dispersion is approximately −0.25 ps2. Additionally, to analyze the vector feature of output pulses, a polarization beam splitter (PBS) together with a third PC is added to evaluate and characterize the output by separating the two orthogonal polarization components.
In the experiment, an optical spectrum analyzer (OSA) (Yokogawa, AQ6375B) and a high-speed oscilloscope (Tektronix, DPO71254C, 12.5 GHz) with a photoelectric detector (ET-5000F, 12.5 GHz) are applied to evaluate the output pulses. The radio frequency (RF) spectrum and the pulse duration of the output are recorded by a RF spectrum analyzer (Keysight, N9322C) and an autocorrelator (FR-103XL), respectively. In addition, to get the real-time pulse characteristics based on the DFT technique, a segment of dispersive fiber with a total dispersion value of −331 ps/nm at 1550 nm is placed before the high-speed oscilloscope with a photoelectric detector. Thus, the spectrum resolution of the DFT configuration is approximately 0.24 nm.
3. Results and discussion
3.1 Stationary mode-locking operation on soliton regime
Figure 2 presents the experimental results of the stationary mode-locking operation under the pump power of 60.3 mW. As depicted in the blue curve of Fig. 2(a), the spectrum with Kelly sidebands locates at 1570 nm and has a 3-dB bandwidth of 6.96 nm. The red curve in Fig. 2(a) shows the averaged result of the real-time spectra obtained by the DFT technique. We can see that they are in good agreement, which demonstrates the good accuracy of the DFT setup. Figure 2(b) illustrates the mode-locking pulse train with a pulse-to-pulse interval of 54.14 ns, corresponding with the fundamental repetition rate of 18.47 MHz, as shown in the RF spectrum in Fig. 2(c). The signal-to-noise ratio (SNR) at the fundamental repetition rate is ∼47 dB, indicating a relatively steady operation state. Figure 2(d) provides the autocorrelation trace with a full width at half maximum (FWHM) of 933 fs. The small pedestal of the autocorrelation trace can be attributed to the dispersive wave, which is consistent with the strong Kelly sidebands in the spectrum. Assuming the sech2 pulse profile, the pulse duration is ∼605 fs. The time-bandwidth product is calculated to be ∼0.512, indicating that the pulses are chirped. The spectral profile with Kelly sidebands, the pulse trains, the RF spectrum and the autocorrelation trace exhibited above shows that the pulses are operating on a soliton regime.
Fig. 2. Experimental results in the stable mode-locking operation regime. (a) Output spectrum; (b) Pulse trains; (c) RF spectrum; (d) Autocorrelation trace.
3.2 Vector characteristics of NLPs
To get the NLPs state, the pump power was increased to 400 mW. With the specific orientations of the intra-cavity PCs, the Kelly sidebands of the output spectrum disappeared and the spectrum was stretched to a broader one. As shown in Fig. 3(a), the NLPs featured smooth black curve is centered at 1567.4 nm with a 3-dB bandwidth of 10.5 nm. The autocorrelation trace shown in Fig. 3(b) was characterized by a spike (less than 1 ps) riding on the wide pedestal (∼188.8 ps), which further verifies the NLP operation. Then, the PBS, combined with a PC, was added to the output coupler to obtain the two orthogonal polarization components for the spectral and temporal characterization. The output spectra of both two portions after the PBS are denoted by the red and blue curves, respectively, as depicted in Fig. 3(a). The red one is centered at 1566.26 nm while the blue one is centered at 1570.26 nm. The wavelength shift between these two orthogonally polarized components is 4 nm. The averaged spectra for both two components resulting from the DFT technique are displayed in Fig. 3(c), which is in good agreement with the respective spectra recorded by the OSA. Considering the different central wavelengths, the two polarization components were required to trap each other based on the birefringence compensation between them and propagate in the cavity as a GVL-NLVP. Figure 3(d) presents the corresponding pulse trains of two orthogonal polarization components and the pulse interval is 54.14 ns. It can be seen that both of them possess the same repetition rate as the stationary soliton while the intensities are no longer uniform as the stationary one (see Fig. 2).
Fig. 3. Results of GVL-NLVPs operation regime. (a) OSA spectra; (b) RF spectrum; (c) DFT averaged spectra; (d) Pulse trains.
By virtue of the DFT technique, the real-time spectral evolutions over 5771 consecutive roundtrips of the two orthogonally polarized components are further displayed in Fig. 4(a) and Fig. 4(c), respectively, the blue curves of which denote the pulse energy evolutions. We can see that the real-time evolutions for both components experience large fluctuations in terms of the spectral width and pulse energy over roundtrips while possessing their intrinsic characteristics. Figure 4(b) and Fig. 4(d) present the three-dimensional evolutionary dynamics of the two polarized components from roundtrip 3400 to roundtrip 4000. Parts of A’, B’ and C’ in Fig. 4(b) refer to the three-dimensional information of sections A, B and C in Fig. 4(a). And parts of D’, E’ and F’ in Fig. 4(d) refer to the three-dimensional information of sections D, E and F in Fig. 4(c). In certain roundtrips where one polarization component reaches the maximum intensity (A’, C’ and E’), the other orthogonal one experiences at its minimum magnitude (B’, D’ and F’). Interestingly, we can also find that not only the spectrum but also the energy evolves aperiodically over roundtrips, and the separations between the peak to peak or bottom to bottom are unfixed. We can see that the duration from A(A’) to B(B’) is 162 roundtrips while the duration from B(B’) to C(C’) is 150 roundtrips. Similarly, the region from D(D’) to E(E’) spans over 128 roundtrips while it lasts over 139 roundtrips from E(E’) to F(F’). This unique phenomenon has not been reported before. We can conclude that there exists energy conversion between these two parts. As complementary roles, these two components can be coupled to one GVL-NLVP as a whole circulating in the cavity.
Fig. 4. Results of GVL-NLVPs operation. (a) Shot-to-shot spectra of horizontal polarized component (b) 3D evolution of horizontal polarized component; (c) Shot-to-shot spectra of vertical polarized component; (d) 3D evolution of vertical polarized component.
Carefully altering the PCs under a fixed pump power of 400 mW, the two polarized components in the NLPs operation regime can couple as another form of vector NLPs. The black curve in Fig. 5(a) represents the typical NLP spectrum which was measured before the PBS and locates at 1566.5 nm with a 3-dB bandwidth of 9.18 nm. After being split into two orthogonal components with the PBS, the vector nature of the NLPs was evaluated and depicted in Fig. 5(a) and Fig. 5(b). In the spectral domain, both of the horizontally and vertically polarized components have the same central wavelength of 1566.5 nm. It can be notably seen from Fig. 5(a) that a dip appears at around 1574.5 nm in the vertical component while the horizontal one is a smooth and swell-up structure. In the vector soliton regime, the extra peak-dip spectral sidebands are attributed to the FWM effect, through which the coherent energy exchange occurs between these two polarized components [37]. The spectral profiles in Fig. 5(a) follows this exchange of energy at around 1566.5 nm. However, the underlying regime of the energy exchange here can be different from FWM effect since the NLPs regime shows a low degree of coherence, which needs further theoretical and numerical analysis. One notable characteristic of PLVS is that the spectra of the two orthogonal polarization components possess the same central wavelengths and extra peak-dip structures. Similarly, we can conclude that these two components in the NLP operation regime are coupled to become one PL-NLVP in the cavity. Figure 5(b) displays the oscilloscope waveforms of the two components with the identical pulse-to-pulse interval of 54.14 ns, which is in accordance with the fundamental repetition rate. To study the internal dynamics of the PL-NLVPs, the shot-to-shot spectra of the two orthogonally polarized components in the NLP operation regime are demonstrated in Fig. 6(a) and Fig. 6(b). It is shown that both the real-time spectra and the pulse energy exhibit obvious and irregular fluctuations. Different from Fig. 4, the spectrum and energy fluctuations in this case do not experience the aperiodical evolutions. It can be concluded that not only the whole vector NLPs but also the two polarized components travel in the NLPs operation regime in the fiber laser.
Fig. 6. Results of PL-NLVPs operation regime. (a) shot-to-shot spectra of the horizontally polarized component; (b) shot-to-shot spectra of the vertically polarized component.
With appropriate adjustment of the PCs, a third type of NLVPs was observed. As demonstrated in Fig. 7(a), the spectrum of the NLVPs is centered at 1565 nm with a 3-dB bandwidth of 7.46 nm. Comparing with the output spectrum of the entire vector NLPs, the center wavelength of the horizontal polarization component red-shifts to 1566 nm while that of the vertical one blue-shifts to 1564 nm. The wavelength shift between the two orthogonal polarization components is 2 nm. The wavelength offset here is smaller than that in the GVL-NLVP, which indicates that the birefringence in this case becomes weaker than in the GVL-NLVP. It is worth noting that, at around 1572.6 nm, a small peak shows up on the horizontal component while a slight dip appears on the vertical component, implying energy exchange between these two components [38]. The pulse train with uneven intensities for both two components are depicted in Fig. 7(b), the repetition rate of which is also 18.47 MHz. Similar to the two types of vector NLPs mentioned above, the spectral width as well as the pulse energy also exhibits notable fluctuations over roundtrips within the cavity, which can be seen in Fig. 8(a) and Fig. 8(b). It is worth noting that, the vector NLPs here present a slightly aperiodical change in the spectrum and energy evolutions, which is similar but less obvious compared to Fig. 4. As discussed above, the NLVPs, illustrated in Fig. 7 and Fig. 8, not only feature a wavelength shift of 2 nm but also possess a complementary peak-to-dip spectral component at a specific offset to the center wavelength for the two orthogonally polarized components. Thus, the vector NLPs can be considered as a transitional state between GVL-NLVPs and PL-NLVPs.
Fig. 8. Results of NLVPs operation regime. (a) Shot-to-shot spectra of the horizontally polarized component; (b) Shot-to-shot spectra of the vertically polarized component.
By properly increasing the pump power to enhance the cavity nonlinearity, the fiber laser can maintain the NLP operation with a broader output spectrum of up to 10.5 nm. The spectral width and the pulse energy of NLPs experience notable fluctuations over roundtrips. In the time domain, the pulse train exhibits uneven intensity envelope instead of a uniform one for the stationary solitons. With the pump power unchanged, the two polarization components of the NLPs can interact with each other in different ways under different birefringence conditions to form the ultimate vector NLPs of various types. Firstly, the GVL-NLVPs are characterized by the 4 nm offset of central wavelength for the two orthogonally polarized components. The large wavelength shift can be attributed to the large cavity birefringence [37]. The spectrum as well as the pulse energy experience obvious aperiodic fluctuations over roundtrips with unfixed periods. Secondly, with proper orientations of the PCs, two orthogonal polarization components can lase at a same central wavelength. The additional complementary peak and dip features emerging on the spectrum of the two components verify the PL-NLVPs. The formation of PLVS generally require a relatively low birefringence in the cavity [30]. Similarly, we believe that there is low cavity birefringence involved in PL-NLVPs without the wavelength shift between two components. There are no obvious aperiodic evolutions of the spectrum and energy in the PL-NLVPs. It is worth noting that, in typical polarization resolved spectra for conventional solitons with Kelly sidebands, other extra sidebands, corresponding to the FWM induced complementary peak and dip features for the two soliton components, can also be observed, indicating the coherent energy exchange [39]. In contrast, in the NLP case without Kelly sidebands, the accompanying additional peak and dip structures in the spectrum are not obvious. Thirdly, another kind of NLVPs possessing some characteristics of both the GVL-NLVPs and PL-NLVPs are obtained by altering the PCs. Besides the central wavelength shift of 2 nm, there is a peak-dip matchup at 1572.6 nm between these two orthogonal polarization components. The wavelength shift here is smaller than that in GVL-NLVPs (4 nm) but larger than the one in PL-NLVPs (0 nm). It can be deduced that the birefringence involved in this case is weaker than GVL-NLVPs but stronger than PL-NLVPs. Besides, this kind of NLVPs goes through a slightly aperiodic evolutions in the spectrum and energy evolutions. Moreover, with further adjustment of the pump power or the PC orientations, there are other kinds of NLVPs that can be possibly observed in the fiber laser.
4. Conclusion
In conclusion, the vector features of the NLPs are investigated in a fiber laser mode-locked by the NALM. In the NLP operation regime, GVL-NLVPs feature a 4-nm spectral shift between the two polarization components in a cavity with relatively strong birefringence. With weaker birefringence, we obtain PL-NLVPs featuring a complementary peak and dip structure on the spectra between two orthogonally polarized components. With further alterations of the PCs, another type of NLVPs, characteristic of a 2-nm center wavelength shift and a complementary peak and dip structure on the spectrum for the two orthogonally polarized components, is observed. Further explanation of the forming mechanism of these observed NLVPs will be the aim of our future work. The experimental results can enrich the vector dynamics of NLPs and might be able to assist in the design of optical systems for super-continuum generation.
Funding
National Natural Science Foundation of China (61805115, 61875132, 62005178); China Postdoctoral Science Foundation (2019M653019); Basic and Applied Basic Research Foundation of Guangdong Province (2020A1515110471); Natural Science Foundation of Guangdong Province (2020KQNCX072); Shenzhen Government’s Plan of Science and Technology (JCYJ20190808143813399); Shenzhen Fundamental Research Program (JCYJ20200109105216803).
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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