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We report an intermediate regime between c.w. emission and noise-like pulses (NLPs) regime in an Er-doped partially mode-locked fiber laser with nonlinear polarization rotation. In this regime, the soliton bunches stochastically turn up from a quasi-cw background in the Q-switched-like envelope. The soliton bunches normally last for tens or hundreds of intracavity round-trips. When the soliton bunches vanish, typical NLPs chains are generated sporadically at location where the soliton bunches collapses. These results would be helpful to understand the generation and property of the NLPs regime.
© 2016 Optical Society of America
1. Introduction
Recent progress in the field of dissipative nonlinear dynamics has led to a renewed interest in the passively mode-locked fiber lasers (PMLFLs) [1], which could not only serve as ultrashort pulse sources but also provide an ideal platform for investigation of chaotic dynamics, such as optical turbulence [2] and rouge wave generation [3, 4]. In a PMLFL, pulsation can be achieved from noisy c.w. regime when the optical power reaches a certain threshold, which could be attributed to a first-order phase transition from disordered to ordered phase of a large number of cavity modes [5]. Subsequently, large numbers of soliton pulses can be produced by controlling pump power and intracavity dispersion. These pulses could interact with each other through some subtle mechanisms, such as gain depletion and recovery [6], and a relatively strong cw component in the partially mode-locked regime [7, 8]. Therefore, some temporal patterns, such as harmonic mode locking and bound states, are formed in the cavities. When the cavities further deviate from the equilibrium state, more complex dynamic processes, such as noise-like pulses (NLPs) [9, 10], would occur. The NLPs can be regarded as a packet of optical noise burst with complex intrinsic characteristics, which normally possess stable, smooth and broad spectra and a double-scaled autocorrelation structure with a narrow spike rooted from a wide baseline [10]. Since a detailed description of NLPs was reported by Horowitz et al. in 1997 [11], the NLP state has attracted considerable research interests due to their correlation with optical rogue waves [12] and applications in optical metrology [13], supercontinuum generation [14–16] and micromachining [17], etc. Whereas, the understanding of the subtle dynamics of NLPs in sub-ps scale is still quite a challenging issue.
Besides cw emission, stable mode locking, and NLPs regimes, PMLFL could also operate in some intermediate regimes, where soliton rain [7] and soliton explosion [18] are the most intriguing phenomena. Soliton rain is an intermediate regime between cw and soliton pulses, in which new soliton pulses spontaneously form from a noisy cw background and drift at nearly constant rate until they reach a condensed soliton phase [7]. Soliton explosion corresponds to a process whereby after a solitary pulse circulating in the laser cavity experiences a transient structural collapse, it would return to its previous state after a few round trips. Therefore, soliton explosion has been considered as a critical regime between stable soliton pulses and NLPs [19]. The investigation of the transition between various order and disorder states would help to understand the chaotic dynamics in PMLFLs. Thus, there is always a strong motivation to investigate the critical regimes between the quasi-cw, stable soliton or soliton bunch, and NLPs operation in PMLFLs.
In this paper, we present experimental results of a new intermediate regime between c.w. regimes and NLPs regimes in an Er-doped partially mode-locked fiber laser with nonlinear polarization rotation and a net anomalous dispersion cavity. By tuning the polarization controller or pump power, the soliton bunches stochastically turn up from quasi-cw background in the Q-switched-like envelope. The soliton bunches normally last for tens or hundreds round-trips. When the soliton bunches vanish, NLP chains are generated sporadically at location where the soliton bunches collapses.
2. Experimental setup
The experimental setup is schematically illustrated in Fig. 1. Mode locking is achieved through nonlinear polarization rotation. A polarization-dependent isolator (PD-ISO) in combination with two polarization controllers (PCs), serving as an artificial saturable absorber, is employed to set up self-started stable mode locking in the fiber laser. A 10 m erbium-doped-fiber (EDF) (NUFERN, EDFC-980-HP) is used as the gain medium, which is pumped by a 980 nm laser diode (LD) through a fused wavelength division multiplexer (WDM). A 90:10 coupler is used at the output port. The EDF used in our experiment has a dispersion of 15.5 ps2/km at 1550 nm. All optical devices are connected by single-mode fibers (SMFs) with a dispersion of −23 ps2/km at 1550 nm. The total cavity length is about 31 m. Considering these parameters, the net cavity dispersion is about −0.328 ps2.
An optical spectrum analyzer (YOKOGAVA AQ6370C) is employed to monitor the laser spectrum in real time. The autocorrelation trace is monitored by an autocorrelator (FR-103XL). The output pulse chain is detected by a 2 GHz oscilloscope with a maximal sampling rate of 20 GS/s (LeCroy WaveRunner 620Zi). The operation shot-to-shot performance is evaluated by a 50 GHz bandwidth photodetector (U2T XPDV2120R) and a 36 GHz oscilloscope with a maximal sampling rate of 80 GS/s (LeCroy LCRY3312N69578).
3. Experimental results and discussion
The PMLFL can operate in cw emission, stable mode locking, and typical NLPs regimes. When the pump power is set to 110 mW, the fundamental conventional solitons with a pulsewidth about 650 fs in terms of the full width at the half maximum (FWHM) and clear Kelly sidelobes in the spectrum can be obtained in stable mode locking regime. Then, by properly changing the PCs, the NLPs could be observed. The optical spectrum, oscilloscope trace and autocorrelation trace of the NLPs are shown in Fig. 2. In this regime, the output of the laser shows the smooth and broadband optical spectrum with a central wavelength of 1570 nm and a pulse chain with a fundamental frequency of 6.46 MHz. The autocorrelation trace of the NLPs, shows a narrow coherent peak of 900 fs (FWHM) in pulse width on a wide pedestal. These characteristics accord with the typical features of the NLPs reported in previous literatures [9, 11, 20–22].
Fig. 2 Output characteristics of the PMLFL operating in typical NLPs regime. (a) Optical spectrum. (b) Output pulse chain. (c) Autocorrelation trace.
Through rotating one paddle of the PC1, the operation regime of the laser is directly converted from typical NLPs into an intermittent pulsation state with other conditions unchanged. By further rotating the paddle of PC1, the intermittent pulsation state could maintain within a rotation angle range of about 20° before it translates into a cw emission regime. The intermittent pulsation can appear at different pump powers. Its temporal traces at 110 mW and 367 mW are recorded by using a 2 GHz oscilloscope with a sampling rate of 5 GS/s, as shown in Figs. 3(a) and 3(b) respectively. From the rightmost of the Fig. 3(b), it could be seen that following the intermittent pulses some tailing structures with lower intensity and longer lifetime are sporadically generated. In order to better clarify the dynamic procedure, we construct the spatial-temporal diagrams based on these temporal traces of 1 ms, which corresponds to about 6459 cavity cycles, as shown in Figs. 3(c) and 3(d). Figures 3(e) and 3(f) are the close-ups of Figs. 3(c) and 3(d) between 4000 and 5000 round trips, respectively. From the envelopes in Figs. 3(c)-3(f), it is clear that each intermittent pulsation in temporal traces consists of some soliton pulse bunches in random amount. These soliton bunches almost simultaneously emerge or disappear for tens to hundreds of intracavity round trips. Due to the quasi-periodic occurrence of these soliton bunches, their temporal traces look like the Q-switched regime even though they have different mechanism. With the increment of pump power, more pulse bunches with shorter lifetime are inclined to turn up in each pulse envelope. In contrast, only one pulse bunch could be found in each tailing structure. As the pump power increases or the paddle of PC1 gradually rotates to the NLP regime, the probability of occurrence and lifetime for the tailing structures would significantly increase.
Fig. 3 Temporal dynamics of the PMLFL. (a) Temporal traces and (c) equivalent spatial-temporal diagram for a pump power of 110 mW. (b) temporal traces and (d) equivalent spatial-temporal diagram for a pump power of 367 mW. (e) and (f) are the close-ups of (c) and (d) between 4000 and 5000 round trips, respectively.
The optical spectra under different pump powers are shown in Fig. 4(a). By comparing Fig. 4(a) and Fig. 2(a), it is apparent that the former has a strong cw component around 1559 nm. Taking into account the spatial-temporal traces in Figs. 3(c) and 3(d), we can find that the comparably strong quasi-cw components coexist with the intermitting soliton bunches, which means the laser operates in the partial mode locked regime. These noisy quasi-cw components consist of a large number of cavity modes whose random fluctuations in amplitude and phase could contribute to the stochastic emergence of soliton bunches. Without considering the cw component, these spectra are smooth and two gently peaks, specified as A and B, would coexist around 1570 nm and 1600 nm. When pump power is 417 mW, due to the operation regime hopping between NLPs and intermittent pulsations, a lot of burrs would emerge in the spectrum. The cw components could also be found in the harmonic mode locking spectra and soliton rain regimes [7]. In those cases, Kelly sidelobes simultaneously appear, which indicates these regimes are closely related with stable mode-locking. Whereas, the relatively broad and smooth spectra shown in Fig. 4(a) imply the intermitting soliton bunches are related with NLPs to some degree.
Fig. 4 Output characteristics of the PMLFL operating in the soliton bunches state. (a) Optical spectra at different pump power. (b) and (c)Autocorrelation trace.
Figures 4(b) and 4(c) show the autocorrelation traces when pump powers are 110 mW, and 310 mW, respectively. Multi-peaks structure is caused by the pulsation intervals. When pump power is 110 mW, the autocorrelation peaks position remains steady while the peak intensity always jumps, which indicates that the pulsations have relatively steady periods but random durations. As pump power increases, the envelope of autocorrelation gradually evolves into a Gaussian shape, as shown in Fig. 4(c), which is due to the statistical average of numerous slight envelopes in each large envelope.
The temporal performances have also been investigated in detail by employing a high-speed oscilloscope (36 GHz and 80 GS/s). Although the details of the packet are beyond the detection resolution, we have still acquired some useful information. Figures 5(a)-5(c) show spatial-temporal features of several soliton bunches at the pump power of 145 mW. Figure 5(a) presents a narrow to broad multi-soliton bunch without tailing pulse envelope, but its power intensity has certain periodic pulsation, which decreases gradually and disappears ultimately. Figure 5(b) shows that certain disturbance turns up to form a shorter trail after the pulse envelope vanishes. A longer tailing could be found in Fig. 5(c), and the inset of Fig. 5(c) refers to the partially enlarged view indicated by the dash line area. This figure shows that the tailing structure with narrower pulse width and lower intensity is produced at the location where a soliton bunch disappears. When pump power increases, the lifetime of tailing structure becomes longer. Figure 5(d) shows the tailing pulse duration lasts for 5000 cavity periods with 417 mW pump power, implying its random evolution.
Fig. 5 Detailed temporal performances of the soliton bunches and NLPs. (a) and (b) Multi-soliton bunch without tailing pulse envelope.(c) multi-soliton bunch with tailing pulse envelope(the inset displays the detail).(d) The tailing pulse envelope soliton and all structure is tailing.
In order to distinguish tailing structure from the intermittent pulsation, we have measured the shot-to-shot optical spectrum by using the dispersive Fourier transformation (DFT) technique [23]. A segment of 25 km SMF is used to stretch output pulses. Therefore, the spectral resolution of our measurements is approximately 0.024 THz (0.19 nm) [23]. A series of about 2800 consecutive round trips spectrum is shown in Fig. 6(a), which presents the shot-to-shot optical spectrum of a soliton bunch with a tailing structure. The spectrum is separated into two parts by a dotted line. The first about 180 round-trips correspond to the soliton bunch, while the upper round-trips are the spectrum of the tailing structure. The averaged spectra of these two parts are shown in Fig. 6(b). It could be seen that the spectrum of soliton bunch presents obvious double-peak structure and the positions of peak A and B are in accordance with those in the spectrum of Fig. 4(a). It is worth noting that a similar dissipative solitons state with double-peak spectrum and intermittent soliton bunches have been described by the cubic–quintic complex Ginzburg–Landau equation (CGLE) and been called spiny soliton in [24] recently. The average spectra of tailing structure shows uni-peak feature, which is very similar to the typical NLPs state shown in Fig. 2(a). Therefore, the tailing pulse train has similar characteristics of general NLPs in both spectral and temporal domain and can be considered as a typical NLPs state.
Fig. 6 (a) Consecutive shot-shot spectral sequence. A dotted line divides the spectrum into two parts. The upper one is the NLPs state and the following one is the soliton bunch state. (b) Averaged spectra within a soliton bunch (blue line) and NLP (red line) regime. Pump power is 145 mW.
In order to investigate the statistical properties of the pulses in the Q-switched-like soliton bunches and their tailing NLP structures, we analyzed a time process including 10336 cavity cycles recording by the oscilloscope with 36 GHz bandwidth and 80 GS/s. Figures 7(a) and 7(b) show the histograms of the peak power distribution for the pulses in the soliton bunches and NLPs, respectively. As shown in Fig. 7, the former is highly skewed and shows a long tail, while the latter exhibits a clear Gaussian distribution. The L-shaped probability distribution in Fig. 7(a) implies that the Q-switched-like soliton bunches could be related to the dissipative rogue wave.
Fig. 7 (a) Peak power distribution of the pulses in soliton bunches pulse and (b) noise-like pulse for a pump power of 139 mW .
4. Conclusion
In summary, we have reported the spatial-temporal features of Q-switched-like soliton bunches in the passively mode-locked fiber laser. The dynamic process illustrated here can be considered as an intermediate regime between cw emission and NLPs. In this regime, the intermitting soliton bunches coexist with some comparably strong quasi-cw intra-cavity components. These noisy quasi-cw components consist of a large number of cavity modes with random fluctuations in amplitude and phase, which contribute to the stochastic creation of Q-switched-like soliton bunches. When these soliton bunches vanish, NLPs train is generated sporadically at location where one of the soliton bunches collapses. Usually, only one NLP packet appears in each cavity round-trip and has lower peak power and longer lifetime than the soliton bunches. The occurrence frequency and duration can be tuned by adjusting the pump power and the angle of the PC. These results will help better understand the formation of solitons in the fiber laser, especially the NLPs. Therefore, we expect our results to pave a way for more experimental investigations and theoretical researches, letting the dynamics and characteristics of more soliton regimes to be fully unveiled.
Acknowledgments
This work was jointly supported by the National Key Basic Research and Development Program of China (Grant No. 2013CBA01702), the National Natural Science Foundation of China (Grant Nos. 61322510, and 11174155), and the Tianjin Natural Science Foundation (Grant No. 14JCZDJC31300). We thank Dr. Jian Zhao of Tianjin University for the help of some experimental measurements.
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