We experimentally report the dynamics of multi-soliton patterns noise-like pulses (NLPs) in a passively mode-locked fiber laser, which the pulse duration can be linearly tuned from 8.21 ns to 128.23 ns by 2.936 ns / 10 mW. Benefiting from the drastically strengthened nonlinear effects in the cavity and the high gain amplification in the unidirectional ring (UR), the transformation from rectangular-shaped NLP to Gaussian-shaped NLP is experimentally achieved. Versatile multi-soliton patterns are observed in NLP regime for the first time, namely, single-scale soliton clusters, high-order harmonic mode-locking, and localized chaotic multiple pulses. In particular, the spectrum evolution with pump power and spectrum stability in 2 hours are also monitored. The obtained results demonstrate the rectangular-shaped NLP can fully transform into Gaussian-shaped NLP, and the multi-soliton patterns can exist in the NLP regime, which contributes to further understanding the nature and mechanism of the NLP in a passively mode-locked fiber laser.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Passively mode-locked fiber lasers have attracted a lot of attentions for over the past decades owing to their numerous applications, such as material micromachining , optical metrology , and multi-photo microscopy . In addition to acting as an excellent ultrashort pulse source, it is a prevailing platform to explore the multifaceted nonlinear phenomena and versatile soliton dynamics in the laser cavity. Up to now, various operating regimes have been observed in mode-locked fiber laser by skillfully managing the cavity parameters, including the conventional solitons regime , the dispersion-managed solitons regime , the self-similar pulses regime , the dissipative solitons regime , and dark pulses regime . According to the soliton quantization effect  in net anomalous dispersion regime, the laser pulses normally split into multiple solitons when the pump power exceeds a certain threshold which depends on the average dispersion and nonlinear parameter in the cavity. Then, interactions among solitons, continuous waves (CW) and dispersive waves in the cavity lead to versatile multi-soliton operations which present more physical features than those of the single soliton in the mode-locked fiber lasers.
A peculiar mode-locked regime named noise-like pulse (NLP) was firstly demonstrated in the early 1990s by Horowitz et al. . Both experiments and theoretical simulations have demonstrated that the NLP is a compact wave packet which contains a bunch of ultrashort pulses with various intensity and pulse duration [11–17]. In the time domain, the NLP always shows an overall stable train of pulse packets, and a smooth and broad spectrum in frequency domain. Actually, the internal structure of a pulse packet is complex and random, and its autocorrelation (AC) trace exhibits a double-scale structure with a narrow coherence peak riding on a broad pedestal. Compared with conventional solitons, the NLP has a higher energy which can reach the level of µJ , and a longer pulse duration which can reach several hundred ns . Because of its broad spectrum and high energy, the NLP can be applied in low-coherence spectral reflectometry to detect the nonuniform regions inside the grating , and the temperature profiles of optical fiber components at a high-power operation . Additionally, NLPs with longer pulse duration can be directly amplified to a higher-power laser source, and applied in micromachining of titanium surfaces . The harmonic NLPs have been used for highly efficient SC generation, and its spectrum flatness is significantly improved [23–25].
Up to date, various NLPs, such as Gaussian-shaped [13–15], rectangular-shaped [26–28], trapezoid-shaped and comb-like-shaped , and dark rectangular-shaped , have been experimentally observed. Among them, the Gaussian-shaped NLP and the rectangular-shaped NLP are more investigated. Generally, the NLP is generated as a Gaussian-shaped packet on the oscilloscope trace, which always possesses a smooth and broad spectrum. The reported broadest 3-dB spectral width of the Gaussian-shaped NLP is 203 nm which resembles the generated supercontinuum in highly nonlinear fiber (HNLF) . The rectangular-shaped NLP is firstly found in a figure-eight mode-locked fiber laser, and the output pulse evolution is similar to the dissipative soliton resonance (DSR) regime . Recently, some unique features of rectangular-shaped NLP have been experimentally demonstrated. In 2016, Y. Huang et al.  reported versatile patterns of multiple rectangular-shaped NLPs in a mode-locked fiber laser which a 65-m HNLF was inserted in the loop. In 2018, G. Zhao et al.  demonstrated the coexistence of the rectangular-shaped NLP and the Gaussian-shaped NLP in a similar cavity structure as . In 2019, E. B. Huerta et al.  experimentally studied of a passive mode-locking single- and dual-wavelength Er/Yb double-clad fiber laser with rectangular, h-like and trapezoidal shapes in NLPs regime. Deeply considering the reported results in [26–28,32,33], a question naturally arises as to if the cavity nonlinearity is further strengthened and a gain amplifier is added in UR, whether more abundant mode-locking patterns in NLPs regime can be observed.
In this paper, via incorporating a 585-m HNLF in NALM and a gain amplifier in UR, we report for the first time, to the best of our knowledge, the transformation process from rectangular-shaped NLP to Gaussian-shaped NLP, and the versatile multi-soliton patterns NLP in a passively mode-locked fiber laser. By adjusting the pump power and polarization controller orientation in the cavity, the dynamics of the rectangular-shaped NLP splitting up, and multi-soliton pattern NLPs formation are experimentally studied. The output characteristics of NLP and spectrum evolution with the increase of pump power are experimentally investigated.
2. Experimental setup
The experimental setup of erbium-doped mode-locked fiber laser is shown in Fig. 1. The laser oscillator cavity consists of a unidirectional ring (UR) and a nonlinear amplifier loop mirror (NALM). The UR and NALM are connected by a 49.5/50.5 fiber optical coupler (OC). In UR module, a polarization-independent isolator (PI-ISO) is employed to promise a unidirectional operation in the cavity, and a 1 m Erbium-dope fiber (EDF) (Nufern, EDFL-980-HP) with a dispersion coefficient of 23.6 ps2/km is used to provide a gain amplification. A 10/90 fiber OC is used as the output coupler, which 90% power is feedback, and 10% power is output. In NALM module, a 585 m HNLF with a −0.7024 ps2/km dispersion coefficient (YOFC, NL-1550-Zero) is inserted in the cavity to strengthen the asymmetric gain and provide sufficient nonlinear phase shifting in bi-directional paths of the loop mirror. Another 1 m EDF (The same type in UR) is added in loop mirror, which is beneficial to serve as an artificial saturable absorber. The EDFs in UR and NALM are pumped by two 980 nm laser diodes (LD) through the 980/1550 nm wavelength-division multiplexer (WDM), respectively. Two three- paddles polarization controllers (PCs) are utilized to adjust the light polarization in the cavity. The spectrum of output laser is measured by an optical spectrum analyzer (AQQ6370D, 600 −1700 nm) with a tunable resolution of 0.05 nm - 2 nm. The time-domain signal of output pulses is detected by a 3 GHz InGaAs photodiode detector (PD), and shown in a real-time oscilloscope (Keysight DSO-X 6004A, 2.5 GHz bandwidth). Besides, the repetition rate of laser pulses is monitored by a radio frequency (RF) signal analyzer (N9030B, Agilent) with a bandwidth from 3 Hz to 50 GHz. The fine structure of laser pulses is analyzed by a commercial autocorrelator (Femtochrome FR-103XL).
3. Experimental results
3.1 Stable and pulse width tunable rectangular-shaped NLPs
Due to the asymmetric gain and high nonlinearity caused by several hundred meters HNLF in NALM, the mode-locked operation can be easily achieved by properly adjusting the paddles of PC in the cavity. The stable mode-locked pulses can be directly obtained for LD1 at 80 mW and LD2 at 130 mW, and the corresponding output characteristics are shown in Fig. 2. The mode-locked spectrum depicted in Fig. 2(a) is smooth and broad, which is a typical NLP spectrum, and the 3-dB spectral bandwidth is 12.83 nm centered at 1560.3 nm. Figure 2(b) shows the oscilloscope trace of output pulse trains produced by the fiber laser. It can be clearly defined that the interval of the neighboring pulses is about 3.139 µs, which is consistent with the cavity round-trip time. The single pulse is a rectangular profile with steep rising and falling edge, and pulse duration is estimated to be 74.8 ns. The screenshot of the single pulse is shown in the inset of Fig. 2(b). To investigate the fine structure of the rectangular pulse, the autocorrelation trace is measured in the experiment and shown in Fig. 2(c). As can be seen, a coherent peak upon a broad pedestal, indicates that the mode-locked fiber laser operates in NLP state. The inset of Fig. 2(c) is the zoom-in of the autocorrelation trace of the coherent peak, and the full width at half maximum of a pulse is about 1.085 ps. We also measure the corresponding radio-frequency (RF) spectral distribution with a resolution bandwidth (RBW) of 1Hz and a span of 5 kHz. It can be found the repetition rate is 318.55625 kHz, which is in accordance with the fundamental repetition rate of the cavity. The signal-to-noise ratio (SNR) is over 86 dB, which means that the mode-locked operation is stable. A wideband RF spectrum up to 100 MHz is presented in the inset of Fig. 2(d). An envelope modulation can be clearly distinguished in the spectrum, and the modulation period is around 13.35 MHz, which corresponds to an approximate 74.8 ns pulse duration in the time domain by the Fourier transformation.
To further understand the rectangular-shaped NLP characteristics, we investigate the evolution of the pulse duration along with the pump power. For the powers of LD1 at 80 mW and LD2 at 30 mW, the stable rectangular pulse with 8.21 ns duration is obtained by properly adjusting the paddles of PC2. When the pulse duration is less than 8.21 ns, the pulses are unstable, and difficult to be maintained. By fixing the PCs orientation and LD1 at 80 mW, the duration of the rectangular pulses can be manipulated by the pump power of LD2, while the pulse amplitude and profiles almost remain invariable. As can be seen in Fig. 3(a), the rectangular pulse duration is broadened from 8.21 ns to 128.23 ns when LD2 power increases from 30 mW to 400 mW. Figure 3(b) shows the relationship between the pulse duration and the pump power. It can be noted that the pulse duration can be linearly tuned by 2.936 ns / 10 mW. Additionally, when the LD2 power is gradually decreased from 400 mW to 30 mW, the pulse duration can be linearly shortened with similar slop efficiency. The pulse duration could also be widened by LD1 power, but it is not obvious. Adjusting the powers of LD1, LD2 simultaneously, the achieved maximum pulse duration is 260 ns at the powers of 320 mW LD1 and 300 mW LD2, which are shown in the inset of Fig. 3(b).
The evolution of the output spectrum along with the pump power is also experimentally studied. The intensity distribution in the spectrum is defined by different colors, and the results are illustrated in Fig. 4(a). The operation conditions are the same as the ones in Fig. 3. It can be noted that the central wavelength of the mode-locked spectrum is red-shifted with the pump power increase. At a relative lower pump power of 30 mW, the 3-dB spectral bandwidth is 9.85 nm centered at 1555.6 nm. While at maximum pump power of 400 mW, the 3-dB spectral bandwidth is 15.12 nm centered at 1561.4 nm, as shown in the upper part of Fig. 4. Furthermore, to evaluate the stability of NLP operation, we also record the spectrum at 300 mW pump power for 120 minutes, and the output spectrum is repeatedly scanned with an interval of 4 minutes. As shown in Fig. 4(b), there is no shift of the central wavelength of the mode-locked spectrum, and the intensity distribution in spectra did not change during the monitor time. The obtained results illustrate the excellent mode-locking operation and long-term stability.
3.2 Multiple-soliton patterns in NLPs regime
3.2.1 Transformation from rectangular-shaped NLP to Gaussian-shaped NLP
Based on the several hundred meters HNLF in the cavity, the nonlinear effects of the cavity can be easily changed by increasing the pump powers of LD1, LD2, and adjusting the intra-cavity PCs simultaneously. Experimentally, when the powers of LD1 and LD2 are individually increased to 130 mW and 90 mW, a stable mode-locking rectangular-shaped NLP could be achieved in the cavity, and the pulse duration is 109.8 ns. When the LD1 power is maintained, and the LD2 power is increased to 100 mW, the rectangular-shaped pulse begins to split in falling edge via carefully rotating the paddles of PCs in NALM. Shown as the blue curve in Fig. 5(a), several pulses with various shapes have been formed, including Gaussian-shaped, rectangular-shaped, and irregular-shaped. This state is unstable, and the splitting pulses are shaking all the time. Continually increasing the LD2 power to 105 mW, the original one rectangular-shaped pulse is split into four rectangular-shaped pulses, and the formed pulses are stable if no parameters are changed in the cavity. The obtained multiple rectangular shaped NLPs in the experiment are uniform spacing but irregular duration. By further increasing the LD2 power to 115 mW, the rectangular-shaped pulses began to break into multiple Gaussian-shaped pulses, which are shown as the pink curve in Fig. 5(a). Among the rectangular-shaped pulses, some of them split into Gaussian-shaped pulses. This state is the reported coexistence of the rectangular-shaped NLP and the Gaussian-shaped NLP . The tendency of transformation from rectangular-shaped pulse to Gaussian-shaped pulse is greatly strengthened at 130 mW, and the rectangular-shaped pulse is completely transformed into a Gaussian-shaped pulses cluster at 140 mW. The zoom-in of the temporal pulse in 13.5 ns time span is shown in Fig. 5(b), where several nearly Gaussian-shaped pulses are bounded together. Note that the formed Gaussian-shaped pulses have similar spacing and intensity, except for the weak pulses in both sides. The transformation process is analogous to the feature of soliton energy quantization of conventional solitons in the mode-locked fiber lasers , and the characteristics of this kind NLPs are similar to those of multi-soliton state.
The corresponding output spectra at different pump powers are present in Fig. 5(b). For the conventional rectangular-shaped NLP at 90 mW, the output spectrum is smooth and broad. While the rectangular pulse begins to split at 100 mW, a weak CW component occurs on the mode-locked spectrum, which implies the CW component plays an important role in the interactions among the internal pulses of NLP. With the increase of the pump power, the rectangular-shaped pulse is gradually broken into a Gaussian-shaped pulses cluster in the time domain, and the intensity of the CW component is improved, which is plotted as the purple curve in Fig. 5(b). This phenomenon is different from the results in , which the CW component does not occur in the spectrum when the rectangular pulse is changed into a hybrid pulse with one/ two rectangular shaped pulses and one/two Gaussian-shaped pulses. By increasing the pump power and adjusting the PCs orientation, the varying nonlinear effects in the cavity greatly influences the interactions among the random ultrashort pulses in wave packet of NLP. Therefore, a part of internal pulses escapes from the initial rectangular-shaped NLP, and reform other pulses. Because of the high nonlinearity and sufficient pulse energy in cavity, the rectangular-shaped NLPs are completely reshaped into a Gaussian-shaped pulses cluster NLP through intense pulse interactions. In [27,32], due to the small energy of the escaped internal pulses, only multiple rectangular pulses and coexistence of rectangular-shaped and Gaussian-shaped pulses are achieved.
3.2.2 Single-scale soliton clusters
To further investigate the dynamics of multi-soliton pattern NLP in the cavity, we fix the LD1 power at 130 mW, and we elaborately adjust the nonlinear effects in cavity by manipulating the LD2 power and intra-cavity PCs orientation. A single-scale solitons cluster can be experimentally observed at LD2 of 80 mW. As shown in Fig. 6(a), multiple solitons are assembled as a bunch with a 3.139 µs time separation, which is in accordance with the cavity round-trip time. The bunch comprises 6 solitons with the same time separation of 21.6 ns, and the solitons in bunch possess a nearly uniform intensities distribution. When the power of LD2 is increased to 100 mW, the number of solitons in a bunch is increased to 15, shown in Fig. 6(b), and the intervals of adjacent bunches and solitons separation are the same as those in Fig. 6(a). Similar phenomenon is observed in an all-normal-dispersion mode-locked fiber laser . The generated multiple solitons are assembled together as a bunch with a 7 ns soliton separation, and the number of solitons in a bunch is influenced by the pump power and the PC states in cavity. Continually increasing the pump power to 150 mW, a broader single-scale solitons cluster is formed which contains 108 solitons in a 2.3328 µs time-scale bunch, but the palpable fluctuation of solitons intensities distribution can be found in Fig. 6(c). The intervals of adjacent bunches and solitons separation are kept the same as 3.139 µs and 21.6 ns. It is noteworthy that the 2nd harmonic cluster is achieved at LD2 power of 205 mW, and a bunch contains 63 solitons in a 1.3608 µs time scale, which is shown in the inset of Fig. 6(d). Experimentally, the solitons separation can be changed by slightly rotating the paddles of PCs. Here the aforementioned 21.6 ns separation is fixed because the PC state is maintained.
Figure 6(e) illustrates the corresponding output spectra with different pump powers. It can be obviously distinguished that two CW components appear in spectra, and the peak wavelengths are 1539.12 nm and 1561.25 nm at 80 mW. The intensities of two CW components are strengthened when the pump power increases. At pump power of 205 mW, the wavelengths of CW components are changed to 1534.65 nm and 1560.86 nm. The obtained results further identify that the CW components can facilitate the interactions of the internal pulses in NLP wave packet, which leads to multi-soliton pattern NLP formation in the cavity.
3.2.3 High order harmonic mode-locking
As discussed in Figs. 5 and 6, the characteristics of multi-solitons NLPs are similar to those in a conventional mode-locked fiber laser. According to soliton energy quantization, the number of the solitons in the cavity is directly proportional to the pump power level. Based on the pump power of single-scale soliton clusters, the power of LD2 is adjusted to 260 mW, and slightly rotating the paddles of PCs simultaneously, the solitons clusters are further broken up, and all solitons finally occupy the whole cavity. The recorded oscilloscope trace of laser pulses is shown in Fig. 7(a). It can be clearly noted that the intensities of solitons are not the uniform distribution in cavity, but the solitons separation is uniform, so this state belongs to the harmonic mode-locking state. For better clarity, the zoom-in of multiple solitons in 0.2 µs time-scale is shown in inset of Fig. 7(a), where the solitons separation is 21.6 ns, and the number of solitons in the whole cavity is estimated to be 145. Figure 7(b) presents the corresponding output spectrum with a 3-dB spectral bandwidth of 13.73 nm. Besides a weak CW component at 1559.36 nm, a higher intensity CW component can be conspicuously found in the spectrum. The zoom in of the higher intensity CW component is shown in Fig. 7(b), and two wavelength peaks of 1531.31 nm and 1533.46 nm are found. The obtained results indicate that three different CW components intensify the interaction of multiple solitons in the cavity, and lead to the formation of high order harmonic mode-locking the cavity. With a 1 Hz resolution bandwidth, the corresponding RF spectrum is shown in Fig. 7(c). The repetition rate of the output pulses is 46.2941 MHz, which is around 145th order harmonic of 318.55625 kHz fundamental repetition rate in a mode-locked fiber laser. The side-mode suppression ratio is estimated to be 36.7 dB, which demonstrates the harmonic mode-locking state operates in a stable regime. Figure 7(d) shows the autocorrelation trace of harmonic mode-locked fiber laser pulses. The result is characterized as a coherent peak located on a broad pedestal, representing that the harmonic mode-locked laser pulses belong to NLP regime.
3.2.4 Localized chaotic bunched pulses
In the experiment, an interesting solitons state NLP can be achieved at the pump powers of 130 mW LD1 and 100 mW LD2 by finely adjusting the PCs orientation in the cavity. Multiple chaotic pulses are bunched together, and the envelope of the bunched pulses is similar to the output pulse of Q-switched mode-locked laser. Figure 8(a) shows the recorded oscilloscope trace of pulses train, and the zoomed-in of a bunch pulse is inserted in Fig. 8(a). Here it can be clearly observed that all chaotic pulses are bounded at a time range of nearly 1µs, the intensity and separation of pulses in the bunch are chaotic, and changing constantly. However, the interval of adjacent punch pulses is well consistent with the cavity round-trip time. The reason for localized bunched pulses performance can be attributed to the strong soliton interactions which can prevent the neighboring solitons from locating too far to each other . Figure 8(b) presents the output spectrum of localized chaotic bunched pulses, and the output spectrum is generally smooth. However, three different CW components can be seen clearly in the spectrum, and the interactions among the internal solitons and CW components may cause the formation of localized chaotic bunched pulses. Compared with mode-locked spectra in the states of single-scale soliton clusters and high order harmonic mode-locking, the 3-dB spectral bandwidth is narrowed, and the corresponding value is 7.84 nm centered at 1556.1 nm.
Thus far, several groups reported the multiple waveforms of rectangular-shaped NLPs in a passively mode-locked fiber laser. In order to obtain versatile patterns NLP by adjusting the nonlinear effects in cavity, a 65 m HNLF [27,32], a 120 m twisted fiber , or a 40 m SMF adding an 8 m dispersion compensation fiber  are inserted in the cavity, and one rectangular-shaped NLPs can be broken up into several rectangular-shaped NLPs or coexistence of rectangular-shaped and Gaussian-shaped NLPs. However, due to the nonlinearity and pulse energy in cavity are not sufficient, the rectangular-shaped NLPs cannot split into versatile multi-solitons patterns.
Considering the typical nonlinear coefficients γ of 1.3 /W/km for SMF , 3.6 /W/km for EDF  and 9.4 /W/km for HNLF  in cavity, the calculated average nonlinear parameters in [27,32,35,36] are 6.04 /W/km, 6.15 /W/km, 1.36 /W/km, and 1.99 /W/km, respectively. In our experiment, the total cavity length is around 642.8 m, including 585 m HLNF, 1 m EDF, and 56.8 m SMF, and the average nonlinear parameter is 8.68 /W/km, which are larger than the published results. Because of the high nonlinearity provided by HNLF and sufficient pulse energy in the cavity, rectangular-shaped NLPs is completely broken up into Gaussian-shaped NLPs, and three types of multi-solitons NLPs are achieved. Although the oscilloscope trace of rectangular-shaped NLP wave packet is stable, it actually contains lots of ultrashort pulses with chaotic amplitudes and durations. The chaotic tiny pulses are bunched together as a wave packet through the nonlinear interactions among internal pulses, hence the nonlinear effects in cavity plays an important role in the dynamics and evolution of versatile patterns NLP formation. Experimentally, the cavity nonlinear effects can be effectively manipulated by adjusting the pump powers of LD1 and LD2, and rotating the intra-cavity PCs orientation simultaneously, interactions among internal pulses of NLP wave packet can vary considerably. This process will lead to a part of internal pulses gradually escape from the original pulses, and the rectangular-shaped pulses are completely changed to Gaussian-shaped pulses, as shown in Fig. 5(a). Additionally, the CW components also play an important role in the interactions among the internal pulses. As can be seen in Figs. 5(b), 6(e), 7(b), and 8(b), the CW components can facilitate the interactions of the internal pulses in NLP wave packet, which is a benefit for the formation of the multi-soliton patterns. The observed versatile multi-soliton patterns NLPs will be useful for further understanding the nature and physical mechanism of the NLPs in a passively mode-locked fiber laser.
In conclusion, we have experimentally demonstrated the versatile multi-soliton patterns NLP in a passively mode-locked fiber laser. By properly adjusting pump powers and finely rotating PCs orientation in cavity, the conventional rectangular-shaped NLP is completely broken up Gaussian-shaped pulses, and three types of solitons patterns NLP, namely, such as, single-scale soliton clusters, high order harmonic mode-locking, and localized chaotic bunched pulses, are achieved. The pulse duration can be linearly tuned from 8.21 ns to 128.23 ns by increasing the pump power from 30 mW to 400 mW with 2.936 ns / 10 mW. The monitoring of spectrum evolutions with pump power and spectrum stability in 2 hours indicates the fiber laser has an excellent mode-locking operation and long-term stability in NLP regime. The obtained results further enhance the understanding of fundamental physics of the NLPs in mode-locked fiber laser.
National Natural Science Foundation of China (61675008, 61805281); Shenzhen Technology and Innovation Council (KQJSCX20170727163424873); Tsinghua-Berkeley Shenzhen Institute (TBSI) Faculty Start-up Fund; Natural Science Foundation of Guangdong Province (2019A1515010732).
The authors declare no conflicts of interest.
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