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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 18969–18974
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Graphene and nanotube mode-locked fiber laser emitting dissipative and conventional solitons

Yudong Cui and Xueming Liu  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 18969-18974 (2013)
http://dx.doi.org/10.1364/OE.21.018969


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Abstract

We propose a bidirectional erbium-doped fiber laser mode-locked with a mixture of graphene and single-walled carbon nanotubes for the first time to our best knowledge. The fiber laser can deliver dissipative soliton (DS) and conventional soliton (CS), circulating in opposite directions. The net-cavity dispersion is normal in the clockwise direction and anomalous in counter clockwise direction, respectively, and then DS and CS are generated with the suitable adjustment of attenuators. The output DS and CS approximately have the same central wavelength, but exhibit different optical spectra, pulse durations, and repetition rates. The all-fiber switchable laser can provide two different pulse sources, which is convenient for practical applications.

© 2013 OSA

1. Introduction

In this paper, we propose a bidirectional fiber laser mode-locked with a mixture of graphene and SWNTs for the first time. By exploiting two 50/50 couplers, two cavities with different length and dispersion are formed in a fiber laser. By adjusting attenuators and pump power, the fiber laser can deliver two different types of pulses in opposite directions. In the clockwise (CW) direction, the net cavity dispersion is ~0.075 ps2 and DS with quasi-rectangular spectrum is achieved. The output DS is highly chirped with the pulse duration of 9.15 ps and the spectral bandwidth of 7.8 nm. In the counter clockwise (CCW) direction, the net cavity dispersion is about −1.02 ps2 and CS with spectral sidebands is obtained. The pulse duration and spectral bandwidth of the CS are 1.64 ps and 2.2 nm, respectively. It is demonstrated that the fiber laser can realize switchable DS and CS mode-locking, which is very convenient for practical applications.

2. Experimental setup

A homogeneous graphene oxide (GO) colloid is yielded through dispersing graphite oxide powder in deionized water, which is synthesized through the Hummers method [26

26. W. Hummers and R. Offeman, “Preparation of graphitic oxide,” J. Am. Chem. Soc. 80(6), 1339 (1958). [CrossRef]

]. Adequate ammonia and hydrazine hydrate are used as efficient reductants. Graphene nanosheets are produced by chemically reducing GO [27

27. S. Stankovich, R. D. Piner, X. Chen, N. Wu, S. T. Nguyen, and R. S. Ruoff, “Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly (sodium4-styrenesulfonate),” J. Mater. Chem. 16(2), 155–158 (2006). [CrossRef]

]. SWNTs with the outside diameter <2 nm are made by the catalytic chemical vapor decomposition method. The mixture is fabricated by the self-assembly of reduced GO nanosheets and SWNTs with a mixing ratio of 1:1 [12

12. D. Yu and L. Dai, “Self-assembled graphene/carbon nanotube hybrid films for supercapacitors,” J. Phys. Chem. Lett. 1(2), 467–470 (2010). [CrossRef]

]. Polyvinyl alcohol (PVA) is chosen as the host polymer for its mechanical property and solvent compatibility. To obtain the composite films, mixture-PVA dispersion is drop-cast on a Petri disk. Figure 1
Fig. 1 Absorption spectra for the graphene (red), SWNTs (blue), and mixture of graphene and SWNTs (black) composite films.
shows the absorption spectra of the graphene, SWNTs, and mixture composite films from 900 nm to 2400 nm, which are measured with a spectrophotometer. The absorption spectrum of SWNTs exhibits absorption peaks at ~1 μm and ~2 μm. Graphene composite film has no strong absorption at specific wavelengths. The wavelength-dependent absorption should be attributed to the incomplete reduction of GO [10

10. G. Sobon, J. Sotor, J. Jagiello, R. Kozinski, M. Zdrojek, M. Holdynski, P. Paletko, J. Boguslawski, L. Lipinska, and K. M. Abramski, “Graphene Oxide vs. Reduced Graphene Oxide as saturable absorbers for Er-doped passively mode-locked fiber laser,” Opt. Express 20(17), 19463–19473 (2012). [CrossRef] [PubMed]

] [28

28. C. Chen, Q. Yang, Y. Yang, W. Lv, Y. Wen, P. Hou, M. Wang, and H. Cheng, “Self-assembled free-standing graphite oxide membrane,” Adv. Mater. 21(29), 3007–3011 (2009). [CrossRef]

], which is similar to the results in [8

8. H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009). [CrossRef]

]. The existence of graphene in mixture weakens the absorption selectivity, as demonstrated by the absorption spectrum of the mixture.

The schematic diagram of the experimental setup is shown in Fig. 2
Fig. 2 Schematic diagram of the experimental setup. The red arrows show the propagation directions
. A section of 18 m erbium-doped fiber (EDF) with the dispersion parameter of −16 ps/nm/km is utilized as the gain medium, and two 980 nm laser diodes (LDs) provide bidirectional pumps via 980/1550 nm wavelength-division-multiplexed (WDM) couplers. Two laser cavities with different length and propagation direction are formed in the fiber laser with two 50/50 optical couplers (OCs), two polarization controllers (PCs), two polarization-independent isolators (PI-ISOs), and two attenuators. The PI-ISOs ensure the unidirectional operation in each branch. PCs are used to tune the linear birefringence of the cavity, and attenuators are employed to control the loss. A 50 m single-mode fiber (SMF) with the dispersion parameter of 17 ps/nm/km is added in the CCW branch. A fused 2 × 2 OC with 10% output ports is used to extract pulses from the cavity. PI-ISOs external to the cavity can prohibit the reflected lightwave from disturbing the signals in fiber laser. The saturable absorber (SA) based on the mixture of graphene and SWNTs is sandwiched by fiber connectors in the ring cavity.

3. Experimental results and discussion

The counter propagating lightwaves share the common EDF, pump sources, and SA, while have different pathways between two 50/50 OCs. By adjusting attenuators, the intensity of lightwave in each direction can be precisely controlled. Lightwave in one direction can obtain sufficient gain to form mode-locking operation, but it is suppressed in the other direction. Then the mode-locking operation can become more stable without the disturbance. Adjusting attenuator-2 to increase the loss of CCW branch and relaxing attenuator-1, lightwave tends to propagate from EDF→OC→SA→OC-1→PC-1→attenuator-1→PI-ISO-1→OC-2. In this direction, the net cavity dispersion is ~0.075 ps2 and the cavity length is ~29.1 m. Increasing the loss of CW branch and relaxing attenuator-2, lightwave tends to propagate from EDF→OC-2→PC-2→PI-ISO-2→SMF→attenuator-2→OC-1→SA→OC. The net dispersion and length of cavity are about −1.02 ps2 and ~79.9 m, respectively. As the cavity dispersion and length are different for two propagation paths, DS and CS can be generated in CW and CCW directions, respectively.

With the total pump power of ~20 mW, bidirectional continuous-wave operations are established. Mode-locking is not observed in both directions, even when the total pump power is increased up to 100 mW. By tuning attenuator-2 to increase the loss, self-started mode-locking in the CW direction can be achieved when the two pump powers are ~19 mW. However, multiple pulses are formed in this case, even including the harmonic multi-pulse operation [29

29. X. M. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18(11), 1357–1361 (2008). [CrossRef]

]. By reducing two pump powers to 13 mW, single-pulse mode-locking operation in the CW direction is obtained. As shown in Fig. 3(a)
Fig. 3 Experimental results of DS in CW direction. (a) optical spectrum, (b) autocorrelation trace, (c) oscilloscope trace, and (d) radio-frequency spectrum.
, the output spectrum has a quasi-rectangular profile with a bandwidth of 7.8 nm, which is the typical characteristic of DS in the normal dispersion regime. The central wavelength of the spectrum is ~1560 nm. The corresponding autocorrelation trace of the DS is illustrated in Fig. 3(b). The full width at half maximum (FWHM) is 12.9 ps, and the pulse duration is given as 9.15 ps if a Gaussian fit is used. The time-bandwidth product (TBP) is calculated as 8.8, which indicates that the pulse is highly chirped. The pulse duration can be compressed to several hundred fs, similar to the report in [30

30. X. M. Liu and D. Mao, “Compact all-fiber high-energy fiber laser with sub-300-fs duration,” Opt. Express 18(9), 8847–8852 (2010). [CrossRef] [PubMed]

]. The pulse train depicted in Fig. 3(c) shows that the separation between adjacent pulses is ~142 ns, which is equal to the cavity round-trip time in CW direction. The radio-frequency (RF) spectrum is shown in Fig. 4(d)
Fig. 4 Experimental results of CS in CCW direction. (a) optical spectrum, (b) autocorrelation trace, (c) oscilloscope trace, and (d) RF spectrum.
. One can observe that the fundamental repetition rate of DS is ~7.05 MHz. The peak-to-background ratio of the RF spectrum is ~60 dB, implying a good mode-locking stability. Based on the experiment results, we conclude that the fiber laser operates at a stable DS mode-locking state.

The propagation of pulses in CCW direction can be achieved by tuning attenuator-1 to increase the loss. Appropriately adjusting PC-2 and pump powers, stable single-pulse mode-locking operation is obtained. Figure 4(a) shows the output spectrum of CS, which has a bandwidth of 2.2 nm. The soliton features of the pulses are reflected by the appearance of spectral sidebands on the spectrum. It stems from the constructive interference between the soliton and dispersive waves [2

2. X. Liu, “Soliton formation and evolution in passively-mode-locked lasers with ultralong anomalous-dispersion fibers,” Phys. Rev. A 84(2), 023835 (2011). [CrossRef]

,15

15. X. M. Liu, “Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion,” Opt. Express 19(7), 5874–5887 (2011). [CrossRef] [PubMed]

,16

16. D. Han and X. Liu, “Sideband-controllable mode-locking fiber laser based on chirped fiber Bragg gratings,” Opt. Express 20(24), 27045–27050 (2012). [CrossRef] [PubMed]

]. The corresponding autocorrelation trace is demonstrated in Fig. 4(b). The FWHM is 2.52 ps, and the pulse duration is estimated as 1.64 ps with a sech2 fit. Consequently, the TBP of CS is calculated as 0.44, indicating that the output CS is slightly chirped. It is worth noting that the fundamental repetition rates of CS and DS are different for their distinct cavity lengths. As depicted in Fig. 4(d), the fundamental repetition rate of pulses in CCW direction is given as 2.57 MHz. The oscilloscope trace in Fig. 4(c) shows that the separation between adjacent pulses is ~389 ns.

The proposed fiber laser can generate DS and CS in CW and CCW directions by adjusting the intracavity attenuators, respectively. As the net cavity dispersion in both directions differ from each other, the pulses in CW and CCW directions have distinct formation mechanisms. During the amplification in EDF, the pulse duration and spectral bandwidth are broadened due to the effects of normal dispersion, self-phase modulation, and other nonlinearities [18

18. X. M. Liu, “Numerical and experimental investigation of dissipative solitons in passively mode-locked fiber lasers with large net-normal-dispersion and high nonlinearity,” Opt. Express 17(25), 22401–22416 (2009). [CrossRef] [PubMed]

,23

23. D. Mao, X. Liu, L. Wang, H. Lu, and L. Duan, “Coexistence of unequal pulses in a normal dispersion fiber laser,” Opt. Express 19(17), 16303–16308 (2011). [CrossRef] [PubMed]

]. In the normal dispersion regime, the spectral filtering effect could cut off the temporal and spectral wings of the highly chirped DS, which results in the steep spectral edges [20

20. X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010). [CrossRef]

22

22. 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]

]. However, the spectral filtering effect almost has no contribution to the formation of pulses in the anomalous regime, because the spectral width of CS is much narrower than that of the gain spectrum [2

2. X. Liu, “Soliton formation and evolution in passively-mode-locked lasers with ultralong anomalous-dispersion fibers,” Phys. Rev. A 84(2), 023835 (2011). [CrossRef]

]. The evolution of CS is mainly determined by the interaction between anomalous dispersion and nonlinearity, which has been demonstrated by the nonlinear Schrödinger equation [2

2. X. Liu, “Soliton formation and evolution in passively-mode-locked lasers with ultralong anomalous-dispersion fibers,” Phys. Rev. A 84(2), 023835 (2011). [CrossRef]

,15

15. X. M. Liu, “Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion,” Opt. Express 19(7), 5874–5887 (2011). [CrossRef] [PubMed]

]. Consequently, the output DS and CS exhibit different characteristics such as spectral profile, pulse duration, and chirp.

The experimental results show that the proposed laser does not deliver the DS and CS if a graphene-based SA is used. The reasons are as the following. Without SWNTs, graphene is prone to agglomerate in the fabrication procedure, which results in high nonsaturable absorption loss and low modulation depth. The absorption loss of graphene is ~65%, which is much larger than that of mixture (~50%), as shown in Fig. 1. After passing through two 50/50 OCs (Fig. 2), >75% of pulse energy is lost. In addition, ~10% of energy is outputted by the 10/90 OC. As a result, the intracavity loss of laser is more than 93% if a grapheme film is used as SA, but it is about 88% if the mixture is used. The total cavity loss of the grapheme-based laser is so large that it is difficult to achieve self-consistent mode-locking operation.

In experiments, simultaneous mode-locking operations in both directions are not realized. This can be partially attributed to the cavity asymmetry in CW and CCW directions. For instance, the cavity length, dispersion, and propagation path are unequal for the CS and DS [26

26. W. Hummers and R. Offeman, “Preparation of graphitic oxide,” J. Am. Chem. Soc. 80(6), 1339 (1958). [CrossRef]

]. In addition, it is difficult to provide simultaneous amplification for two counter propagating pulses due to the gain competition effect. However, the unidirectional mode-locking operation in CW or CCW direction can be easily achieved alternatively. Compared to traditional unidirectional ring fiber lasers, the proposed fiber laser is capable of emitting two distinct kinds of solitons in a fiber laser. And the two counter propagating pulses can be switched by adjusting attenuators. Our scheme has significantly reduced the cost, and it is more convenient than employing two independent fiber lasers. Additionally, by inserting spectral filter in each branch, wavelength-tunable DS and CS can be obtained in the laser.

4. Conclusions

We have proposed a bidirectional passively-mode-locked fiber laser based on the mixture of graphene and SWNTs. Two different types of pulses are generated in opposite directions by adjusting the intracavity loss. In the CW direction, the net cavity dispersion is normal and then DS with the quasi-rectangular spectrum is achieved. In the CCW direction, the net cavity dispersion is anomalous and CS with spectral sidebands is obtained. The DS and CS approximately have the same central wavelength, while they exhibit distinct optical spectra, pulse durations, and repetition rates owing to the distinct formation mechanisms. We believe this all-fiber switchable fiber laser can find more applications in the future.

Acknowledgments

The authors would like to thank Leiran Wang, Guoxi Wang, Dongdong Han, Ling Yun, Chao Zeng, Dewei Wang, Pengfei Zhao, Lu Li, and Tengfei Shi for help. This work was supported by the National Natural Science Foundation of China under Grants 10874239, 10604066, and 11204368.

References and links

1.

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum Electron. 15(1), 191–206 (2009). [CrossRef]

2.

X. Liu, “Soliton formation and evolution in passively-mode-locked lasers with ultralong anomalous-dispersion fibers,” Phys. Rev. A 84(2), 023835 (2011). [CrossRef]

3.

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

4.

L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express 20(19), 20992–20997 (2012). [CrossRef] [PubMed]

5.

X. Liu, “Dissipative soliton evolution in ultra-large normal-cavity-dispersion fiber lasers,” Opt. Express 17(12), 9549–9557 (2009). [CrossRef] [PubMed]

6.

Z. Luo, A. Luo, W. Xu, C. Song, Y. Gao, and W. Chen, “Sideband controllable soliton all-fiber ring laser passively mode-locked by nonlinear polarization rotation,” Laser Phys. Lett. 6(8), 582–585 (2009). [CrossRef]

7.

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22(1), 51–56 (2004). [CrossRef]

8.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009). [CrossRef]

9.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010). [CrossRef] [PubMed]

10.

G. Sobon, J. Sotor, J. Jagiello, R. Kozinski, M. Zdrojek, M. Holdynski, P. Paletko, J. Boguslawski, L. Lipinska, and K. M. Abramski, “Graphene Oxide vs. Reduced Graphene Oxide as saturable absorbers for Er-doped passively mode-locked fiber laser,” Opt. Express 20(17), 19463–19473 (2012). [CrossRef] [PubMed]

11.

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003). [CrossRef] [PubMed]

12.

D. Yu and L. Dai, “Self-assembled graphene/carbon nanotube hybrid films for supercapacitors,” J. Phys. Chem. Lett. 1(2), 467–470 (2010). [CrossRef]

13.

Y. Xu, Z. Liu, X. Zhang, Y. Wang, J. Tian, Y. Huang, Y. Ma, X. Zhang, and Y. Chen, “A graphene hybrid material covalently functionalized with porphyrin: synthesis and optical Limiting property,” Adv. Mater. 21(12), 1275–1279 (2009). [CrossRef]

14.

H. Haus and W. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68(2), 423–444 (1996). [CrossRef]

15.

X. M. Liu, “Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion,” Opt. Express 19(7), 5874–5887 (2011). [CrossRef] [PubMed]

16.

D. Han and X. Liu, “Sideband-controllable mode-locking fiber laser based on chirped fiber Bragg gratings,” Opt. Express 20(24), 27045–27050 (2012). [CrossRef] [PubMed]

17.

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

18.

X. M. Liu, “Numerical and experimental investigation of dissipative solitons in passively mode-locked fiber lasers with large net-normal-dispersion and high nonlinearity,” Opt. Express 17(25), 22401–22416 (2009). [CrossRef] [PubMed]

19.

L. R. Wang, X. M. Liu, Y. K. Gong, D. Mao, and H. Feng, “Ultra-broadband high-energy pulse generation and evolution in a compact erbium-doped all-fiber laser,” Laser Phys. Lett. 8(5), 376–381 (2011). [CrossRef]

20.

X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010). [CrossRef]

X. M. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A 82(6), 063834 (2010). [CrossRef]

21.

F. W. Wise, A. Chong, and W. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1–2), 58–73 (2008). [CrossRef]

22.

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]

23.

D. Mao, X. Liu, L. Wang, H. Lu, and L. Duan, “Coexistence of unequal pulses in a normal dispersion fiber laser,” Opt. Express 19(17), 16303–16308 (2011). [CrossRef] [PubMed]

24.

K. Kieu and M. Mansuripur, “All-fiber bidirectional passively mode-locked ring laser,” Opt. Lett. 33(1), 64–66 (2008). [CrossRef] [PubMed]

25.

C. Ouyang, P. Shum, K. Wu, J. H. Wong, H. Q. Lam, and S. Aditya, “Bidirectional passively mode-locked soliton fiber laser with a four-port circulator,” Opt. Lett. 36(11), 2089–2091 (2011). [CrossRef] [PubMed]

26.

W. Hummers and R. Offeman, “Preparation of graphitic oxide,” J. Am. Chem. Soc. 80(6), 1339 (1958). [CrossRef]

27.

S. Stankovich, R. D. Piner, X. Chen, N. Wu, S. T. Nguyen, and R. S. Ruoff, “Stable aqueous dispersions of graphitic nanoplatelets via the reduction of exfoliated graphite oxide in the presence of poly (sodium4-styrenesulfonate),” J. Mater. Chem. 16(2), 155–158 (2006). [CrossRef]

28.

C. Chen, Q. Yang, Y. Yang, W. Lv, Y. Wen, P. Hou, M. Wang, and H. Cheng, “Self-assembled free-standing graphite oxide membrane,” Adv. Mater. 21(29), 3007–3011 (2009). [CrossRef]

29.

X. M. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18(11), 1357–1361 (2008). [CrossRef]

30.

X. M. Liu and D. Mao, “Compact all-fiber high-energy fiber laser with sub-300-fs duration,” Opt. Express 18(9), 8847–8852 (2010). [CrossRef] [PubMed]

OCIS Codes
(060.2410) Fiber optics and optical communications : Fibers, erbium
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.4050) Lasers and laser optics : Mode-locked lasers
(060.3510) Fiber optics and optical communications : Lasers, fiber

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 24, 2013
Revised Manuscript: July 26, 2013
Manuscript Accepted: July 29, 2013
Published: August 1, 2013

Citation
Yudong Cui and Xueming Liu, "Graphene and nanotube mode-locked fiber laser emitting dissipative and conventional solitons," Opt. Express 21, 18969-18974 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-18969


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References

  1. M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum Electron.15(1), 191–206 (2009). [CrossRef]
  2. X. Liu, “Soliton formation and evolution in passively-mode-locked lasers with ultralong anomalous-dispersion fibers,” Phys. Rev. A84(2), 023835 (2011). [CrossRef]
  3. D. Mao, X. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett.37(13), 2619–2621 (2012). [CrossRef] [PubMed]
  4. L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express20(19), 20992–20997 (2012). [CrossRef] [PubMed]
  5. X. Liu, “Dissipative soliton evolution in ultra-large normal-cavity-dispersion fiber lasers,” Opt. Express17(12), 9549–9557 (2009). [CrossRef] [PubMed]
  6. Z. Luo, A. Luo, W. Xu, C. Song, Y. Gao, and W. Chen, “Sideband controllable soliton all-fiber ring laser passively mode-locked by nonlinear polarization rotation,” Laser Phys. Lett.6(8), 582–585 (2009). [CrossRef]
  7. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol.22(1), 51–56 (2004). [CrossRef]
  8. H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett.95(14), 141103 (2009). [CrossRef]
  9. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano4(2), 803–810 (2010). [CrossRef] [PubMed]
  10. G. Sobon, J. Sotor, J. Jagiello, R. Kozinski, M. Zdrojek, M. Holdynski, P. Paletko, J. Boguslawski, L. Lipinska, and K. M. Abramski, “Graphene Oxide vs. Reduced Graphene Oxide as saturable absorbers for Er-doped passively mode-locked fiber laser,” Opt. Express20(17), 19463–19473 (2012). [CrossRef] [PubMed]
  11. U. Keller, “Recent developments in compact ultrafast lasers,” Nature424(6950), 831–838 (2003). [CrossRef] [PubMed]
  12. D. Yu and L. Dai, “Self-assembled graphene/carbon nanotube hybrid films for supercapacitors,” J. Phys. Chem. Lett.1(2), 467–470 (2010). [CrossRef]
  13. Y. Xu, Z. Liu, X. Zhang, Y. Wang, J. Tian, Y. Huang, Y. Ma, X. Zhang, and Y. Chen, “A graphene hybrid material covalently functionalized with porphyrin: synthesis and optical Limiting property,” Adv. Mater.21(12), 1275–1279 (2009). [CrossRef]
  14. H. Haus and W. Wong, “Solitons in optical communications,” Rev. Mod. Phys.68(2), 423–444 (1996). [CrossRef]
  15. X. M. Liu, “Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion,” Opt. Express19(7), 5874–5887 (2011). [CrossRef] [PubMed]
  16. D. Han and X. Liu, “Sideband-controllable mode-locking fiber laser based on chirped fiber Bragg gratings,” Opt. Express20(24), 27045–27050 (2012). [CrossRef] [PubMed]
  17. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics6(2), 84–92 (2012). [CrossRef]
  18. X. M. Liu, “Numerical and experimental investigation of dissipative solitons in passively mode-locked fiber lasers with large net-normal-dispersion and high nonlinearity,” Opt. Express17(25), 22401–22416 (2009). [CrossRef] [PubMed]
  19. L. R. Wang, X. M. Liu, Y. K. Gong, D. Mao, and H. Feng, “Ultra-broadband high-energy pulse generation and evolution in a compact erbium-doped all-fiber laser,” Laser Phys. Lett.8(5), 376–381 (2011). [CrossRef]
  20. X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A81(2), 023811 (2010). [CrossRef]
  21. X. M. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A82(6), 063834 (2010). [CrossRef]
  22. F. W. Wise, A. Chong, and W. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev.2(1–2), 58–73 (2008). [CrossRef]
  23. 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. Express17(10), 8506–8512 (2009). [CrossRef] [PubMed]
  24. D. Mao, X. Liu, L. Wang, H. Lu, and L. Duan, “Coexistence of unequal pulses in a normal dispersion fiber laser,” Opt. Express19(17), 16303–16308 (2011). [CrossRef] [PubMed]
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