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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JPHOT.2017.2772439, IEEE Photonics Journal

Observation of duration-tunable soliton explosion in passively mode-locked fiber laser ,*

Pan Wang†, Xiaosheng Xiao† , Member, IEEE, Hang Zhao, and Changxi Yang †

These authors contributed equally to this work

State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China Abstract: We report on the first observation, to the best of our knowledge, of soliton explosions in an ultrafast fiber laser mode-locked by nonlinear polarization evolution. The soliton explosion is a transition state between stable mode-locking and noise-like pulses regimes. By tuning the waveplates and the spectral filter, the duration of soliton explosions is widely tunable from ~100 roundtrips to thousands of roundtrips. Our experimental results together with the numerical simulations reveal the dissipative nature of soliton explosions, and may be beneficial for further understanding of this striking phenomenon. Index Terms: Soliton explosions, mode-locked fiber lasers, pulse propagation and solitons.

1. Introduction Mode-locked fiber lasers have attracted considerable attention due to numerous applications in the fields of optical communications, optical frequency metrology, biomedicine, material processing, etc. In addition to practical usage, they are also excellent platforms for investigating fundamental physics. Due to the complex dissipative interplay of linear and nonlinear effects, ultrafast fiber lasers can be host to plenty of dissipative structures and self-organization effects [1]. In the past decade, various dissipative structures have been investigated in mode-locked fiber lasers, such as soliton molecules [2-4], dissipative rogue waves [5-7], soliton rains [8-10], dissipative soliton resonances [11-13], high-order solitons [14] and vector solitons [15]. Soliton explosion, as one of the most striking dissipative phenomena in mode-locked lasers, becomes a hot topic in the field of laser physics in recent years. The soliton explosion features that a solitary pulse circulating in the cavity undergoes an abrupt structural collapse, but ultimately returns back to the previous state after several roundtrips, continuing stable evolution until another explosion occurs [16-29]. It is different from stable dissipative soliton, whose evolution of each roundtrip is the same. Since first theoretically proposed by N. Akhmediev et al. in the cubic-quintic complex Ginzburg-Landau equation (CGLE) [16], most of the soliton explosion investigations are focused on theoretical predictions in the framework of dissipative systems. However, regarding the direct experimental verifications of the soliton explosions, the investigation is relatively deficient with only a few works reported in the past decades [18, 25-28]. The first experimental observation of soliton explosion was reported in 2002 by Cundiff et al. in a Kerr-lens mode-locked Ti:sapphire laser, where a six-element detector array was utilized to measure the temporally resolved spectrum [18]. Very recently, the first experimental demonstration of soliton explosion in fiber laser was reported [25], using a high-resolution real-time diagnostic based on the dispersive Fourier transformation (DFT) [30]. The laser was mode-locked by nonlinear amplifying loop mirror (NALM), and the soliton explosion was a transient status between the stable mode-locking and unstable "noise-like" (NL) pulse emission. The work was expanded by subsequent experimental research [26] using the same mode-locking technique, highlighting the connection between soliton explosions and multipulsing instability. For lasers with real material based SA, different soliton explosion effects could also be obtained by adjusting the cavity parameters. Last year, several other experimental investigations were also conducted, employing a different mode-locking technique of carbon nanotube (CNT)-saturable absorber [27-28]. Successive soliton explosions [27] as well as soliton-explosion-induced dissipative rogue waves [28] were reported in ultrafast fiber lasers. According to the theoretical analysis, soliton explosion, periodically exhibiting explosive instability, is the localized pulsating solution of the dissipative systems governed by the CGLE [16-17, 19-29]. The state of soliton explosions can be controlled by modifying the system parameters of the CGLE. As experimentally demonstrated in Ref. [18] and Ref. [26], the soliton explosion duration or the explosion occurrence frequency could be adjusted by changing the cavity dispersion or the pump power, respectively. However, it would be interesting to know whether the soliton explosion state could be significantly influenced by modifying other parameters of the dissipative systems, such as the saturable absorption (SA) and spectral filtering effects. In this paper, we report on the first experimental observation, to the best of our knowledge, of soliton explosions in an ultrafast fiber laser mode-locked by nonlinear polarization evolution (NPE). The effective SA (i.e. NPE) and spectral filtering 1943-0655 (c) 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


effects can be adjusted by tuning the waveplates and the birefringent filter, which consequently influences the state of the soliton explosion process. The DFT method is utilized to characterize the ultrafast pulse dynamics. The duration of soliton explosions can be widely tuned from about one hundred roundtrips to thousands of roundtrips, which is much longer than those of the previous experimental reports [18, 25-28].

2. Experimental Setup and Results The experimental setup is schematically shown in Fig. 1. The laser is composed of all-normal dispersion fibers, mode-locked by NPE [31]. A polarization-insensitive isolator is used to assure unidirectional operation. The gain fiber is 1.1-m-long Yb-doped fiber (Nufern SMF-YSF-HI), backward pumped by a laser diode. Following the active fiber is a segment of 1-m-long single-mode fiber (SMF, Hi-1060). A birefringent filter, composed of two polarization beam splitters (PBSs) and a birefringent plate (thickness of 2.85 mm), is used to assist the mode-locking. The center wavelength of the filter can be tuned by rotating the birefringent plate. An additional segment of 14-m-long SMF (Hi-1060) is inserted before the isolator. The total cavity length is ~18 m corresponding to the cavity fundamental repetition rate of 10.8 MHz. The total cavity group velocity 2 dispersion (GVD) is about 0.4 ps . Mode-locking can be achieved without the 14-m-long SMF, however, soliton explosion cannot be observed. The output ejected from the NPE port is measured by an optical spectrum analyzer (Agilent 86142B) with 0.06 nm resolution for average spectra, and by the DFT method for shot-to-shot spectra [30]. The pulses are stretched in 12-km-long G.652 fiber to map the spectra into temporal waveform on a 2 GHz real-time oscilloscope with a 100-ps-risetime fast photodetector.

Fig. 1. Experimental setup of the mode-locked fiber laser and the shot-to-shot spectra measurement by DFT. WDM: wavelength division multiplexer, λ/2: half wave plate, λ/4: quarter wave plate, PBS: polarization beam splitter, BP: birefringent plate, YDF: Yb-doped fiber, PD: photodetector, DFT: dispersive Fourier transformation.

Fig. 2. (a) (b) Stable mode-locking regime, and (c) (d) NL pulse emission regime of the oscillator. (a) and (c) Average spectra measured by the OSA. (b) and (d) Shot-to-shot spectra recorded by DFT method, corresponding to the operation states shown in (a) and (c), respectively. Insets in (a) and (c) give the autocorrelation trace of stable mode-locking and NL pulses.

The cavity possesses more tunable-devices, including the waveplates and birefringent plate, than the previous fiber laser cavities where soliton explosion were reported [25-28]. By tunning the waveplates and birefringent plate, the parameters of the effective SA, the coupling ration of output, and the center wavelength of filter could be adjusted, therefore more operation states would be possibly sustained in our cavity. With appropriate rotation settings of the waveplates and birfringent plate, stable mode-locking is obtained at the pump power of 221 mW. By rotating the waveplates at the same pump power, the 1943-0655 (c) 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


laser operation state transits to the NL pulses emission. Typical average spectrum of stable mode-locking and NL pulses states are depicted in Fig. 2 (a) and (c), respectively. As shown in Fig. 2(a), the sharp peaks at the edges of the spectra is typical of the dissipative soliton lasers [31]. For NL pulses state, the spectrum broadens and becomes smooth, as shown in 2 Fig. 2(c). The measured full width at half-maximum (FWHM) of the autocorrelation trace in Fig. 2(a) is 29.8 ps. If a sech pulse profile is assumed, the pulse duration is estimated to be 19.4 ps. As shown in the inset of Fig. 2(c), the autocorrelation trace of NL pulses regime is also measured (by FR-103XL, Femtochrome Research Inc.). The coherence spike of 0.75 ps upon a pedestal is typical of NL pulses state [32], different from the autocorrelation trace of mode-locking state shown in the inset of Fig. 2(a). The corresponding shot-to-shot spectra evolutions of the two states are given in Figs. 2(b) and (d), respectively, further confirming the states of stable mode-locking and NL pulses. By rotating the waveplates and the birefringent plate, a transition state is observed, apart from the mode-locking and NL pulses regimes. The recorded shot-to-shot spectra measured by the DFT method validate that this transition state is soliton explosion. It is worth to note that, in our case of soliton explosion, a unique characteristic is observed. The duration of the explosions can be widely, but not continuously, changed, from ~100 roundtrips to thousands of roundtrips, by tuning the waveplates and the birefreingent plate. Figure 3 presents an example of the soliton explosion state with relatively short duration (~100 roundtrips). The main part of the spectrum in Fig. 3(a) is stable and similar to that of stable mode-locking, except for a stable cw component around 1037 nm. Meanwhile, there are several (1~3) unstable spectral spikes on both sides of the spectrum. These unstable spikes, as a signature of sliton explosion, were also observed in Ref. [27]. As shown in Fig. 3(b), the DFT stretched pulse train experiences an abrupt distortion and finally returns back to the stable state. A closer and more accurate inspection of the shot-to-shot spectra is shown in Fig. 3(c). The detailed spectral evolutions at a typical explosion and at the relatively drastic explosion are given in Fig. 3(d). Figure 3(c) indicates that, the explosion begins with the rising of a small spectral component around 1038 nm. This component increases gradually, then suddenly causes the distortion of the whole spectrum, as shown in the 121~127th roundtrips of Fig. 3(d). The explosions of whole spectra continue about 50 roundtrips (121~170th), where a relatively drastic explosion occurs (136~142nd roundtrips) and generates several spectra with abrupt increase in amplitude. Eventually, the explosion vanishes and the spectrum recoveries.

Fig. 3. Soliton explosion regime with short duration (~100 roundtrips). (a) A typical average spectrum measured by an OSA, (b) Pulse train stretched by DFT method, recorded by the oscilloscope with sample rate of 20 Gsample/s. (c) Shot-to-shot spectra obtained from (b). (d) Spectral evolutions at indicated roundtrip numbers at a typical explosions (121~127) and at the relatively drastic explosion (136~142).

By rotating the waveplates and birefringent plate, the duration of the soliton explosion increases. Typical experimental examples of explosion with duration of ~500 roundtrips are shown in Fig. 4. More unstable spectral spikes exhibit in the spectrum, as shown in Fig. 4(a), though the main part of the spectrum is similar to Fig. 3(a). The soliton explosions are measured by the DFT method, as depicted in Figs 4(b)-(d) with 1000 roundtrips. Limited by the memory depth of the oscilloscope, we have to decrease the sampling rate to record more roundtrips. The results indicate much longer explosion duration (about ~500 roundtrips) and more drastic explosion level. Interestingly, abrupt temporal shifts can be observed after the explosions, which is similar to the early observation in Ref. [25]. During the drastic soliton explosion process, the double-pulsing is observed. The competition between two pulses continues for hundreds of roundtrips, and finally only one pulse remains, leading to the temporal shift. The amounts of temporal shifts are different for each explosion, confirmed by experimental measurements of the direct output pulse trains without DFT. With the same pump power as above experiments and properly settings of the waveplates and birefringent plate, another operation of soliton explosion with relatively long duration is also achieved, as shown in Fig. 5. The central part of the average spectrum is similar to that of stable mode-locking state while both sides of the spectrum are similar to that of NL pulses state. The whole average spectral shape of the soliton explosion is a mixture of those of stable mode-locking and NL regimes, which was also observed in Ref. [25]. The explosion continues for thousands of roundtrips and ultimately returns back to the previous stable mode-locking state. However, due to the limited memory depth of the oscilloscope, we cannot tell the total number of roundtrips of this explosion process. A captured stretched pulse train, as shown in Figs. 5(b)-(c), presents the process where an explosion starts. Unlike the two 1943-0655 (c) 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


kinds of previous explosion states, the intensity of the shot-to-shot explosion spectrum is comparable to that of the stable mode-locking state. In addition, by tuning the pump power alone, the soliton explosions can also be achieved as a transition state between the stable mode-locking and NL pulses regimes, which is similar to those of Ref. [25, 27]. Stable mode-locking, soliton explosion, and NL pulses regimes can be observed consequently by increasing the pump power with other cavity parameters fixed. Our experimental results indicate that the soliton explosion state could be significantly influenced by modifying the cavity parameters, revealing the dissipative nature of soliton explosions.

Fig. 4. Soliton explosion regime with moderate duration (~500 roundtrips). (a) A typical spectrum measured by an OSA, (b), (c), and (d) Three typical pulse trains stretched by DFT method, recorded by the oscilloscope with sample rate of 5 Gsample/s. (e), (f) and (g) Shot-to-shot pulses obtained from (b) (c) and (d), respectively, reflecting the spectral evolutions as well as the temporal shifts.

Fig. 5. Soliton explosion regime with long duration (thousands of roundtrips). (a) Average spectra measured by an OSA, (b) Pulse train stretched by DFT method, recorded by the oscilloscope with sample rate of 5 Gsample/s. (c) Shot-to-shot spectra obtained from (b).

3. Discussion To give more insight into the soliton explosion regime in the fiber laser mode-locked by NPE, we also conduct numerical simulations to qualitatively describe the laser dynamics of our case. The extended Ginzburg-Landau equation is used, including the effects of dispersion, Kerr nonlinearity, saturable gain with a finite bandwidth, and stimulated Raman scattering [32-34]:

i





 2 A  2  2 A ig ( z )  2 A 2 A    A R  A z , t   d   ig ( z ) A   i      c  z 2 t 2  g 2 t 2 t 2

(1)

where A(z,t) is the pulse envelope and t is the time in a frame of reference moving with the group velocity. β2 is the group velocity dispersion, γ is the Kerr nonlinearity of the fibers. Lumped model is utilized to simulate the pulse propagation in the cavity. The birefringent filter model is used to describe the controllable spectrally selective losses. ρc describes the frequency dispersion for the transmission due to the uncontrolled spectrally selective losses related with intracavity elements [32-33]. 2 The gain of the YDF is modeled through g(z) = g0×exp(-∫|A| dt/Esat) and Ωg is the bandwidth of the gain fiber. 2 2 2 The Raman scattering R(t) is given by R(t) = (1-fR)δ(t)+fRhR(t) where hR(t) = (τ1 +τ2 )/ τ1/τ2 ×exp(-t/τ2)sin(t/τ1). For silica fibers, the derived values from the Raman gain spectrum are τ1 = 12.2 fs, τ2 = 32 fs and fR = 0.18 [34]. The effective SA is modeled by the following transfer function:

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T  Tunsat  T 

T 1  A(t ) / Psat 2

(2)

where Tunsat, ΔT and Psat represent the unsaturable transmission, modulation depth, and saturation power, respectively. The 2 following cavity parameters are used for the simulations: LYDF = 1.0 m , γYDF = 4.7 W/km , β2,YDF = 22 ps /km , LSMF = 17.2 m , 2 -1 2 γSMF = 4.7 W/km , β2,SMF = 22 ps /km , g0 = 2.2 m , Esat = 1.2 nJ , Ωg = 40 nm, ρc = 1.3 ps /km. We appropriately adjust the parameters of the effective SA as well as φ (the angle of the birefringent plate optical axis from the incident plane) to numerically reproduce the experimental rotation of the waveplates and birfringent plate. By modifying the parameters, the transition from stable mode-locking to NL pulses operation can be obtained. Under appropriate cavity parameters, soliton explosion is also achieved. Examples of the spectrum evolutions of soliton explosion are given in Fig. 6. The explosion starts with the increase of spectrum component near the center, gradually leading to the distortion of the whole spectrum. As shown in Fig. 6(a), the most drastic explosion process lasts for about 60 roundtrips. The explosion finally vanishes and returns back to the stable state. Since soliton explosion is the localized pulsating solution of the dissipative systems governed by the CGLE [16-17, 19-29], the state of soliton explosions can be controlled by modifying the system parameters of the CGLE. Interestingly, it is discovered in our numerical simulations that the duration of soliton explosion can be strongly influenced by the setting of the parameters of SA and spectral filtering (i.e., φ), which is shown in Fig. 6(b). In Fig. 6(b), the most drastic explosion process lasts for about 150 roundtrips.

Fig. 6. Numerical simulation results of soliton explosion regime with different durations. (a) φ = 44.3°, Tunsat = 0.94, ΔT = 0.6, Psat = 0.5, (b) φ = 43.0°, Tunsat = 0.92, ΔT = 0.2, Psat = 0.5

It has to be noted that the stimulated Raman scattering (SRS) is considered in our simulation. To clarify the role of SRS in soliton explosions, additional numerical investigations are conducted without the SRS term. Similar qualitative results are also obtained, excluding the importance of SRS in soliton explosion in our case. In order to understand the soliton explosion deeply, further theoretical and experimental investigations are required in the future. It is worth to note that the coupled GLEQs are more accurate, at the cost of calculating time, considering the computational procedure of our long cavity every roundtrip. Although we have achieved qualitative results by using the extended Ginzburg-Landau equation, the coupled GLEQs will be used in further investigations.

4. Conclusions We report soliton explosion in an NPE mode-locked fiber laser for the first time. By tuning the waveplates and spectral filter, the duration of soliton explosion can be widely tuned from ~100 roundtrips to thousands of roundtrips. The soliton explosion duration can be dramatically influenced by all the parameters of effective SA as well as the spectral filtering. Our experimental observations in conjunction with numerical simulations reveal the dissipative nature of soliton explosions. The investigation of soliton explosions might contribute to physical insight of dissipative rogue waves, and also benefit the design of stable systems (e.g. long distance communication systems and ultrafast mode-locked lasers) to avoid the instabilities of soliton explosions. Our results with duration tunable soliton explosions might have potential application in random pulses generation by utilizing an extra cavity spectrum filter, whose transmission wavelength is deviated from the central wavelength of stable mode-locking spectrum, and the numbers of generated random pulses could be tuned by adjusting the explosion duration.

Acknowledgement National Natural Science Foundation of China under Grants 51527901, 61377039 and 61575106, the initiative Research Program of State Key Laboratory of Precision Measurement Technology and Instruments, and Tsinghua University Student Research Training (SRT) Project under Grant No. 1521T0062. The authors thank Dr. Chengying Bao for inspirational 1943-0655 (c) 2017 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


discussion of the phenomena of soliton explosion.

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