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Abstract
The stable multipulse emission from an erbium-doped mode-locked fiber laser in dissipative soliton resonance (DSR) regime is numerically and experimentally investigated. It shows that in the multipulse operation of DSR, all pulses have identical characteristics. The number of these pulses is determined by the initial conditions, and keeps constant with the growth of pump power. Experimental results match well with the theoretical simulations. In the experiment, we obtain as high as 86 dual-wavelength DSR pulses, which have the same characteristics and are equally spaced in the cavity. Since the pulses behave similarly to harmonic mode-locking (HML), we call this phenomenon HML under DSR. By properly adjusting the polarization controllers, other numbers of multipulse emission in DSR region can be observed, which confirms that the number of DSR pulses depends on the initial conditions.
© 2017 Optical Society of America
1. Introduction
Passively mode-locked fiber lasers have been extensively investigated during the past two decades due to their compact and stable performance for generating ultrafast pulse with high peak power. By appropriately designing the cavity structure, different kinds of pulse formation have been observed in fiber lasers with either positive or negative cavity dispersion, such as conventional soliton [1], stretched pulse [2], self-similar pulse [3], dissipative soliton (DS) [4], and noise-like pulse (NLP) [5]. These pulses mentioned above share one trait: with the increase of pump power, the multipulse operation is unavoidable due to the so-called wave breaking in nonlinear optical fibers [6]. Although multipulse operation limits the single pulse energy, it can be useful in various fields. Harmonic mode-locking (HML) [7], where identical solitons are equally spaced in the cavity, is a simple way to dramatically scale the repetition rate of fiber lasers, which can be applied in optical communication and precision metrology.
Recently, Chang et al. have theoretically predicted a new soliton formation named dissipative soliton resonance (DSR) in the frame of complex cubic-quantic Ginzburg-Landau equation with certain parameter selections in 2008 [8]. The model predicts that in the DSR regime, the pulse energy and width increase indefinitely without wave breaking while keeping its peak power constant. So far, the DSR phenomena have been theoretically studied in net normal and anomalous dispersion cavities [8–15]. According to these theoretical predictions, by appropriately choosing parameters of the laser cavity, the observation of DSR pulse is independent of the mode-locking technique or the wavelength of emission. In fact, the DSR phenomena have been experimentally observed in fiber lasers using nonlinear polarization rotation (NPR) [16–19], figure-8 cavity [20–22] or saturable absorbers (SA) [23, 24].
Although the mode-locked pulses operating in the DSR regime are wave-breaking free, multipulse operation can still exist. Komarov et al. have theoretically investigated the competition and coexistence of DSR pulses in normal dispersion regime [13]. They used several pulses of different amplitudes as the initial field. It was found that with a sufficiently large value of the pump power and a sufficiently small amplitude difference of the initial pulses, steady-state multipulse operation in the DSR region could be obtained. All these pulses of steady-state multipulse operation had identical parameters. The number of these pulses depends on the initial conditions, but it does not change with increasing pump power. In 2015 Guo et al. experimentally observed multipulse operation of DSR in an erbium-doped fiber laser with net anomalous dispersion [24]. The pulses were equally spaced in the cavity with different amplitudes.
In this paper, we investigate the pulse dynamics of multipulse operation under the DSR conditions. Numerical and experimental properties of both the pulses’ temporal and spectral behaviors are presented. Simulation results show that increasing pump power step by step can only increase the pulse energy and width, and the laser keeps operating in single pulse regime. However, with sufficiently high initial pump power, multipulse operation of DSR is obtained. The experimental results match well with the simulations, which confirms the existence of multipulse operation of DSR in mode-locked fiber lasers. We have experimentally observed that as many as 86 DSR pulses can coexist in a passively mode-locked fiber ring laser by properly adjusting the pump power and the polarization state. The obtained pulses all have identical characteristics and are equally spaced in the laser cavity. Consequently, the repetition rate is 1019.7 MHz, which is as high as the 86th order of the fundamental frequency of 11.86MHz. We call this operation regime HML under DSR. By properly adjusting the polarization controllers, other orders of HML under DSR conditions can be observed.
2. Numerical model and simulation
The simulated laser cavity is made up of a 1-m-long erbium-doped fiber (EDF), 5-m-long single mode fiber (SMF) and a sinusoidal SA. A 10% coupler is used to output the light. The light propagation in the EDF and SMF is based on a scalar nonlinear Ginzburg-Landau equation [14]:
where A is the slowly varying electric field envelope, z is the propagation distance, and t is the pulse local time. β2 and γ represent the 2nd order dispersion and the fiber nonlinearity, respectively. In the simulation both EDF and SMF are assumed with the same dispersion β2 = 20 ps2/km, and nonlinearity γ = 5 (W·km)−1. g is the saturable gain of the fiber and Ωg = 64 nm is the bandwidth of the laser gain. For the SMF g = 0; for the EDF, the gain saturation is considered aswhere g0 = 3 m−1 is the small signal gain coefficient, and Esat refers to the gain saturation energy. g0 is related to the doping concentration of the doped fiber and Esat corresponds to the pumping strength.For the sinusoidal SA in the simulated laser, a relatively simple model based on nonlinear optical loop mirror (NOLM) was adopted [14, 25],
where q is the modulation depth, Φ0 accounts for linear bias, and Isat is the saturation power. Other types of sinusoidal SA such as NPR, are described by more complex models, but eventually they have similar oscillating patterns. The parameter q or Φ0 has little impact on the pulses under the stable mode-locking regime. Thus, for simplification we set q = 0.4, Φ0 = 0, and Isat = 40 W.The single pulse operation of DSR was first studied. The simulation starts from an arbitrary weak signal. At the first 200 roundtrips, we set the pumping strength Esat = 0.5 nJ. As shown in Fig. 1(a), the initial noise signal gradually converges to a stable state, which is the DSR pulse with the typical rectangular shape. To study the behavior of the DSR pulse under different pumping strength, we increase the Esat to 1 nJ, 1.5 nJ, 2 nJ at the roundtrip of 200, 400, 600, respectively. Figure 1(a) and 1(b) show the evolution of the DSR pulse. With the growth of Esat, the DSR pulse broadens its width proportionally and no multipulse operation of DSR is observed. Figure 1(c) shows the bell shape spectrum at the last roundtrip with a 3-dB bandwidth of around 1.8 nm. This spectrum form and its narrow bandwidth can be attributed to rectangular shape of the pulse, where the edges of the pulse with large chips are responsible for the broadband rectangular portion of the spectrum, and the central part with a low chip results in the narrowband bell-shaped portion of the spectrum [13,14]. To observe the multipulse operation of DSR, we set the initial signal as 3 sech-shaped pulses with the same amplitude and an interval of 40 ps, and keep all the other parameters unchanged. As shown in Fig. 2(a), with increasing gain in the cavity, the 3 initial pulses firstly transform to rectangular DSR pulses, and then broaden their widths simultaneously. The temporal profiles at the roundtrip of 200, 400, 600, and 800 are shown in Fig. 2(b). It is found that the 3 pulses always have the same amplitude and width, which indicates that the gain competition exists between the multiple DSR pulses. Consistent with the previous simulation, no wave-breaking is observed. Figure 2(c) shows the spectrum at the last roundtrip with a periodic modulation structure. The 3-dB bandwidth is around 0.7 nm, and the peak intensity of spectrum is about 6 dB higher than that of single DSR pulse condition, which indicates that the variation of pulse amplitude is smaller than before.
Fig. 1 (a) Pulse evolution when the Esat increased from 0.5 nJ to 2 nJ. (b) Pulse temporal profiles and (c) optical spectrum at the last roundtrip.
Fig. 2 (a) Pulse evolution when the Esat increased from 0.5 nJ to 2 nJ. (b) Pulse temporal profiles and (c) optical spectrum at the last roundtrip.
However, the observations of spontaneous multipulse operation under DSR in fiber lasers cannot be explained by the above simulation results. In accordance with the experimental condition, the initial signal is set back to a noise signal in the following simulation. Here, we set the pumping strength Esat = 2 nJ and keep it constant at this high level. As shown in Fig. 3, stable multipulse operation under DSR is obtained. From Fig. 3(a), the evolution of multipulse under DSR is clearly observed. With this high-level pumping strength, firstly many weak pulses emerge from the background noise. Then, 6 pulses selected by the gain competition are further amplified, which eventually become 6 DSs. Two pairs of DSs are merged since they are too close to each other. Thus, finally only 4 pulses reach a stable state and then translate into rectangular DSR pulse. Figure 3(b) and 3(c) show the temporal and spectral profiles at the last roundtrip, respectively. It can be found that the 4 DSR pulses still have identical amplitude, and the value is the same with the result in Fig. 1 and Fig. 2, which is around 5.5 W. This result indicates that the multipulse operation under DSR is derived from the generation of multiple DSs. Similar results are obtained when the chromatic dispersion of SMF is varied in the proper range.
Fig. 3 (a) Pulse evolution when the Esat = 2 nJ. (b) Pulse temporal profile and (c) optical spectrum at the last roundtrip.
3. Experimental setup
The configuration of the fiber laser for observing multiple DSR pulses is schematically shown in Fig. 4, which is a simple all fiber ring laser mode-locked by NPR. It has a ring cavity of 17.3 m long, which corresponds to a fundamental repetition rate of 11.86 MHz. The gain medium is a 0.8-m erbium-doped fiber (EDF) with a dispersion parameter of 15.5 ps/nm/km. A 5-m highly nonlinear fiber (HNLF) is used to enhance the nonlinearity of the cavity, which has a nonlinear coefficient γ = 10 W−1km−1 with dispersion of 0 ± 1 ps/nm/km. The high nonlinearity plays an important role in broadening the tuning range of the pulse width [20, 26] and multipulse operation [4, 24]. The rest of the fibers in the cavity are the standard single mode fibers (SMF) with dispersion of 17 ps/nm/km. Thus, the net dispersion in the cavity is estimated as −0.28 ps2. A polarization-dependent isolator (PD-ISO) together with two polarization controllers (PC) act as an equivalent saturable absorber, which also ensure the unidirectional operation of the ring. A 980-nm laser diode with the maximum pump power of 800 mW is used to pump the EDF via a 980/1550 nm wavelength division multiplexer (WDM). The 10% laser output is taken by a 90:10 optical coupler (OC). An optical spectrum analyzer (YOKOGAWA AQ6370C), a photodetector (Agilent 11982A, 20 GHz) connected to an oscilloscope (Agilent 86100A, 50 GHz) and a radio-frequency (RF) spectrum analyzer (R&S FSU50, 50 GHz) are employed to monitor the laser output simultaneously.
4. Experimental results
In the proposed laser, by carefully adjusting the two PCs, self-started mode-locking can be achieved when the pump power is beyond a threshold value of about 76 mW. When we continue to increase the pump power beyond 140 mW, stable DSR operation can be easily obtained by adjusting the PCs. After having the laser stabilized in DSR regime, we then keep the two PCs fixed and vary the pump power to study the single pulse operation. Figure 5(a) shows the typical pulse evolution in DSR regime. The pulse profile transforms from sech2 shape to rectangular shape, and its duration broadens linearly from 1.9 to 10.1 ns with the pump power increasing from 200 to 800 mW (with a step of 100 mW), while the peak power almost keeps invariable due to the peak-power-clamping effect induced by the NPR. The corresponding optical spectra are presented in Fig. 5(b). The spectra of rectangular pulses exhibit the conventional soliton sidebands, due to the interference between the soliton pulse and dispersive waves, which is an intrinsic feature in a passively mode-locked fiber laser with net anomalous dispersion [16, 22]. Despite the increasing spectral intensity, the 3-dB bandwidths of the spectra are almost constant at ~4.8 nm. Fig. 2(c) displays the RF spectrum under the maximum pump power of 800 mW. The repetition rate of the pulse train is 11.86 MHz as determined by the cavity length. The signal-to-noise ratio (SNR) is higher than 65 dB in the 20 MHz span and 70 dB in the 5 MHz span. Note that the NLP mode-locking regime can generate noise-like rectangular pulses, whose pulse dynamics are very similar to that of DSR pulses. Autocorrelation measurement of the pulses can determine whether the rectangular pulse is a single coherent pulse or bunch of solitons. Under the pump power of 800 mW, the autocorrelation trace of the obtained rectangular pulse measured by a commercial autocorrelator (Alnair Labs, HAC 200) with a scan range of 100 ps which is sufficient to detect any bunch of solitons, is presented in Fig. 5(d). The autocorrelation trace shows a constant level, and no NLP-characteristic fine structure pulses were observed. However, when achieving bunch of solitons, the autocorrelation trace could be clearly observed, which proves that the laser was operating in DSR regime [18, 23, 27].
Fig. 5 Single pulse operation in DSR regime. (a) Pulse profile versus pump power. (b) Corresponding optical spectra. (c) RF spectrum under 800 mW pump power. (d) Autocorrelation trace for a 100 ps scan range under 800 mW pump power.
By further carefully adjusting the two PCs, steady-state multipulse operation under DSR conditions can also be achieved in our fiber laser when the pump power is above 220 mW. As shown in Fig. 6(a) and 6(d), the pulse dynamics of DSR in this multipulse operation exhibit similar features to that in single pulse operation. With the pump power increasing from 300 to 700 mW (with a step of 100 mW), the pulse duration and the amplitude increase at the same time, since the pulse peak power does not reach the peak-power-clamping limitation. When the pump power increases from 700 to 800 mW, the pulse amplitude remains almost the same, while its width continues to broaden. This observation matches well with the simulation in Fig. 2 and each individual pulse in this multipulse operation behaves similarly to the single DSR pulse. In this steady-state multipulse operation, all these pulses are evenly spaced in the cavity with identical shape, duration and peak amplitude, while the number of pulses keeps constant with the growth of pump power. The uniform interval of the pulse train is ~1.277 ns corresponding to a repetition rate of ~783 MHz, which indicates that 66 pulses coexist in the laser cavity. Figure 6(b) shows the evolution of optical spectrum versus the pump power. The 3-dB bandwidth broadens from 0.3 nm to 0.58 nm with a slight growth of spectral intensity, which is narrower than that in single pulse operation, similar to the results in our simulations. The spectrum broadening is induced by the self-phase modulation (SPM), since the pulse amplitude grows. The RF spectrum under the maximum pump power of 800 mW in Fig. 6(c) shows that the super-mode suppression ration (SMSR) is beyond 37 dB in the 1.5 GHz span and 44 dB in the 100 MHz span. The fundamental peak locates at 782.6 MHz. The autocorrelation trace still shows a constant level, which is not presented here. Obviously, the pulses behave similarly to HML of conventional soliton, thus we call this phenomenon HML under DSR. Note that in HML of conventional soliton, increasing pump power leads to the growth in number of solitons; while in HML under DSR, it only broadens the pulse duration.
Fig. 6 HML under DSR, 66 pulses. (a) Profile of pulse train versus pump power. (b) Corresponding optical spectra. (c) RF spectrum under 800 mW pump power. (d) Comparison of the pulses under different pump power.
Based on the results of simulations and experiments above, the formation of HML under DSR can be clearly understood. The generated single DS in the cavity firstly split into multiple DSs due to the high pump power and accumulated nonlinearity, and then with appropriate cavity parameters these DSs are transformed to rectangular DSR pulses. Usually the multiple DSs are randomly spaced in the cavity. However, under certain conditions, they can arrange themselves automatically and equally locate in the cavity with identical characteristics, which is the HML state. These DSs in the HML state eventually translate to rectangular DSR pulses, and we consequently obtain the HML under DSR. Obviously, the number of DSR pulses depends on how many multiple DSs reach the stable state in the cavity, since they never split in DSR regime.
To confirm that the number of pulses depends on the initial conditions, we further adjust the PCs in the laser cavity. Several other HML under DSR operation can be observed. An example of 82 DSR pulses with a repetition rate of 972.2 MHz is shown in Fig. 7. Since the high-speed oscilloscope requires a trigger signal beyond a certain value, and thus only when the pump power is above 630 mW can these 82 DSR pulses be detected by the oscilloscope. Therefore, here we just present the result under the pump power of 800 mW. Figure 7(a) and 7(b) show the oscilloscope traces of the observed pulse emission and the RF spectrum, respectively. The SMSR is around 30 dB in the 1.5 GHz span and 40 dB in the 100 MHz span, which is significantly lower than that in Fig. 6(c). Meanwhile, the temporal profile of the DSR pulse is not as square as before. This performance degradation can be attributed to the lower energy of every individual pulse and the closer distance between them, since the number of pulses increases while the pump power remains unchanged. When we change the pump power, the repetition rate remains unchanged, which proves that the laser operates in HLM of DSR. Surprisingly, by carefully adjusting the PCs, we also observed the HML of 86 dual-wavelength DSR pulse with a repetition rate of 1019.7 MHz under the pump power of 800 mW. Figure 8 shows the spectrum of the HML of the dual-wavelength DSR pulse centered at 1547.7 and 1550.6 nm, with a 3-dB bandwidth of 0.26 nm and 0.52 nm, respectively. The SMSR is around 35 dB in the 100 MHz span. Such dual-wavelength DSR pulse has been reported previously, and it was found that the high nonlinearity and the spectral filtering effect induced by NPR play important roles in multiwavelength emission [18, 24, 28]. Note that as the high-speed oscilloscope requires a periodic trigger signal from the output, we cannot observe unevenly spaced pulses in the cavity. However, this does not mean unevenly spaced DSR pulses cannot exist in our laser cavity. We believe that using other fast oscilloscopes, the unevenly spaced DSR pulses could also be observed by carefully adjusting the PCs, which are similar to the operation in Fig. 3.
Fig. 8 Optical spectrum of the HML of the dual-wavelength DSR pulse. Inset: RF spectrum and pulse train.
5. Conclusion
In conclusion, we have numerically and experimentally studied multipulse dynamics in DSR regime. Numerical results show that the rectangular DSR pulses in multipulse operation are transformed from multiple DSs, and once the DSs reach a stable state, the number of pulses will keep unchanged, regardless of pump power. Besides, every individual DSR pulse behaves similarly to that in single DSR pulse region. The experimental observations are in good agreement with the simulation results. In the proposed laser, we have observed different DSR pulses in HML state by carefully adjusting the two PCs in the cavity. Our experiments verify the existence of the steady-state multipulse or even HML operation under DSR regime, which can contribute to a better understanding of the pulse dynamics in DSR regime.
Funding
National Natural Science Foundation of China (NSFC) (61435003, 61421002, 61327004, 61377042, 61505024, 61378028); Science and Technology Project of Sichuan Province (2016JY0102).
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