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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 10199–10204
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Vector dissipative soliton resonance in a fiber laser

Zhi-Chao Luo, Qiu-Yi Ning, Hai-Lan Mo, Hu Cui, Jin Liu, Li-Jun Wu, Ai-Ping Luo, and Wen-Cheng Xu  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 10199-10204 (2013)
http://dx.doi.org/10.1364/OE.21.010199


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Abstract

We report on the vector nature of rectangular pulse operating in dissipative soliton resonance (DSR) region in a passively mode-locked fiber laser. Apart from the typical signatures of DSR, the rectangular pulse trapping of two polarization components centered at different wavelengths was observed and they propagated as a group-velocity locked vector soliton. Moreover, the polarization resolved soliton spectra show different spectral distributions. The observed results will enhance the understanding of fundamental physics of DSR phenomenon.

© 2013 OSA

1. Introduction

Temporal solitons in optical fibers, which were first observed by Mollenauer et al. in 1980 [1

1. L. F. Mollenauer, R. H. Stolen, and J. G. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980). [CrossRef]

], have been the fascinating subject of considerable theoretical and experimental studies over the past decades. The passively mode-locked fiber lasers are deemed as the powerful tools to generate optical solitons, as well as the excellent platforms for investigating nonlinear dynamics of optical solitons. So far, depending on the cavity design and parameter selections, different soliton formation and dynamics have been observed in fiber lasers, such as dissipative soliton [2

2. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001). [CrossRef] [PubMed]

,3

3. K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, “Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser,” Opt. Lett. 34(5), 593–595 (2009). [CrossRef] [PubMed]

], bound soliton [4

4. D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, and H. Y. Tam, “Bound-soliton fiber laser,” Phys. Rev. A 66(3), 033806 (2002). [CrossRef]

], similariton pulse evolution [5

5. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004). [CrossRef] [PubMed]

,6

6. B. Oktem, C. Ülgüdür, and F. Ö. Ilday, “Soliton–similariton fiber laser,” Nat. Photonics 4(5), 307–311 (2010). [CrossRef]

] and so on. The investigations of soliton generation and propagation in fiber lasers were always motivated by skillfully selecting the cavity parameters.

Recently, a new soliton formation mechanism, namely dissipative soliton resonance (DSR), was theoretically proposed through selecting certain parameters in the frame of complex Ginzburg-Landau equation [7

7. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372(17), 3124–3128 (2008). [CrossRef]

12

12. Ph. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012). [CrossRef]

]. The pulse in DSR region features the wave-breaking-free phenomenon and the flat-top pulse profile. The pulse width broadens with the increasing pump power while maintaining its amplitude constant, indicating that the pulse energy operating in DSR region can be greatly enlarged despite of the overdriven intracavity nonlinear effect. However, the above-mentioned DSR pulses are only addressed with a scalar theory.

In fact, since single mode fiber (SMF) actually supports two orthogonal polarization modes, the vector nature is also interesting to be considered when the soliton pulse propagates in fiber lasers [13

13. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12(8), 614–616 (1987). [CrossRef] [PubMed]

,14

14. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5(2), 392–402 (1988). [CrossRef]

], as we called vector soliton. By designing a polarization-insensitive laser cavity and detecting two orthogonal polarization components of the pulse, different pulse dynamics have been observed in vector soliton fiber lasers, i.e., polarization-locked vector soliton (PLVS) [15

15. S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999). [CrossRef]

17

17. C. Mou, S. Sergeyev, A. Rozhin, and S. Turistyn, “All-fiber polarization locked vector soliton laser using carbon nanotubes,” Opt. Lett. 36(19), 3831–3833 (2011). [CrossRef] [PubMed]

], polarization-rotation vector soliton (PRVS) [18

18. L. M. Zhao, D. Y. Tang, X. Wu, H. Zhang, and H. Y. Tam, “Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM,” Opt. Lett. 34(20), 3059–3061 (2009). [CrossRef] [PubMed]

,19

19. H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express 17(2), 455–460 (2009). [CrossRef] [PubMed]

], soliton trapping [20

20. D. Mao, X. M. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett. 37(13), 2619–2621 (2012). [CrossRef] [PubMed]

], and coherent energy exchange [21

21. H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express 16(17), 12618–12623 (2008). [CrossRef] [PubMed]

]. On the other hand, regarding to the experimental demonstrations of DSR phenomenon, so far most of them were observed in nonlinear polarization rotation (NPR) based fiber lasers [22

22. X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009). [CrossRef] [PubMed]

25

25. Z. C. Luo, W. J. Cao, Z. B. Lin, Z. R. Cai, A. P. Luo, and W. C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012). [CrossRef] [PubMed]

]. However, since a polarizer is required in the fiber ring laser based on NPR technique, it is not suitable for the generation of vector solitons. According to the theoretical prediction, the DSR phenomenon in mode-locked fiber lasers is independent of the mode locking technique. Therefore, a question naturally arises as to whether the DSR phenomenon could be obtained in fiber lasers based on other mode-locking techniques. And more importantly, taking the significance of DSR phenomenon in the field of laser physics into account, it would be worthy of investigating the vector nature of mode-locked pulse operating in DSR region in a polarization-insensitive laser cavity.

2. Experimental setup

Figure 1
Fig. 1 Schematic of the polarization-insensitive figure-eight fiber laser.
shows the schematic of the figure-eight fiber laser for investigating the vector nature of mode-locked pulse in DSR region. It is based on a nonlinear amplifying loop mirror (NALM) that is coupled to a unidirectional ring cavity through a 50/50 fiber coupler. A piece of 1.8 m long erbium-doped fiber (EDF) with group velocity dispersion (GVD) parameter of −15 ps/nm/km is used as the gain medium, which is pumped by a 980 nm laser diode. The other fibers are all standard SMFs with length of 57.5 m. Thus, the total cavity length is 59.3 m, corresponding to 3.44 MHz fundamental repetition rate. Two polarization controllers (PCs) are introduced to adjust the cavity birefringence. A polarization-independent isolator (ISO) ensures the unidirectional operation. A 10% fiber coupler is used to output laser. For the purpose of resolving the two orthogonal polarization components, a polarization beam splitter (PBS) is connected to the output coupler. An optical spectrum analyzer (OSA, Anritsu MS9710C) and an oscilloscope (LeCroy WaveRunner 104MXi, 1GHz) with a photodetector (Tektronix P6703B, 1.2GHz) were used to record the output laser, respectively.

3. Experimental results and discussions

The NALM acts as the saturable absorber in our fiber laser. The mode-locking threshold is about 150 mW. By simply rotating the PCs, the conventional soliton operation could be achieved [27

27. Q. Y. Ning, S. K. Wang, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Bright–dark pulse pair in a figure-eight dispersion-managed passively mode-locked fiber laser,” IEEE Photon. J. 4(5), 1647–1652 (2012). [CrossRef]

]. However, in this case the multi-pulse would be observed if the pump power was high enough. With further proper adjustment of the PCs, the pulse became breaking-free and the pulse width broadened with the increasing pump power, which is the typical signature of DSR phenomenon. Figure 2(a)
Fig. 2 (a) Typical spectrum of DSR pulse; (b) pulse trains under the pump power of 190 mW and 250 mW.
shows the pulse spectrum operating in DSR region at the pump power of 250 mW. As can be seen here, the soliton sidebands are observed due to the net anomalous dispersion of the laser cavity [28

28. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–807 (1992). [CrossRef]

]. Figure 2(b) presents the mode-locking pulse-trains recorded by the oscilloscope at the pump power of 190 mW (red curve) and 250 mW (blue dotted curve). Here, the pulse profiles are rectangular. Moreover, the pulse width increased from 41.7 ns to 58.1 ns when the pump power was adjusted from 190 mW to 250 mW. These observations demonstrate that the pulse obtained in our fiber laser operates in DSR region.

As mentioned above, the laser cavity is polarization-insensitive. Thus, vector soliton generation is an intrinsic feature in our figure-eight fiber laser. To investigate the vector nature of the DSR pulse, a PBS was employed to analyze the characteristics of two polarization components in both spectral domain and time domain. Firstly we selected a proper pump power of 100 mW. Figure 4(a)
Fig. 4 Vector nature of DSR pulse at the pump power of 100 mW. (a) Polarization-resolved spectra; (b) Autocorrelation traces.
illustrates the spectrum of vector soliton as well as the corresponding two orthogonal polarization components under the 100 mW pump power. It can be seen that the two orthogonal polarization components located at different wavelengths with a separation of 0.26 nm, whose intensity difference is ~6.1 dB. Consequently, although the fiber birefringence exists in the laser cavity, the two polarization components could compensate the fiber birefringence-induced polarization dispersion by shifting the center frequencies. Then they could trap each other as a group-velocity locked vector soliton. Based on the experimental observation, it is worthy of noting that the rectangular pulse trapping in DSR region is similar to that of conventional vector soliton [20

20. D. Mao, X. M. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett. 37(13), 2619–2621 (2012). [CrossRef] [PubMed]

], demonstrating that the pulse trapping is a universal phenomenon of vector soliton despite of the soliton formation mechanism. In addition, the wavelength locations of soliton sidebands shown in the spectra of two polarization components are also different due to the center wavelength shift. Meanwhile, the vector nature of DSR in time domain was also investigated corresponding to the case of Fig. 4(a). By employing a commercial autocorrelator, it was found that the pulse profiles of two polarization components were both rectangular shapes, as shown in Fig. 4(b). The horizontal and vertical pulse widths are both about 9.3 ps.

Note that only the pulse trapping and group-velocity locked vector soliton operating in DSR region was observed in this experiment. However, by further adjusting the cavity parameters, it is expected that other vector soliton dynamics of DSR such as PLVS, PRVS and coherent energy exchange may be obtained. These observations would be beneficial for complementing the understanding of soliton characteristics in DSR region. Furthermore, the vector nature of DSR phenomenon could be also investigated in passively mode-locked fiber lasers based on other polarization-insensitive saturable absorbers, such as graphene, carbon nanotube and semiconductor saturable absorber mirror (SESAM).

4. Conclusion

In summary, we have investigated the vector characteristics of the pulse operating in DSR region in a polarization-insensitive figure-eight fiber laser. With proper adjustment of the PCs, the DSR phenomenon could be observed in our fiber laser. The mode-locked pulse presents typical signatures of DSR. The frequency shift of two orthogonal polarized components of DSR pulse was observed to achieve the pulse trapping and propagating as a group-velocity locked vector soliton. It was also found that the spectral distributions of two polarization components were different from each other. The observed results demonstrate that the vector nature of DSR pulse also shows similar characteristics to the conventional vector soliton, which would increase the understanding of fundamental physics of DSR phenomenon.

Acknowledgments

Z.C.L. and Q.Y.N. contribute equally to this work. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11074078), and the Key Program for Scientific and Technological Innovations of Higher Education Institutes in Guangdong Province (Grant No. cxzd1011), the Project of High-Level Professionals in the Universities of Guangdong Province and the Key Program of Scientific Research of South China Normal University, China (Grant No. 12GDKC04).

References and links

1.

L. F. Mollenauer, R. H. Stolen, and J. G. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980). [CrossRef]

2.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001). [CrossRef] [PubMed]

3.

K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, “Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser,” Opt. Lett. 34(5), 593–595 (2009). [CrossRef] [PubMed]

4.

D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, and H. Y. Tam, “Bound-soliton fiber laser,” Phys. Rev. A 66(3), 033806 (2002). [CrossRef]

5.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004). [CrossRef] [PubMed]

6.

B. Oktem, C. Ülgüdür, and F. Ö. Ilday, “Soliton–similariton fiber laser,” Nat. Photonics 4(5), 307–311 (2010). [CrossRef]

7.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372(17), 3124–3128 (2008). [CrossRef]

8.

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008). [CrossRef]

9.

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009). [CrossRef]

10.

Ph. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010). [CrossRef]

11.

E. Ding, Ph. Grelu, and J. N. Kutz, “Dissipative soliton resonance in a passively mode-locked fiber laser,” Opt. Lett. 36(7), 1146–1148 (2011). [CrossRef] [PubMed]

12.

Ph. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012). [CrossRef]

13.

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12(8), 614–616 (1987). [CrossRef] [PubMed]

14.

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5(2), 392–402 (1988). [CrossRef]

15.

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999). [CrossRef]

16.

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). [CrossRef] [PubMed]

17.

C. Mou, S. Sergeyev, A. Rozhin, and S. Turistyn, “All-fiber polarization locked vector soliton laser using carbon nanotubes,” Opt. Lett. 36(19), 3831–3833 (2011). [CrossRef] [PubMed]

18.

L. M. Zhao, D. Y. Tang, X. Wu, H. Zhang, and H. Y. Tam, “Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM,” Opt. Lett. 34(20), 3059–3061 (2009). [CrossRef] [PubMed]

19.

H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express 17(2), 455–460 (2009). [CrossRef] [PubMed]

20.

D. Mao, X. M. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett. 37(13), 2619–2621 (2012). [CrossRef] [PubMed]

21.

H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express 16(17), 12618–12623 (2008). [CrossRef] [PubMed]

22.

X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009). [CrossRef] [PubMed]

23.

X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010). [CrossRef]

24.

L. Duan, X. M. Liu, D. Mao, L. Wang, and G. Wang, “Experimental observation of dissipative soliton resonance in an anomalous-dispersion fiber laser,” Opt. Express 20(1), 265–270 (2012). [CrossRef] [PubMed]

25.

Z. C. Luo, W. J. Cao, Z. B. Lin, Z. R. Cai, A. P. Luo, and W. C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012). [CrossRef] [PubMed]

26.

S. K. Wang, Q. Y. Ning, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Dissipative soliton resonance in a passively mode-locked figure-eight fiber laser,” Opt. Express 21(2), 2402–2407 (2013). [CrossRef] [PubMed]

27.

Q. Y. Ning, S. K. Wang, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Bright–dark pulse pair in a figure-eight dispersion-managed passively mode-locked fiber laser,” IEEE Photon. J. 4(5), 1647–1652 (2012). [CrossRef]

28.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–807 (1992). [CrossRef]

29.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71(5), 053809 (2005). [CrossRef]

OCIS Codes
(140.3500) Lasers and laser optics : Lasers, erbium
(140.3510) Lasers and laser optics : Lasers, fiber
(140.4050) Lasers and laser optics : Mode-locked lasers
(250.5530) Optoelectronics : Pulse propagation and temporal solitons

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 18, 2013
Manuscript Accepted: March 28, 2013
Published: April 16, 2013

Citation
Zhi-Chao Luo, Qiu-Yi Ning, Hai-Lan Mo, Hu Cui, Jin Liu, Li-Jun Wu, Ai-Ping Luo, and Wen-Cheng Xu, "Vector dissipative soliton resonance in a fiber laser," Opt. Express 21, 10199-10204 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-10199


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References

  1. L. F. Mollenauer, R. H. Stolen, and J. G. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett.45(13), 1095–1098 (1980). [CrossRef]
  2. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(5), 056602 (2001). [CrossRef] [PubMed]
  3. K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, “Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser,” Opt. Lett.34(5), 593–595 (2009). [CrossRef] [PubMed]
  4. D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, and H. Y. Tam, “Bound-soliton fiber laser,” Phys. Rev. A66(3), 033806 (2002). [CrossRef]
  5. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett.92(21), 213902 (2004). [CrossRef] [PubMed]
  6. B. Oktem, C. Ülgüdür, and F. Ö. Ilday, “Soliton–similariton fiber laser,” Nat. Photonics4(5), 307–311 (2010). [CrossRef]
  7. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A372(17), 3124–3128 (2008). [CrossRef]
  8. W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A78(2), 023830 (2008). [CrossRef]
  9. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A79(3), 033840 (2009). [CrossRef]
  10. Ph. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B27(11), 2336–2341 (2010). [CrossRef]
  11. E. Ding, Ph. Grelu, and J. N. Kutz, “Dissipative soliton resonance in a passively mode-locked fiber laser,” Opt. Lett.36(7), 1146–1148 (2011). [CrossRef] [PubMed]
  12. Ph. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics6(2), 84–92 (2012). [CrossRef]
  13. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett.12(8), 614–616 (1987). [CrossRef] [PubMed]
  14. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B5(2), 392–402 (1988). [CrossRef]
  15. S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett.82(20), 3988–3991 (1999). [CrossRef]
  16. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008). [CrossRef] [PubMed]
  17. C. Mou, S. Sergeyev, A. Rozhin, and S. Turistyn, “All-fiber polarization locked vector soliton laser using carbon nanotubes,” Opt. Lett.36(19), 3831–3833 (2011). [CrossRef] [PubMed]
  18. L. M. Zhao, D. Y. Tang, X. Wu, H. Zhang, and H. Y. Tam, “Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM,” Opt. Lett.34(20), 3059–3061 (2009). [CrossRef] [PubMed]
  19. H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express17(2), 455–460 (2009). [CrossRef] [PubMed]
  20. D. Mao, X. M. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett.37(13), 2619–2621 (2012). [CrossRef] [PubMed]
  21. H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express16(17), 12618–12623 (2008). [CrossRef] [PubMed]
  22. X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express17(7), 5580–5584 (2009). [CrossRef] [PubMed]
  23. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A81(5), 053819 (2010). [CrossRef]
  24. L. Duan, X. M. Liu, D. Mao, L. Wang, and G. Wang, “Experimental observation of dissipative soliton resonance in an anomalous-dispersion fiber laser,” Opt. Express20(1), 265–270 (2012). [CrossRef] [PubMed]
  25. Z. C. Luo, W. J. Cao, Z. B. Lin, Z. R. Cai, A. P. Luo, and W. C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett.37(22), 4777–4779 (2012). [CrossRef] [PubMed]
  26. S. K. Wang, Q. Y. Ning, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Dissipative soliton resonance in a passively mode-locked figure-eight fiber laser,” Opt. Express21(2), 2402–2407 (2013). [CrossRef] [PubMed]
  27. Q. Y. Ning, S. K. Wang, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Bright–dark pulse pair in a figure-eight dispersion-managed passively mode-locked fiber laser,” IEEE Photon. J.4(5), 1647–1652 (2012). [CrossRef]
  28. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett.28(8), 806–807 (1992). [CrossRef]
  29. A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A71(5), 053809 (2005). [CrossRef]

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Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

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