We report flexible dissipative soliton generation from an all-fiberized all-normal-dispersion (ANDi) long cavity actively mode locked ytterbium doped fiber laser based on improved harmonic mode locking technique. The laser is featured with unusually wide and fine tunabilities in repetition rate and operating wavelength, meanwhile superior stability is maintained. The repetition rate of the laser can be flexibly controlled from 226 kHz to 6.25 GHz (corresponding to the highest 27655th order harmonic mode locking) in the interval of 226 kHz, while supermode suppression is confined above 50 dB and the pulse duration is retained in the range of 38 ps~80 ps. As high as 4.3 nJ pulse energy can be achieved with a low pump power of 160 mW when operating at the fundamental mode locking regime. The operating wavelength of the laser can be tuned in the wide range of 1005 nm~1100 nm. As far as we know, it is the first demonstration of up to ten thousands order stable harmonic mode locking in ANDi fiber laser, which manifests the capability of generating both high energy pulse and ultra-high repetition rate pulse in a single ANDi cavity. The destabilization of dissipative soliton under strong pump is also demonstrated.
© 2015 Optical Society of America
Attribute to the unparalleled simplicity, versatility and robustness of fiber laser, fiber-based mode-locked lasers have been widely investigated in kinds of active ways as well as passive methods, and miscellaneous mode-locked fiber lasers with different performances have played critical roles in various applications, such as optical communications , supercontinuum generation , material machining , and the seed of high power fiber amplification system . The specific requirements on pulse parameters differ a lot among these applications, especially the repetition rate and pulse energy. In applications like material machining and nonlinear effects research, high pulse energy or high peak power is needed. Many methods have been explored to reduce the repetition rate and boost the pulse energy directly from an oscillator, such as by employing long cavity with large or all normal dispersion [5, 6]. While, in those applications where speed and precision is required, like optical communications and frequency metrology, high repetition rate is necessary. Although various cavity designs have been developed for different applications, in some researches and optical systems, the demand on the repetition rate of the pulsed laser widely ranges from sub-MHz to above GHz, which is hardly fulfilled with traditional parameter-fixed mode locked fiber laser. The development of pulsed laser whose repetition rate is widely and finely tunable in a large range would significantly simplify the procedure of research, provide more flexibility, and reduce the complexity of the system. Hence, it is worthwhile to explore the possibility of realizing the generation of both low repetition rate pulse with high energy and very high repetition rate pulse in one single cavity.
Actually, the building of mode-locked fiber laser whose repetition rate is widely and finely tunable in a large range is feasible. Here we propose a scheme to cover the requirements on the pulse energy and repetition rate in one single cavity, which is generating relatively low repetition rate pulses with high pulse energy in a long all-normal-dispersion (ANDi) cavity mode locked fiber laser, and simultaneously enhance the laser's capability of operating in ultra-high order harmonic mode locking regime. When operating in fundamental mode locking regime, due to the long cavity length and ANDi, the pulse repetition rate is low and the pulse energy is easy to boost to high value with low pump power. By operating in ultra-high order harmonic mode locking, the repetition rate can be enhanced to meet the requirements of some high speed applications. Furthermore, with long cavity length, the repetition rate can be finely tuned in a small interval. Because in harmonic mode locking regime, the repetition rate of the laser can be adjusted to the integer-multiple of the cavity round-trip frequency.
Conventionally, anomalous dispersion cavity is utilized to achieve high order passive HML, and as high as 928th HML has been achieved in this regime [7–9]. By contrast, an ANDi system is usually adopted to achieve higher pulse energies with relatively low repetition rate, and it is deemed difficult to obtain HML in ANDi fiber lasers because the pulse may experience large nonlinear phase shifts in an ANDi fiber . However, there are several emerging works featuring in high order passive harmonic mode locking in ANDi fiber laser [11–18]. As high as 30th order HML was achieved in a Graphene oxide based ANDi fiber laser . As for passively mode locked fiber laser, the common way to achieve harmonic mode locking is raising the pump power. The harmonic order of the passive mode locking fiber laser is difficult to control precisely by adjusting the pump power and the relationship of HML order and pump power level is inconclusive, especially in ultra-high order harmonic mode locking. Besides, high pump power and additional adjustments of cavity devices are commonly required to generate repetition rates of several GHz. By contrast, with active mode locking, HML of different orders can be conveniently and precisely achieved by altering the modulation frequency. Besides, there are applications where an active mode-locking scheme is preferred, e.g., the system where synchronization among lasers, instruments and clocks are required. There are few reports on active harmonic mode locking in ANDi cavity. Recently, Li et al.  and our previous work  achieved high order stable HML (30th order and 475th order, respectively) in ANDi actively mode locked Yb-doped fiber laser based on pulse modulated electro-optic modulator.
In this manuscript, based on the fore-mentioned motive of achieving widely and finely tunable repetition rate in one single cavity, we report a qualified all-fiberized ANDi actively mode locked Yb-doped fiber laser. In the aid of flexible short pulse modulation, widely tunable narrow band spectrum filter and long cavity length, we realize an exceptionally large tunable range and fine tuning precision of repetition rate from 226 kHz to 6.25 GHz in the interval of 226 kHz as well as operating wavelength from 1005 nm to 1100 nm continuously. Up to 27655th order stable harmonic mode locking is achieved, with as high as 50 dB supermode suppression ratio (SMSR), proving the capability of achieving stable ultra-high order HML in long ANDi fiber cavity. As far as we know, it is the first demonstration of up to ten thousands order stable harmonic mode locking in ANDi fiber laser.
2. Experimental setup
The experimental setup is shown in Fig. 1. In this structure the gain media is a section of 1.5 meters piece of Yb-doped fiber, which is core-pumped with a 500 mW 976 nm laser diode through a wideband wavelength division multiplexer (WDM). The Yb-doped fiber has a nominal absorption coefficient of 250 dB/m at 975 nm and a group velocity dispersion (GVD) of −35 ps/nm/km at 1060 nm. An etalon-based widely tunable optical filter with a nominal 3 dB-bandwidth of 1-1.2 nm (10 nm at 20 dB) is located after the WDM to select the operating wavelength and confine the gain bandwidth of the laser. The central wavelength of the filter can be manually adjusted from 1000 nm to 1100 nm. A polarization-sensitive LiNbO3 Mach-Zehnder intensity modulator (10GHz bandwidth) is employed in the cavity as the mode locker to achieve active mode locking, fed by amplified pulse signal from a pulse generator. The pulse generator is capable of generating electrical short rectangular pulse with ~30 ps rising/falling time, as narrow as 80 ps in duration and as high as 6.25 GHz in repetition rate. Due to the polarization sensitivity of the modulator, a polarization controller is applied before the modulator to control the polarization state of light into the modulator. A polarization-insensitive optical isolator is utilized to ensure the unidirectional propagation of the light in the cavity. The optical pulses in the cavity are coupled to the output port through a 30/70 coupler (70% in cavity and 30% output). A section of around 900 meters single mode fiber (Corning HI 1060) is incorporated between the polarization controller and the output coupler to increase the cavity length and increase the normal dispersion of the total cavity. The fiber has a GVD of −30.8 ps/nm/km and the total cavity dispersion was estimated to be 16.6 ps2 (without counting the dispersion of the filter and modulator). The output pulses are monitored by an optical spectrum analyzer (measurement scale of 600~1700 nm, 0.02 nm minimum resolution), and converted to electrical pulses by a high speed photodetector (25 GHz bandwidth), then analyzed by a 25 GHz real-time oscilloscope and a radio frequency spectrum analyzer (13.5 GHz bandwidth).
3. Experimental results and discussion
3.1 Fundamental mode locking
When the intra-cavity modulator is modulated by the pulse signal from the generator, the modulation pulse width is set at 100 ps, and the repetition rate is tuned to meet the round-trip cavity frequency. The laser can operate in stable and self-starting fundamental mode locking regime. Figure 2 shows a typical mode locking state observed. In this case, the pass band center of the tunable filter is adjusted at 1040 nm, the pump power is raised to 160 mW and the average output power is 0.98 mW. Figure 2(a) shows the pulse waveform observed in the oscilloscope and the pulse train in the range of 25 μs in the inset figure. The full width at half maximum (FWHM) of the pulse is measured to be 78 ps. The fundamental repetition rate is 226 kHz, corresponding to a cavity length of 909 m. The optical spectrum of the pulse train is shown in Fig. 2(b). The spectrum has a quasi-rectangular shape with sharp edges. There are small peaks on the both sides of the spectrum. The 3dB spectrum width is 2.1 nm and the edge-to-edge bandwidth is 4 nm. The time-bandwidth product is calculated to be 45.4, indicating a large chirp in pulses. The radio frequency (RF) spectrum observed in the radio frequency spectrum analyzer is shown in Fig. 2(c) with a span of 12 kHz and a span of 24 MHz in the inset. It is revealed that the signal-to-noise ratio (SNR) is suppressed better than 60 dB, indicating a high temporal stability. Figure 2(d) shows the output power variations with an increasing pump power.
Considering the large normal dispersion in the cavity and the sharp edges of the spectrum, it can be concluded that dissipative solitons are formed in this laser [21–23]. With the average power of 0.98 mW and the repetition rate of 226 kHz, the pulse energy is calculated to be 4.3 nJ. Actually dissipative soliton generation in ANDi actively mode locked fiber laser was previously demonstrated [19, 24]. However, in those works, because of relatively short cavity and limited pump power, the pulse energy is relatively low (limited at 1.58 nJ). In our setup, the cavity length is elongated to achieve high pulse energy with low pump power. The experimental results manifest the capability of high energy pulse generation in ANDi actively mode locked Yb-doped fiber laser, which were mainly realized in passively mode locked fiber laser before.
Additionally, in this case, when the pump power exceeds 160 mW, the pulse dynamics will be destabilized. This phenomenon occurs in fundamental mode locking and low order HML regime, which will be later demonstrated in detail in section 3.4.
3.2 Harmonic mode locking
By altering the repetition rate of the modulation pulses to the integer multiple of the round-trip cavity frequency and simultaneously keeping the pulse width of the modulation signal, HML can be instantaneously achieved, without the demand of PC adjustment or raising the pump power, which is much more convenient than the case of passive mode locking. Ascribe to the combination of the flexible short pulse signal modulation, the optical spectrum narrow bandpass filtering, and the long cavity length, the laser can achieve stable HML from the 2nd order HML (repetition rate 452 kHz) continuously to the highest 27655th order HML (repetition rate 6.25 GHz), while maintaining ultra-high temporal stability. In other words, the laser can operate in 27655 selectable repetition rates, from 226 kHz to 6.25 GHz in the interval of 226 kHz, almost continuously tunable in repetition rate. The order of HML is only limited by the frequency upper-limit of the pulse generator.
To demonstrate the temporal characteristics and stability of the laser's HML status, Figs. 2(a)-2(h) illustrate the pulse trains observed in the oscilloscope and the RF spectra observed in the radio frequency spectrum analyzer, under different orders of HML, all of which are acquired with a fixed pump power of 320 mW. Figures 2(a) and 2(b) exhibit the pulse train and RF spectrum of the 10th HML. The repetition rate is measured to be 2.26 MHz, and the SNR and SMSR are suppressed better than 66 dB and 60 dB in the RF spectrum respectively, indicating a stable and low noise operating status. Additionally, Figs. 2(c) and 2(d) show the pulse train and RF spectrum of the 160th HML. The repetition rate is measured to be 36.16 MHz, and the SNR and SMSR are suppressed better than 69 dB and 57 dB respectively. Moreover, Figs. 2(e) and 2(f) further illustrate the case of 5120th HML. The repetition rate is measured to be 1.157 GHz, and the SNR and SMSR are suppressed better than 65 dB and 53 dB in the RF spectrum respectively. At last, Figs. 2(g) and 2(h) exhibit the pulse train and RF spectrum of the highest 27655th HML. The repetition rate is measured to be 6.25 GHz, and the SNR and SMSR are suppressed better than 62 dB and 50 dB in the RF spectrum. As we can see, the results at the 27655th HML shows an amplitude-even high repetition rate pulse train with ultra-high stability and pure RF spectrum without additional significant noise, which positively manifests the utility of this active mode locking laser in many demanding applications. Essentially, the laser can operate in any repetition rates of integer-multiple of 226 kHz below 6.25 GHz, which is a critical capability in the applications where large range and fine tunability in repetition rate is required (see Fig. 3).
As the orders of HML increases, besides the repetition rate, the pulse duration, average power, pulse energy and optical spectrum have regulative variations. Figure 4(a) further shows the evolution of the experimentally measured pulse width and output power with an increasing repetition rate of the HML laser, at a fixed pump power of 320 mW. Figure 4(b) shows the calculated pulse energy with regard to the repetition rate. As can be seen in Fig. 4(a), the pulse widths decrease from 80 ps to 38 ps when the repetition rate increases from 2.26 MHz to 6.25 GHz, corresponding to the 10th order and the 27655th order HML, respectively. And the pulse energy also decreases from 1.7 nJ to 2.9 pJ, as the repetition rate increases.
The optical spectrum of the output pulse narrows as the order of the HML increases. Figure 4(c) shows the evolution of the optical spectrum with repetition rate. As illustrated, in the HML of different orders, the optical spectra retain the basic shape of fundamental mode locking, which is featured with two sharp edges, indicating that the pulses are still formed as dissipative solitons. However, as the repetition rate increases, the width of the spectrum narrows down accordingly. As the repetition rate increases from 2.26 MHz to 6.25 GHz, the 20 dB-spectrum bandwidth decrease from 3.2 nm to 0.8 nm.
The experimental results indicate that higher HML order corresponds to narrower optical spectrum bandwidth. The phenomenon is consistent with the theoretical predictions which are established by Haboucha et al. , in which it is shown numerically that larger number of pulses per cavity round-trip corresponds to narrower filter bandwidth in the normal dispersion regime passively mode-locked fiber laser. Similar experimental results can be found in Ref . Although, the nominal 3 dB bandwidth of the filter is as narrow as 1 nm, and fixed, the pulses with wider spectrum bandwidth can pass the filter, but with larger loss, that is one of the reasons why the output power is relatively low when operating in low repetition rate, because low order HML corresponds to wider spectrum bandwidth and larger cavity losses.
The short pulse modulation and narrow bandwidth filter take a critical role in maintaining stability in ultra-high HML regime. The short pulse modulation, which is slightly wider than the output optical pulse, restricts the generated pulse within small range in time domain, which is helpful to control the timing jitter of the pulse in a low level. The narrow band filter is deemed to be another critical cause of largely improved HML stability, which is one of the distinctness compared with the works demonstrated in Ref . High order HML is mainly limited by the onset of supermode noise, which is essentially caused by the beating between supermodes of different frequency. Restricting the gain spectrum of the laser in a certain and narrow band with narrow bandwidth filter will control the mode beating in small range, thus effectively suppress the supermode noise to low level and improve the stability of high order HML.
3.3 Operating wavelength tunability
Because a manually tunable narrow bandwidth intra-cavity filter is utilized, the laser's operating wavelength is thus tunable by carefully adjusting the knob of the filter. Due to the relationship between the cavity round-trip frequency and the operating wavelength, it is necessary to trim the frequency of the modulation signal simultaneously. The wavelength tunability can be achieved in fundamental mode locking as well as HML regime. The experimental results exhibited in the previous context are all obtained at the wavelength of 1040 nm. For the sake of briefness, here we only demonstrate the wavelength tunability at the 40th order HML.
Figure 5(a) illustrates the laser's optical spectrum figures when the pass band of the filter is adjusted to different wavelength and the pump power fixed at 320 mW. As we can see the central wavelength of the laser can be tuned in the wide range from 1005 nm to 1100 nm, and the corresponding repetition rate is measured to be ranging from 9.038 MHz to 9.044 MHz. Additionally, the laser could also operate in continuous wave mode by simply turning off the modulation signal and adjusting the voltage applied on the modulator. Wide wavelength tunability with the same tunable range can also be achieved as illustrated in Fig. 5(b). In continuous wave mode, the 3 dB optical spectrum widths are around 0.08 nm, which are much narrower than the pulsed mode. Because the laser is coupled out immediately after the intra-cavity spectrum filter, there is no sign of amplified spontaneous emission light in the optical spectrum, and the spectrum figure shows excellently low noise level and high optical signal-to-noise ratio, in pulsed as well as continuous wave mode. Figure 5(c) further shows the variation of output power versus operating wavelength, at the fixed 320 mW pump power.
3.4 The destabilization of pulse dynamics under strong pump
Increasing the cavity length and pump power is a common method of obtaining high pulse energy in mode locking laser. However, overdriven nonlinear effects caused by high pulse peak power may lead to pulse splitting and destabilization of the mode locking pulses, which was previously observed in soliton formed mode locking lasers [26, 27]. Dissipative soliton in normal dispersion cavity was regarded as a way to achieve high pulse energy in mode locked fiber laser, because the normal dispersion in cavity broaden the pulse duration and increase the tolerance level of pulse peak power. However, destabilization under strong pump also exists in dissipative soliton mode locking regime, and the cases has been reported in passively mode locking fiber laser [28–31].
In our mode locking laser, when operating at low repetition rate, relatively high pump power would lead to pulse destabilization. Taking the case of the 5th HML for example, at the 5th HML, namely the repetition rate of 1.13 MHz, when the pump power exceed 350 mW, the pulse waveform will transform from stable state to the instable state with pulse intensity and pulse shape fluctuating randomly, as illustrated in Fig. 6(a), where multiple random instantaneous waveforms are superimposed in one figure. The corresponding optical spectrum evolution with regard to increasing pump power (150 mW, 350 mW, 375 mW and 400 mW, respectively) is shown in Fig. 6(b). As we can see, the optical spectra with pump powers of 150 mW and 350 mW are typical spectra of dissipative soliton, indicating a stable pulse state. By contrast, the optical spectra shape of 375 mW and 400 mW transform to a triangular one, which correspond to the instable pulse state shown in Fig. 6(a).
There are two possible explanations for the destabilization. One is the optical-filter-restricted gain bandwidth. Owing to the self-phase modulation becoming stronger under higher pump power, the width of optical spectrum will broaden as the pump power increase, as shown in Fig. 6(b), also demonstrated in Ref [23, 24, 32, 33]. As the optical spectrum broadens beyond the bandwidth of the optical filter, the cavity loss will be too high to achieve the balance between gain, loss, dispersion and nonlinear effects, which is the critical requirement of dissipative soliton formation. Hence, stable solitons are hardly formed when pump power exceeds the limits, then the pulse become fluctuating. Additionally, because near one kilometer long cavity is utilized in this laser and pulses with peak power of above 50 W are formed in cavity, the destabilization may also be induced by the stimulated Raman scattering in long cavity, which is lately demonstrated in Ref . However, because the pulses are coupled out directly after the optical filter, there is no sign of Stocks light in output spectrum. The exact origin of pulses destabilization may require further specific investigations.
We develop an all-fiberized versatile pulsed Yb-doped fiber laser which is widely and finely tunable in repetition rate and operating wavelength based on improved active harmonic mode locking technique. The pulse dynamics shows the characteristics of dissipative soliton. Taking advantages of the ultra-long ANDi cavity, the laser can generate high pulse energy (as high as 4.3 nJ) with low pump power. Meanwhile, in the aid of flexible short pulse modulation and widely tunable narrow band filter, the laser can achieve unusually wide and fine tunable range in repetition rate (226 kHz to 6.25 GHz in the interval of 226 kHz) and operating wavelength (1005 nm to 1100 nm). And the variation of pulse duration is retained in a small range of 38-80 ps, even at repetition rate of several hundred kilohertz. This scheme is proven to be capable of achieving ultra-high order HML without significant degradation of stability. The highest order of HML in ANDi mode locked fiber laser is thus significantly advanced from the magnitude of several hundred to ten thousands. The results manifest the capability of generating both high energy pulse and ultra-high repetition rate pulse in single ANDi cavity. Owing to the exceptionally wide tunabilities in repetition rate and operating wavelength, this versatile laser may find interests in a wide range of applications.
This work was supported by the State Key Program of National Natural Science of China (Grant No. 61235008) and the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No.12JJ1010).
References and links
1. K. W. Holman, D. J. Jones, D. D. Hudson, and J. Ye, “Precise frequency transfer through a fiber network by use of 1.5-μm mode-locked sources,” Opt. Lett. 29(13), 1554–1556 (2004). [CrossRef] [PubMed]
2. T. Jiang, G. Wang, W. Zhang, C. Li, A. Wang, and Z. Zhang, “Octave-spanning spectrum generation in tapered silica photonic crystal fiber by Yb:fiber ring laser above 500 MHz,” Opt. Lett. 38(4), 443–445 (2013). [CrossRef] [PubMed]
3. F. Ilday, J. Chen, and F. Kärtner, “Generation of sub-100-fs pulses at up to 200 MHz repetition rate from a passively mode-locked Yb-doped fiber laser,” Opt. Express 13(7), 2716–2721 (2005). [CrossRef] [PubMed]
8. Z.-C. Luo, M. Liu, H. Liu, X.-W. Zheng, A.-P. Luo, C.-J. Zhao, H. Zhang, S.-C. Wen, and W.-C. Xu, “2 GHz passively harmonic mode-locked fiber laser by a microfiber-based topological insulator saturable absorber,” Opt. Lett. 38(24), 5212–5215 (2013). [CrossRef] [PubMed]
9. F. Amrani, A. Haboucha, M. Salhi, H. Leblond, A. Komarov, P. Grelu, and F. Sanchez, “Passively mode-locked erbium-doped double-clad fiber laser operating at the 322nd harmonic,” Opt. Lett. 34(14), 2120–2122 (2009). [CrossRef] [PubMed]
10. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2(1-2), 58–73 (2008). [CrossRef]
11. X. Zhu, C. Wang, S. Liu, and G. Zhang, “Tunable high-order harmonic mode-locking in Yb-doped fiber laser with all-normal dispersion,” IEEE Photon. Technol. Lett. 24(9), 754–756 (2012). [CrossRef]
12. J. Peng, L. Zhan, S. Luo, and Q. Shen, “Passive harmonic mode-locking of dissipative solitons in a normal-dispersion Er-doped fiber laser,” J. Lightwave Technol. 31(16), 3009–3014 (2013). [CrossRef]
13. S. Huang, Y. Wang, P. Yan, G. Zhang, J. Zhao, H. Li, and R. Lin, “High order harmonic mode-locking in an all-normal-dispersion Yb-doped fiber laser with a graphene oxide saturable absorber,” Laser Phys. 24(1), 015001 (2014). [CrossRef]
14. J. Wang, X. Bu, R. Wang, L. Zhang, J. Zhu, H. Teng, H. Han, and Z. Wei, “All-normal-dispersion passive harmonic mode-locking 220 fs ytterbium fiber laser,” Appl. Opt. 53(23), 5088–5091 (2014). [CrossRef] [PubMed]
15. W. Sheng-Min, J. Siao-Shan, H. Wei-Wei, and L. Yinchieh, “Asynchronous harmonic mode locking in an all-normal dispersion Yb-doped fiber laser,” IEEE Photon. J. 5(1), 1500207 (2013). [CrossRef]
16. X. Wu, D. Tang, L. Zhao, H. Zhang, and R. J. Knize, “Evidence of high-order vector dissipative soliton in a fiber laser,” in Frontiers in Optics 2010/Laser Science XXVI(Optical Society of America, Rochester, New York, 2010), p. FTuJ2.
17. L. Dongfeng, Z. Xiaojun, W. Chinhua, Y. Jianjun, Z. Guiju, F. Erxi, and W. Jiajun, “Passive harmonically mode-locked Yb3+-doped fiber laser free from anomalous dispersion,” IEEE Photon. Technol. Lett. 22(23), 1726–1728 (2010). [CrossRef]
19. W. Li, Z. Yin, J. Qiu, J. Wu, and J. Lin, “Tunable active harmonic mode-locking Yb-doped fiber laser with all-normal dispersion,” IEEE Photon. Technol. Lett. 25(23), 2247–2250 (2013). [CrossRef]
20. H. Chen, S.-P. Chen, Z.-F. Jiang, K. Yin, and J. Hou, “All fiber actively mode-locked ytterbium-doped laser with large range temporal tunability,” IEEE Photon. Technol. Lett. 26(17), 1786–1789 (2014). [CrossRef]
21. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012). [CrossRef]
22. W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008). [CrossRef]
25. A. Haboucha, A. Komarov, H. Leblond, F. Sanchez, and G. Martel, “Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers,” Opt. Fiber Technol. 14(4), 262–267 (2008). [CrossRef]
26. D. Anderson, M. Desaix, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave breaking in nonlinear-optical fibers,” J. Opt. Soc. Am. B 9(8), 1358–1361 (1992). [CrossRef]
27. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005). [CrossRef]
28. X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]
29. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007). [CrossRef]
30. L. Wang, X. Liu, Y. Gong, D. Mao, and X. Li, “Transitional and steady mode-locking evolution of dissipative solitons,” Appl. Opt. 49(14), 2665–2669 (2010). [CrossRef]
33. Z. Zuxing and D. Guoxing, “All-normal-dispersion dissipative soliton ytterbium fiber laser without dispersion compensation and additional filter,” IEEE Photon. J. 3(6), 1023–1029 (2011). [CrossRef]
34. C. Aguergaray, A. Runge, M. Erkintalo, and N. G. Broderick, “Raman-driven destabilization of mode-locked long cavity fiber lasers: fundamental limitations to energy scalability,” Opt. Lett. 38(15), 2644–2646 (2013). [CrossRef] [PubMed]