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Abstract
For the first time the phenomenon of soliton rain is observed in a mode-locked fiber laser with all-polarization-maintaining (all-PM) architecture. The laser is mode-locked using a semiconductor saturable absorber mirror (SESAM) and operates in the all-normal dispersion (ANDi) regime. The operation state of the laser can be switched from dissipative soliton to soliton rain by simply raising the pump power, without any manipulation of the intracavity polarization state given that all components of the resonator are made of PM fibers. The soliton rain generated in the laser is self-starting and replicable, since it occurs in every individual operation of the laser as the pump power is increased to an approximately invariant value.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode-locked fiber lasers exhibit rich forms of multi-pulsing dynamics, such as soliton molecule [1], soliton bunch [2], and soliton rain [3]. The multi-pulsing dynamics attract intense attention due to their potential applications in plasma physics, chemical reactions, and complex networks. Among the dynamics, soliton rain is particularly intriguing since it includes dramatic motion of multiple solitons. Soliton rain involves the formation, drift, and annihilation of solitons, analogous to the cycle of water in the nature. First discovered by Chouli et al. in a 1.5 µm Er-doped fiber laser mode-locked via nonlinear polarization evolution (NPE) [3,4], soliton rain is widely observed in mode-locked fiber lasers. The phenomenon can occur in both anomalous dispersion [5–10] and normal dispersion regime [11–13]. It is achievable in fiber lasers mode-locked through various mechanisms, either saturable absorber [two-dimensional materials, carbon nanotube (CNT), SESAM, etc.] or nonlinear effect [NPE, nonlinear optical loop mirror (NOLM), etc.] [14–16]. Moreover, soliton rain can occur with even more puzzling behaviors, including harmonic soliton rain [10,15], vector soliton rain [17–19], soliton rain in h-shaped pulse [20], and soliton rain in noise-like pulse (NLP) [21–23].
As soliton rain occurs, there are three lasing components which coexist: a condensed soliton phase, the drifting solitons, and a noisy constant-wave (CW) background. The condensed soliton phase behaves like an anchor, whilst the drifting solitons possess different group velocities with the condensed soliton phase. The drifting solitons can either emerge from the CW background or be released from the condensed soliton phase. Similarly, the drifting solitons can abruptly vanish in the CW background or be absorbed into the condensed soliton phase. There are some literatures which reveal the laws governing the dynamics of soliton rain. All of them indicate the critical role of the noisy CW background [24–27]. The mechanism is elucidated as that soliton rain occurs when multiple solitons interact in the presence of a noisy continuum field. The fluctuations of the noise floor trigger the formation of new solitons, and the solitons interact as a by-product of the timing jitter caused by the interaction between the solitons and the noisy floor. The mechanism is therefore denominated as noise-mediated interaction (NMI), which shares some properties with the Casimir effect in quantum electrodynamics [24,25].
As aforementioned, soliton rain is recognized as a common phenomenon. It is observed in almost all categories of mode-locked fiber lasers. A notable exception, however, is the lasers with all-PM architectures. Thus far, soliton rain is only acquired from mode-locked fiber lasers of which the intracavity polarization state cannot be conserved. In practice, in most previously reported cases soliton rain is activated by manipulating the intracavity polarization state of the laser using polarization controller (PC) or waveplate; that is, soliton rain is not a self-starting operation state, and it cannot be stably replicated given that the polarization state is highly sensitive to the environment.
In this paper, we report an interesting case in which soliton rain is achieved in an all-PM mode-locked fiber laser. The laser operates at ∼976 nm with an all-normal dispersion. The wavelength is attractive in a variety of applications such as pump source for the nonlinear frequency conversion system which generates visible, near-infrared, and mid-infrared lasers [28–30]. All elements of the laser are made of PM fibers, and the gain medium is a piece of PM ytterbium (Yb) doped fiber. The fast axes of the fiber components used in the laser are blocked, a management that enforces the laser to operate with linear polarization. No polarization-controlling element is employed in the laser. The experimental results indicate that soliton rain can be self-started in the laser by simply elevating the pump power. The laser is operated for hundreds of times (in the end of each individual operation the laser is switched off), and the phenomenon of soliton rain is observed in all attempts as the pump power is raised to an approximately invariant value. By increasing the pump power, various patterns of soliton rain can be acquired. In the experiments we also find that the peak intensities of the drifting solitons are in an interesting distribution. It seems that the peak intensities of the drifting solitons are discrete, or even quantized. Under a given pump power, the peak intensities of the drifting solitons can only occupy the values which are integer multiples of a certain minimum unit, instead of random values. The essence of such peculiar distribution of the peak intensities of the drifting solitons is yet to be revealed. To the best of our knowledge, this is the first time that the phenomenon of soliton rain is observed in an all-PM mode-locked fiber laser. This work can be informative and helpful for further understanding the dynamics regarding soliton rain.
2. Experimental setup
The schematic of the all-PM mode-locked fiber laser is shown in Fig. 1. In this work, all fibers (including the Yb-doped fiber and the passive fiber used for fabricating the components of the laser) are supplied by Fiber Optics Research Center of the Russian Academy of Sciences. These fibers are panda-type PM fibers of which the diameters of the core and cladding are respectively 13 µm and 80 µm. The gain medium is a 10-cm-long, double clad Yb-doped fiber. The concentration of Yb3+ in the fiber is only 0.16 mol%, a fact that is beneficial for suppressing the reabsorption at 976 nm. On the other hand, thanks to the large ratio between the areas of the core and the cladding, the cladding absorption rate at 915 nm of the lightly doped fiber is as high as 3.4 dB/m. A 915 nm semiconductor laser diode (LD) with a maximum available output power of 20 W is used as the pump. The pump is delivered into the Yb-doped fiber through a combiner. The splicing point between the output port of the combiner and the Yb-doped fiber is carefully recoated with low index polymer. A circulator is employed to guarantee the unidirectional operation of the laser. A homemade cladding power stripper (CPS) is fabricated at the splicing point between the Yb-doped fiber and one port of the circulator for eliminating the unabsorbed pump. Another port of the circulator is made into a FC/PC connector, and a SESAM is placed on the surface of the ceramic ferrule of the connector. The SESAM is sealed in a mating sleeve using an additional FC/PC connector. The SESAM (provided by BATOP GmbH) is designed to be operated at 980 nm, and is of a modulation depth of 9%, a saturation fluence of 60 µJ/cm2, and a relaxation time of 500 fs. The third port of the circulator is spliced with a fiberized bandpass filter which is of a central operation wavelength at 976 nm and a bandwidth of 10 nm. Finally, a 50:50 fiber coupler (of which one port is intentionally terminated so the coupler is only used in the one-to-two manner) is employed as the output port of the laser. The net cavity dispersion of the laser is estimated to be 0.21 ps2 (at 976 nm). It should be noted that all elements of the setup (combiner, circulator, filter, and coupler) are blocked in the fast axes, and hence, the laser generated in the resonator is inherently linear polarized.
Fig. 1. Diagram of the all-PM mode locked fiber laser. LD: laser diode; YDF: Yb-doped fiber; CPS: cladding power stripper.
In this work, the Yb-doped fiber laser is operating at a disadvantageous wavelength, namely 976 nm. It is well known that 976 nm is exactly the absorption peak of Yb3+, and thus, the lasing at the wavelength suffers from heavy reabsorption. Owing to the heavy reabsorption there is a strong tendency to establish the lasing at longer wavelength (e.g., 1030 nm) instead of 976 nm, although the latter is of a larger emission cross section. In order to facilitate the 976 nm lasing and suppress the parasite lasing at longer wavelength, we operate the laser with a high pump power and a short gain medium. In this work the Yb-doped fiber used in the resonator is quite short, and the specific length of the fiber is optimized by multiple attempts. Also, the utilization of the bandpass filter is necessary for stabilizing the operation wavelength of the laser.
3. Experimental results
The output characteristics of the all-PM mode-locked fiber laser is acquired using the following devices: optical spectrum analyzer (OSA, Yokogawa AQ6373B), oscilloscope (Teledyne LeCroy SDA 820Zi-B), RF spectrum analyzer (Rohde & Schwarz FSWP8), and autocorrelator (Femtochrome FR-103XL).
The threshold pump power of the CW operation is 3.02 W (in this paper, all values regarding the pump power is the launched power, instead of the absorbed power). As the launched pump power is raised to 5.2 W, self-started mode-locking is achieved with an average output power of 1.73 mW. Owing to the ANDi configuration of the laser, the pulse generated in the mode-locking operation is dissipative soliton. The spectrum of the dissipative soliton is shown in Fig. 2(a), from which the central wavelength of the laser is determined as 976.5 nm. The full width at half maximum (FWHM) of the spectrum is 0.6 nm. The oscilloscope trace of the dissipative soliton is shown in Fig. 2(b). The pulse train is highly stable. The radio frequency (RF) spectrum is presented in Fig. 2(c), from which the repetition frequency of the laser is determined as 28.09 MHz. There are two spurs in the RF spectrum. In view of the separation between the spurs and the fundamental frequency, the spurs cannot be attributed to relaxation oscillation. The spurs may indicate some invisible modulations on the pulse train [31], or they are simply caused by electronic noise [32]. The autocorrelation (AC) trace of the dissipative soliton is presented in Fig. 2(d). The pulse duration is determined as 11.8 ps.
Fig. 2. Output characteristics of the mode-locked Yb-doped fiber laser: (a) optical spectrum, inset: optical spectrum in linear format, (b) pulse train, inset: pulse train in 10 µs span, (c) RF spectrum, inset: RF spectrum in 2 GHz span, (d) AC trace. All characteristics are registered under 5.2 W pump.
The mode-locking operation of the dissipative soliton gradually becomes unstable as the pump power is raised beyond 5.2 W, and finally collapses into multi-pulsing state. As the launched pump power is increased to 6.8 W, the phenomenon of soliton rain emerges with an output power of 4.71 mW. Figure 3 demonstrates the characteristics of the soliton rain. The soliton rain achieved under 6.8 W pump is peculiar and interesting. As presented in Fig. 3(b) and Visualization 1, there is only one drifting soliton in a round trip. To our knowledge, such a phenomenon is never reported in previously published literatures. It is unknown whether the special behavior is associated with the all-PM architecture of our setup. The long-term pulse train presented in the inset of Fig. 3(b) exhibits a noisy envelope, which indicates a weak stability of the peak intensities of condensed soliton phases. The optical spectrum shown in Fig. 3(a) provides no information that can be used to distinguish the soliton rain from the dissipative soliton presented in Fig. 2(a). This is different with the soliton rain occurring in anomalous dispersion in which prominent CW spike [5] or jitter [9] is usually observed, but accords to the soliton rain occurring in ANDi lasers [13]. We attribute it to the fact that the shape of the spectrum of dissipative soliton is much more irregular than that of soliton, and thus, weak modulation on the spectrum cannot be identified. Similarly, the AC trace shown in Fig. 3(d) exhibits no difference with that of the normal dissipative soliton presented in Fig. 2(d). This is attributed to the fact that there is only one drifting soliton which is in chaotic motion across the entire round trip, and thus, no pedestal or sub-peaks can be generated in the AC trace. If the involved drifting solitons are really numerous, on the other hand, the AC trace of soliton rain can exhibit a pedestal [6]. The RF spectra reveal the difference between the soliton rain and the dissipative soliton. As presented in Fig. 3(c), strong sidelobes are observed in the RF spectrum of the soliton rain, a phenomenon that is absent in the RF spectrum of the dissipative soliton. It is found that the single-drifting-soliton operation mode is highly stable. We monitor the operation mode for ∼30 minutes, and it does not evolve into other states. More importantly, the operation mode is replicable. We restart the laser for several times, and the single-drifting-soliton operation almost regularly occurs as the first achievable soliton rain (but not always). The pump power to activate the single-drifting-soliton operation is roughly invariant, ranging from 6.77 W to 6.91 W.
Fig. 3. Output characteristics of the mode-locked Yb-doped fiber laser: (a) optical spectrum, inset: optical spectrum in linear format, (b) pulse train, CSP: condensed soliton phase, inset: pulse train in 10 µs span, (c) RF spectrum, inset: RF spectrum in 2 GHz span, (d) AC trace. All characteristics are registered under 6.8 W pump.
As the launched pump power is further increased, a puzzling dynamic of soliton rain is observed. The single drifting soliton splits into several individual ones, and they are roughly spaced equidistantly in the temporal domain (in other words, they are of the same group velocity). By tuning the pump power, several operation states which are of different numbers of drifting solitons can be established. We observe the states with three, four, five, and six drifting solitons, whereas the state with two drifting solitons is not achieved in the experiments. Figure 4 shows the oscilloscope traces of the states with three and six drifting solitons (the latter is also shown in Visualization 2), respectively. It should be noted that the oscilloscope trace is the only way to identify the puzzling dynamic, whilst the optical spectrum, the RF spectrum, and the AC trace are all identical with those of the “conventional” soliton rain. The motion of the spaced drifting solitons is highly stable, and is not affected by the setting of the trigger of the oscilloscope. These drifting solitons are always separated with regular intervals (in other words, they are drifting in the same group velocity), free of collision or merging. Neither the vanishment of the existing solitons nor the emergence of the new solitons are observed. Moreover, the puzzling dynamic is replicable. We successfully realize the soliton rain with regularly spaced drifting solitons in multiple experiments. As far as we know, such an odd dynamic is never reported previously.
Fig. 4. Oscilloscope trace of the soliton rain with (a) three drifting solitons, and (b) six drifting solitons. CSP: condensed soliton phase.
The puzzling dynamic can be partially explained by the NMI theory that is well established in the previous research works [24,25]. The pulse interaction occurs as a by-product of the timing jitter caused by the nonlinear overlap between the pulses and noisy CW background. The diffusion strength that induces the drift of the pulse is proportional to the local intensity of the CW background. The CW background is proportional to the gain: its intensity is sharply reduced after a pulse passage (in other words, the gain is depleted by the pulse), and recovers gradually afterwards. The diffusion of a pulse can be expressed as
As the launched pump power is raised beyond 7.3 W, the soliton rain with regularly spaced drifting solitons cannot be maintained, and finally, the operation mode of the laser evolves into “conventional” soliton rain. In the conventional soliton rain the motion of the drifting solitons is chaotic, and the irregular appearance (or vanishment) of individual drifting soliton is common. The soliton rain operation can be maintained in a large tuning range of the pump, until the launched pump power is beyond 10.3 W. As the launched pump power is elivated above 10.3 W, the operation mode of the laser collapses into multi-wavelength CW lasing.
The output characteristics of the soliton rain registered under 10 W pump is demonstrated in Fig. 5. The optical spectrum is presented in Fig. 5(a). There are no features of the spectrum which can be used to distinguish the conventional soliton rain from the peculiar soliton rains discussed above. On the other hand, the oscilloscope trace and the RF spectrum are remarkably different with the aforementioned peculiar soliton rain. As presented in the inset of Fig. 5(b), the long-term pulse train is highly unstable, with prominent modulation on the peak intensities of condensed soliton phases. Figure 5(c) exhibits that the sidelobes in the RF spectrum become stronger, a fact which results in a much smaller SNR compared with the one shown in Fig. 3(c). The AC trace presented in Fig. 5(d) indicates a larger pulse duration than that of the disspative soliton and the soliton rain with single drifting soliton.
Fig. 5. Output characteristics of the mode-locked Yb-doped fiber laser: (a) optical spectrum, inset: optical spectrum in linear format, (b) pulse train, CSP: condensed soliton phase, inset: pulse train in 10 µs span, (c) RF spectrum, inset: RF spectrum in 2 GHz span, (d) AC trace. All characteristics are registered under 10 W pump.
The resonator of the laser reported in this paper is entirely built with PM fibers, and no element used for polarization manipulation is included in the resonator. In all experimental works the phenomenon of soliton rain is introduced by merely raising the pump power, that is, the soliton rain operation is self-starting for the laser. In most published literatures, however, soliton rain is activated by adjusting the intracavity polarzation state. In this work, soliton rain is an inherent operation mode of the laser; it occurs in every individual operation of the laser, as long as the pump power is tuned to an appropriate value. It should be noted that the pump power required to support the mode-locking operation of the laser is very high, due to the fact that the short Yb-doped fiber (of which the length is 10 cm) can only absorb a tiny fraction of the total launched pump. The slope efficiency with respect to the launched pump power of the laser is only 0.12%.
4. Discussion
In this work, for the first time the phenomenon of soliton rain is realized in an all-PM fiber laser. In the laser the transition from stable mode-locking to soliton rain is induced by increasing the pump power. This is remarkably different with the soliton rain observed in fiber lasers without all-PM architecture which are intensely studied previously. In these studies, soliton rain is activated with external intervention on the intracavity polarization state using PC or waveplate [3,4,5,9,10,12,14,15]. Due to the non-PM architecture the soliton rain observed in these works is non-self-starting, given that the intracavity polarization state can be easily changed by the perturbation on the fiber or the variation of environment. For the laser investigated in is work, however, the soliton rain is self-starting. The all-PM configuration guarantees the immunity of the intracavity polarization state to the external factors (twist of fibers, change of temperature, etc.). As a result, the state of soliton rain can be stably acquired by simply raising the pump power. Obviously, such a stable source is beneficial to the research on the dynamics of soliton rain since it saves the management of polarization state. Moreover, our works provide an insight into the mechanism of soliton rain. In previous studies polarization is usually perceived as a non-trivial factor in the formation of soliton rain [4]. The results of this work, however, indicate that the formation of soliton rain should be associated with some more essential factors.
In the experimental works, it is found that as the chaotic (“conventional”) soliton rain occurs, the drifting solitons are of various intensities. Such a phenomenon is not rare, and is reported in many literatures [6,8,10,12,14,15,25,33]. In our work, an intriguing fact is discovered via investigating the peak amplitudes of the drifting solitons. It seems that the peak intensities of the drifting solitons are discrete, and the distribution of the intensities is governed by some rules. As presented in Fig. 5(b), the amplitudes of the drifting solitons are approximately quantized, which are integer multiples of a certain minimum unit. A more comprehensive demonstration of the puzzling behavior is presented in Visualization 3. Such a quasi-quantized distribution of the peak intensities of the drifting solitons is reported in some literatures [8,14,25], but the mechanism of it is not revealed yet. Some researchers suggest explaining the quasi-quantized distribution of the intensities as a product of the merging between drifting solitons [25], however the explanation is denied by the experimental results of this work. Figure 6 presents the evolution of the drifting solitons across 8000 round trips. Here, the oscilloscope trace is recorded with a narrow bandwidth (the full bandwidth of the detection system is 12.5 GHz), or the volume of the generated data will be too huge for the processing capacity of our computer. It is found that the peak intensities of the drifting solitons experience significant variation without merging or any other interactions. As a result, the mechanism of the puzzling distribution manner of the drifting solitons’ intensities is still unknown. It also should be noted that a similar phenomenon is observed in NLP lasers [21,22].
Fig. 6. Trajectory and evolution of the drifting solitons. Green line indicates the location of CSP. Red arrow indicates the direction of motion. The drifting solitons without red arrows are at stagnation points.
5. Conclusion
In this paper, soliton rain is observed in a mode-locked fiber laser with all-PM architecture for the first time. The soliton rain operation is self-starting and replicable in the investigated laser, which can be activated by simply raising the pump power without any manipulation of the intracavity polarization state. Various modes of soliton rains are realized using the laser, including some interesting ones which are never reported previously. We hold a view that our work can be informative for understanding the dynamics regarding soliton rain.
Funding
National Key Research and Development Program of China (2022YFB3605800); National Natural Science Foundation of China (61935014, 61975136, 62105222, 62105225, 62275174, 62375187); Shenzhen Science and Technology Innovation Program (CJGJZD20200617103003009, GJHZ20210705141801006, JCYJ20210324094400001).
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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