We report on the generation of versatile patterns of multiple rectangular noise-like pulses (NLPs) in a fiber laser mode-locked by nonlinear amplifying loop mirror (NALM). Benefiting from the strengthened nonlinear effect of a segment of highly nonlinear fiber (HNLF) in the loop, multiple rectangular NLPs with various patterns are formed depending on the cavity parameter settings. In particular, the multiple rectangular NLPs could possess unequal packet durations, which is different from the conventional multi-soliton patterns. The experimental results contribute to further understanding the characteristics of the rectangular NLP and the dynamics of multi-pulse patterns.
© 2016 Optical Society of America
Ultrafast fiber lasers, as powerful platforms for generation of ultra-short pulses, have attracted much attention due to their wide range of applications in fields such as optical communications, material processing, microscopy, and sensing [1–4 ]. In addition to acting as ultrashort pulse sources, the ultrafast fiber lasers also play significant roles in investigating soliton nonlinear phenomena for fundamental physics [5–7 ]. Due to the dissipative structures and self-organization effects, the mode-locked soliton in ultrafast fiber laser could exhibit interesting and complex nonlinear behaviors. Indeed, depending on the cavity parameter selections, so far different soliton nonlinear dynamics could be observed in ultrafast fiber lasers, such as dissipative soliton resonance [8–12 ], soliton rain [13–16 ], soliton molecules [17,18 ], soliton explosions [19–21 ], and multi-soliton patterns [22–24 ]. The observations of aforementioned nonlinear phenomena are beneficial for understanding soliton dynamics in nonlinear optics.
Apart from the conventional soliton, the noise-like pulse (NLP), which is another typical operation regime in fiber lasers, becomes a hot topic in very recent years [25–28 ], motivated by its versatile applications in fields such as supercontinuum generation , coherence tomography [30,31 ], optical data storage  as well as sensing . Moreover, the NLP is also demonstrated to be an excellent platform for investigating the rogue wave generation in ultrafast fiber lasers [34,35 ]. In fact, the NLP is a wave packet that consists of many ultra-short pulses with randomly varying amplitudes and durations. The unique properties of NLP make it possess distinct features differing from the conventional solitons, that is, the NLP has a very wide and smooth average spectrum, a double-scaled autocorrelation trace presenting a narrow spike riding on a broad pedestal . Up to date, the investigations of NLP mainly focus on the physical mechanism of NLP , obtaining the spectrum as broad as possible [38,39 ], and the practical applications of NLP [30–33 ]. Generally, the NLP is detected as a Gaussian-like packet shape on the oscilloscope trace. Very recently we have found that the NLP could possess a rectangular wave packet shape by virtue of peak-power clamping effect and the high nonlinearity induced by the long laser cavity. The duration of the rectangular NLP increases with the rising pump power, while the peak amplitude maintains constant. The phenomenon is very similar to the pulse evolution of DSR . Thus, the rectangular NLP seems to exhibit the packet-breaking free feature. However, being different from the DSR pulse which is a coherent one, the rectangular NLP is a partially coherent pulse. In spite of the demonstration of rectangular NLP, there are still many other characteristics regarding rectangular NLP needing to be investigated. As mentioned above, the conventional solitons in fiber lasers would exhibit versatile multi-pulse patterns when either the pump power or intra-cavity nonlinear effect is high enough [22–24 ]. Therefore, enlightened by the patterns of conventional multiple solitons, it would be interesting to know whether the versatile patterns of multiple rectangular NLPs could be observed if we further increase the cavity nonlinearity.
In this work, we address this issue. Herein, we experimentally demonstrated that, by incorporating a section of 65 m highly nonlinear fiber (HNLF) into the laser cavity, the multiple rectangular NLPs can be easily obtained in a fiber laser mode-locked through a nonlinear amplifying loop mirror (NALM). Depending on the cavity parameter settings, the multiple rectangular NLPs could evolve into various patterns. In particular, it was found that the multiple rectangular NLPs could possess different wave packet durations, which is different from the conventional multi-soliton patterns that have the same features among the generated multiple solitons. The experimental results would further enhance the understanding of fundamental physics of the rectangular NLPs and the multi-pulse dynamics.
2. Experimental setup
Figure 1 depicts the schematic of the figure-eight fiber laser in our experiment. It consists of a NALM and a unidirectional ring (UR) cavity, which are connected through a 2 × 2 3-dB optical fiber coupler. The NALM is composed of a 65-m-long HNLF used to enhance the nonlinear effects, a polarization controller (PC), and a 4-m-long erbium-doped fiber (EDF) pumped by a 980 nm laser diode (LD) with the maximum power of 350 mW. In the UR, there is a PC, a polarization-independent isolator (PI-ISO) providing unidirectional operation and a 30% output fiber coupler (OC). An optical spectrum analyzer (OSA, Yokogawa AQ6317C), an oscilloscope (Tektronix DSA-70804, 8 GHz) with a photodetector (Newport 818-BB-35F, 12.5 GHz) and an autocorrelator (FR-103XL) are employed to analyze the laser output spectrum, pulse train and profile, respectively.
3. Experimental results
The passive mode-locking of the fiber laser could be easily achieved due to the NALM playing the role of a saturable absorber. When the pump power was above 35 mW, a single NLP operating at the cavity fundamental repetition rate of 2.01 MHz was always formed by simply rotating the PCs. Figure 2 shows a representative operation state of a single NLP. The 3-dB spectral bandwidth in Fig. 2(a) is 9.7 nm. The pulse train shown in Fig. 2(b) appears a rectangular shape with the duration about 1 ns. Compared with the conventional soliton spectrum with Kelly sidebands, the spectrum in Fig. 2(a) is obviously smoother and broader, which is the typical spectral characteristic of NLP . To further demonstrate that this type of pulse is the NLP, the autocorrelation trace was measured, as presented in Fig. 2(c). It has a narrow coherent peak riding on a broad pedestal, which is another typical characteristic of NLP. Note that the asymmetric autocorrelation trace was caused by the imperfect adjustment of the autocorrelator. Therefore, both spectral and temporal characteristics demonstrate that the rectangular pulse in our experiment is NLP.
Once the NLP is formed, if we increased the pump power, the energy of the NLP could be accumulated without pulse breaking with the proper PC settings. By fixing the PCs at noise-like mode-locking state, the rectangular pulse broadens with the pump strength while the pulse amplitude almost remains invariable. The evolutions of the pulse spectrum and pulse width are shown in Fig. 3 . It is noted that the central wavelength of the rectangular NLP is always kept at 1562 nm and the 3-dB bandwidth changes very slightly as the pump power increases. Correspondingly, the rectangular pulse width broadens from 1 ns to 10 ns with pump power increasing from 40 mW to 350 mW, as shown in Fig. 3(b), which is quite similar to that of the DSR pulse. It seems that the rectangular NLP would not split as we reported in .
3.1 Multiple rectangular NLPs with uniform duration but irregular spacing
On the basis of the mode-locked threshold, we continue to increase the pump power and adjust the intra-cavity PCs simultaneously, aiming for changing the nonlinearity parameters of the cavity. It should be noted that the PCs used in this work are fiber squeezing ones. Thus, we could not quantitatively study the influence of the polarization states on the formation of the multi-pulse pattern. In this case, we note that the single rectangular NLP would break into multiple rectangular NLPs with different patterns. Firstly, we introduced the multiple NLPs with uniform duration but irregular spacing, as presented in Fig. 4 . The inserts of Fig. 4 are the zoom-in of the single NLP. Under this operation state, each pulse was steady and static without merging or annihilation in a round trip time. Here each pulse keeps the rectangular shape, and the wave packet duration of NLP is about 1 ns. Besides, all of the pulses in the laser cavity have similar pulse durations and intensities, which is analogous to the feature of soliton energy quantization of conventional solitons in the fiber lasers. Note that the separations between the pulses vary randomly depending on the interaction between the discrete pulses. The characteristics of this kind of multiple NLPs are similar with those of multi-soliton. The number of multiple NLPs can be enhanced regularly up to 7 as the variation of the intra-cavity parameters, i.e., pump power level. However, no matter how the number of the NLPs changes, the corresponding pulses possess broad and smooth spectra, and the autocorrelation traces with a narrow coherent peak riding on broad shoulders, demonstrating that the fiber laser always operated in NLP regime.
3.2 Multiple rectangular NLPs with both uniform duration and spacing
If we further finely manipulated the PCs, the interaction among the multiple NLPs would change accordingly due to the variations of the phase relationships. Meanwhile, another pattern of multiple rectangular NLPs was presented on the oscilloscope, in which the separations between the rectangular NLPs could become uniform. Figure 5 illustrates the multiple NLPs with both uniform duration and spacing. Obviously, the separations between the adjacent multiple NLPs are identical, which is about 22 ns. The tiny pulses inside the envelope of every rectangular NLP are grouped in a tight packet and maintain a stable transmission state. It is noteworthy that the shape of each pulse is also rectangular. The duration of each rectangular pulse is measured to be about 1 ns. In fact, the phenomenon of the appearance of additional pulse one by one could be obtained through adjusting the pump power and the PCs. Note that when the pump power was increased to 330 mW, 10 rectangular NLPs could be obtained by properly setting the orientations of the PCs, as shown in Fig. 5(c). Although the maximum output power of the pump is 350 mW, there are no more pulses to appear no matter how we adjust the PCs after the pump power exceeding 330 mW.
3.3 Multiple rectangular NLPs with both non-uniform duration and spacing
In order to discover more details about the relationship between the polarization state and the interaction among the multiple NLPs, we compared multiple NLPs under different polarization states at the same pump power. After the achievement of 10 NLPs, the pump power was fixed at 330 mW. In this case, we further carefully adjusted the PCs and the third type pattern of multiple NLPs could be observed on the oscilloscope, namely, the NLPs pattern shows both uneven width and spacing of pulses, as presented in Fig. 6 . Note that the adjustments of the PCs would lead to the variations of the intracavity pulse power due to the change of NALM transmission function . Here, it is intuitively that the number, separation and duration of multiple NLPs are changed. Although the durations of all the NLPs are unequal, the shape of each pulse packet is still rectangular. In the experiment, when the orientations of the PCs were adjusted, the interaction among the multiple pulses correspondingly varied. Therefore, some rectangular NLPs could be reconstructed again and grouped to be a single rectangular NLP with longer (shorter) envelope duration. In addition, the relative motion among the rectangular NLPs would also occur and finally come to an equilibrium state. In this case, the spacing between the pulses and the duration of the NLP wave packet shown on the oscilloscope changed accordingly. Note that this pattern of multiple NLPs is different from the conventional multi-soliton patterns that has the same features among the generated multiple solitons. We think it comes from that the NLP is a wave packet which consists of many ultra-short pulses with randomly varying amplitudes and duration.
3.4 Chaotic state of multiple rectangular NLPs
As we know, reducing the cavity loss will be conducive to increase the nonlinear accumulation that is expected to form either multi-pulse pattern or chaotic states. Therefore, in order to further investigate the rectangular NLP evolution, particularly on the generation of a chaotic state of the multiple rectangular NLPs, we decreased the loss of the cavity by replacing the 30% output coupler with a 10:90 ratio one, namely, the 10% port was used as the output. As we expected, a stable mode-locked single rectangular NLP at the fundamental repetition frequency could be observed with a lasing threshold of ~29 mW, which was 6 mW smaller than that of using a 30% output coupler. By gradually increasing pump power and slightly rotating the PCs, the aforementioned three patterns of multiple rectangular NLPs could be also obtained. When the launched pump power was further increased, the whole lasing system would be unstable. Then the chaotic state of the multiple rectangular NLPs could be observed, as shown in Fig. 7 . Being different from the above-mentioned static patterns of the multiple rectangular NLPs, the chaotic states of rectangular NLPs continually split and randomly emerge new pulse packets developing into successional drifting, which are similar to the soliton rain [13–16 ]. However, as long as the PCs were carefully adjusted, the chaotic state of the multiple rectangular NLPs could evolve into a stable pattern of the multiple rectangular NLPs.
In the experiment, it is worth noting that the nonlinear effect plays an important role in the evolution and dynamics of various pulse patterns in passively mode-locked fiber lasers. In fact, although the rectangular NLP wave packet is regarded as a special “single” pulse in this work, there are many tiny pulses with randomly varying amplitudes and durations in the wave packet. As we know, the tiny pulses are localized inside the noise-like wave packet through the nonlinear pulse interactions among each other. In addition, when the cavity nonlinear effect is changed by adjusting the pump power level or PCs, the pulse interactions will also vary as well. Supposing that the nonlinear effect is high enough, a portion of the tiny pulses will escape from the rectangular NLP due to the variation of the nonlinear pulse interactions. By the random reconstruction, the escaped tiny pulses will evolve into other rectangular NLPs. That is to say, the multiple rectangular NLPs can be formed in this case. Then via the nonlinear interactions among the generated multiple rectangular NLPs, the various patterns of the multiple rectangular NLPs will be observed, which is similar to the generation of the conventional multi-soliton patterns. Nevertheless, being different from the conventional multi-soliton patterns, the multiple rectangular NLPs could possess unequal packet durations. The observed patterns of multiple rectangular NLPs would be useful for further understanding the physical mechanism of the rectangular NLPs.
In conclusion, we experimentally demonstrated the formation of multiple rectangular NLP patterns from a figure-eight mode-locked fiber laser. Although the rectangular NLP also retained a single pulse sate with the pulse width tuning from 1 ns to 10 ns, it could operate in multi-pulse states via adjusting the PCs and tuning the pump power, whose individual pulse maintained rectangular shape. In addition, it was shown that the multiple rectangular pulses not only have similar multi-soliton properties of conventional solitons, but beyond this, it can possess unequal packet durations. The achieved results would further reveal the basic characteristics of the rectangular NLP.
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61378036, 61307058, 11304101, 11474108), Key Program of Natural Science Foundation of Guangdong Province, China (2014A030311037), Open Fund of the State Key Laboratory of Luminescent Materials and Devices (South China University of Technology) (Grant No. 2016-skllmd-12). Z.-C. Luo acknowledges the financial support from the Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2014A030306019), Program for the Outstanding Innovative Young Talents of Guangdong Province (Grant No. 2014TQ01X220), and the Zhujiang New-star Plan of Science & Technology in Guangzhou City (Grant No. 2014J2200008).
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