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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8409–8416
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Harmonic mode locking counterparts of dark pulse and dark-bright pulse pairs

Xingliang Li, Shumin Zhang, Yichang Meng, and Yanping Hao  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8409-8416 (2013)
http://dx.doi.org/10.1364/OE.21.008409


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Abstract

We have investigated experimentally different operational states of an all-normal-dispersion ytterbium-doped fiber (YDF) ring laser with a long cavity. Various operational states were obtained by adjusting a polarization controller (PC) and the pump power. Self-pulsing, bright pulses, dark-bright pulse pairs and their harmonic mode locking (HML) counterparts, as well as dark pulses and their HML counterparts have all been obtained. Numerical simulations reproduce well the formation processes of dark pulses and dark-bright pulse pairs.

© 2013 OSA

1. Introduction

Sustained self-pulsing (SSP) is one of the instabilities of fiber lasers that has been extensively studied. This unstable regime is particularly annoying in many applications because the SSP may make it extremely difficult to realize stable CW operation of the laser. SSP has been found to result from the interaction of ion pairs [1

1. F. Fontana, M. Begotti, E. M. Pessina, and L. A. Lugiato, “Maxwell-Bloch modelocking instabilities in erbium-doped fiber lasers,” Opt. Commun. 114(1–2), 89–94 (1995). [CrossRef]

6

6. L. Luo and P. L. Chu, “Suppression of self-pulsing in an erbium-doped fiber laser,” Opt. Lett. 22(15), 1174–1176 (1997). [CrossRef] [PubMed]

] or from the interplay between the laser signal and the population inversion, which can act as a weakly saturable absorber [7

7. F. Brunet, Y. Taillon, P. Galarneau, and S. LaRochelle, “A simple model describing both self-mode locking and sustained self-pulsing in ytterbium-doped ring fiber lasers,” J. Lightwave Technol. 23(6), 2131–2138 (2005). [CrossRef]

, 8

8. J. Li, K. Ueda, M. Musha, and A. Shirakawa, “Residual pump light as a probe of self-pulsing instability in an ytterbium-doped fiber laser,” Opt. Lett. 31(10), 1450–1452 (2006). [CrossRef] [PubMed]

].

Almost all of the experiments in the references cited above have been carried out under the bright pulse regime. However, in addition to bright pulses, other types of solitons, e.g. dark solitons, are also solutions of the nonlinear Schrödinger equation (NLSE) [9

9. V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37(5), 823–828 (1973).

]. Dark solitons are also solutions of the complex Ginzburg-Landau equation (CGLE) [10

10. W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992). [CrossRef]

, 11

11. N. Bekki and K. Nozaki, “Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation,” Phys. Lett. A 110(3), 133–135 (1985). [CrossRef]

]. The physical reason is that, in contrast to the NLSE and its Hamiltonian generalizations, solitons of the CGLE arise as a result of a balance between the nonlinearity and dispersion on the one hand, and between the gain and loss on the other hand. Dark solitons were first observed by Emplit et al. in 1987 [12

12. P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987). [CrossRef]

], and since then several experiments have been proposed to generate dark solitons. An antiphase square pulse emission along the two orthogonal polarization eigenstate directions of the cavity has also been reported in [13

13. B. Meziane, F. Sanchez, G. M. Stephan, and P. L. François, “Feedback-induced polarization switching in a Nd-doped fiber laser,” Opt. Lett. 19(23), 1970–1972 (1994). [CrossRef] [PubMed]

]. They interpreted the antiphase square pulse as being caused by the joint action of the gain competition between the two cavity polarization modes and the cavity feedback. Sylvestre et al. experimentally demonstrated the generation of dark pulse trains in a so called self-induced modulation instability laser for which the passive mode-locking mechanism relied on a dissipative four-wave mixing process [14

14. T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002). [CrossRef] [PubMed]

]. Zhang et al. experimentally demonstrated single and multiple dark pulse emission in a fiber laser in 2009 [15

15. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

]. Based on numerical simulations, they interpreted dark pulse formation as resulting from dark soliton shaping in the laser.

The present paper reviews and extends various aspects of the generation of dark solitons in a fiber laser [13

13. B. Meziane, F. Sanchez, G. M. Stephan, and P. L. François, “Feedback-induced polarization switching in a Nd-doped fiber laser,” Opt. Lett. 19(23), 1970–1972 (1994). [CrossRef] [PubMed]

18

18. S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52(4), 881–883 (2010). [CrossRef]

]. In particular, to the best our knowledge, there have been no reports concerning the formation of the HML counterparts to dark pulses in a fiber laser. In this paper, by using the interactions between two dark pulses or between a dark pulse and background noise, the third, fourth, fifth and sixth order HML counterparts of the dark pulse could also be obtained with different polarized states and pump strength.

Dark-bright soliton pairs may also coexist when they propagate together in a nonlinear optical medium as has been theoretically demonstrated using the coupled nonlinear Schrödinger equation [19

19. V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14(15), 805–807 (1989). [CrossRef] [PubMed]

, 20

20. R. Radhakrishnan and K. Aravinthan, “A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(43), 13023–13030 (2007). [CrossRef]

]. Dark-bright soliton pairs have also been observed in Kerr-type nonlinear mediums [21

21. Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Y. S. Kivshar, and V. V. Afanasjev, “Incoherently coupled dark-bright photorefractive solitons,” Opt. Lett. 21(22), 1821–1823 (1996). [CrossRef] [PubMed]

23

23. Z. H. Musslimani and J. Yang, “Transverse instability of strongly coupled dark-bright Manakov vector solitons,” Opt. Lett. 26(24), 1981–1983 (2001). [CrossRef] [PubMed]

], optical fiber systems [24

24. K. W. Chow and K. Nakkeeran, “Bright-dark and double-humped pulses in averaged, dispersion managed optical fiber systems,” in Optical Fibers Research Advances (Nova Science Publisher, 2007), pp. 301–313.

], and fiber lasers [25

25. Y. Meng, S. Zhang, H. Li, J. Du, Y. Hao, and X. Li, “Bright-dark soliton pairs in a self-mode locking fiber laser,” Opt. Eng. 51(6), 064302 (2012). [CrossRef]

, 26

26. H. Y. Wang, W. C. Xu, W. J. Cao, L. Y. Wang, and J. L. Dong, “Experimental observation of bright-dark pulse emitting in an all-fiber ring cavity laser,” Laser Phys. 22(1), 282–285 (2012). [CrossRef]

]. In this paper, we show experimentally that under appropriate operating conditions, not only can single dark-bright pulse pairs be formed in an all-normal-dispersion fiber laser, but the HML counterparts of dark-bright pulse pairs can also be obtained.

The formation processes of dark pulses and dark-bright pulse pairs in our fiber laser systems were also investigated numerically. The results suggest that various pulses can be automatically formed by the interactions between the fiber gain and loss, the cavity dispersion and fiber nonlinearity, the laser signal and the population inversion acting as a weakly saturated absorption effect, with an initial light seed of the corresponding pulse type arising from SSP.

2. Experimental setup

The experiment setup is illustrated in Fig. 1
Fig. 1 Schematic of the fiber ring laser cavity, WDM: wavelength-division multiplexer. PC: polarization controller; PI-ISO: polarization-independent isolator; OC: output coupler.
. A fiber-pigtailed 976 nm laser diode with a maximum pumping power of 300 mW was used to pump the YDF through a 976/1060 nm wavelength-division multiplexer (WDM). A 1 m long segment of YDF with a peak core absorption of 1200 dB/m at 976 nm (Yb1200-6/125, LIEKKITM) was used as the gain medium. All the other fibers used (126 m in total) were standard single-mode fibers (HI1060, Corning). A polarization controller (PC) was used to control the polarization of the light in the resonant cavity. A polarization-independent isolator (PI-ISO) was employed to force unidirectional operation of the laser. A 10% fiber coupler was used to output the signal. An optical spectrum analyzer (Yokogawa AQ6317C) with a minimum resolution of 0.01 nm, a 1 GHz oscillograph (Yokogawa DL9140) with a 1 GHz bandwidth photodetector and a commercial optical autocorrelator (FP-103XL) were used to monitor the pulse train, spectrum and the pulse width simultaneously.

3. Experimental results and discussion

3.1 Self-pulsing

The laser threshold pumping power for CW operation was ~46 mW. When the pumping power exceeded this threshold, SSP was easily achieved. Figures 2(a)
Fig. 2 Oscilloscope trace (a) and optical spectrum (b) of the self-pulsing with the pumping power of 56 mW.
and 2(b) show, respectively, the oscilloscope trace and the optical spectrum of this state with a pump power of 56 mW. The period of the SSP was ~625 ns, which corresponds to the cavity length. The central emission wavelength was approximately 1070 nm. The SSP in the SML [1

1. F. Fontana, M. Begotti, E. M. Pessina, and L. A. Lugiato, “Maxwell-Bloch modelocking instabilities in erbium-doped fiber lasers,” Opt. Commun. 114(1–2), 89–94 (1995). [CrossRef]

, 7

7. F. Brunet, Y. Taillon, P. Galarneau, and S. LaRochelle, “A simple model describing both self-mode locking and sustained self-pulsing in ytterbium-doped ring fiber lasers,” J. Lightwave Technol. 23(6), 2131–2138 (2005). [CrossRef]

] regime could also be observed over a wide range of pump powers, even close to threshold.

3.2 Bright pulses

By carefully adjusting the PC, a typical pulse train of giant bright pulses caused by self-mode locking (SML) could be observed. The pulse train had the fundamental cavity repetition rate of 1.6 MHz as shown in Fig. 3(a)
Fig. 3 Output of the laser: Oscilloscope trace (a); inset: an expanded version of a single pulse. Optical spectrum (b) and autocorrelation trace (c).
. The inset of Fig. 3(a) shows an expanded version of a single pulse. Being limited by the resolution of the electronic-detection system, we can only observe the cluster pattern, which is due to the weak SML effect, as a giant pulse. The SML effect involves laser signal modulations at a period corresponding to the fundamental cavity repetition period. This effect originates from the beats between the oscillating longitudinal modes of the cavity and is further supported by mode coupling resulting from gain saturation in a CW fiber laser [7

7. F. Brunet, Y. Taillon, P. Galarneau, and S. LaRochelle, “A simple model describing both self-mode locking and sustained self-pulsing in ytterbium-doped ring fiber lasers,” J. Lightwave Technol. 23(6), 2131–2138 (2005). [CrossRef]

]. The corresponding spectrum is shown in Fig. 3(b). The central wavelength was approximately 1071 nm. The weak modulation of the optical spectrum is due to a birefringence-induced filtering effect in the long cavity length [27

27. E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, “Nanosecond-pulse fiber lasers mode-locked with nanotubes,” Appl. Phys. Lett. 95(11), 111108 (2009). [CrossRef]

, 28

28. X. Tian, M. Tang, P. P. Shum, Y. Gong, C. Lin, S. Fu, and T. Zhang, “High-energy laser pulse with a submegahertz repetition rate from a passively mode-locked fiber laser,” Opt. Lett. 34(9), 1432–1434 (2009). [CrossRef] [PubMed]

]. The autocorrelation trace is shown in Fig. 3(c), where it may be seen that the pulse width was ~3.35 ps, assuming a sech2-shape pulse.

3.3 Dark-bright pulse pairs and their HML counterparts

By increasing the pumping power to 66 mW and adjusting the PC carefully, dark-bright pulse pairs could be observed. Figures 4(a)
Fig. 4 Oscilloscope traces(a), the corresponding spectrum (b) of dark-bright pulse pairs.
and 4(b) show the oscilloscope trace and spectrum of single dark-bright pulse pairs, respectively. Differently from [29

29. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Observation of polarization domain wall solitons in weakly birefringent cavity fiber lasers,” Phys. Rev. B 80(5), 052302 (2009). [CrossRef]

], (where the bright and dark solitons can be observed separately in the orthogonal polarization components, due to the cross-polarization coupling of the two orthogonal principal-polarization components), in our experiment the dark-bright soliton pairs could be observed simultaneously at any polarization component in different condition. To confirm this result, we added a polarization beam splitter at the output end. The output pulses of the two axis had the same pulse shape and pulse spectrum as Figs. 4(a) and 4(b). Consequently, we believe that the dark-bright pulse pairs coexist.

At a fixed pump strength of 66 mW, the HML counterparts of dark-bright pulse pairs could also be easily obtained by tuning the PC. We observed that the HML counterparts of dark-bright pulse pairs arose from either the interaction of dark-bright pulse pairs or were generated directly from the background noise. As examples, Figs. 5(a)
Fig. 5 Oscilloscope traces of the HML counterparts of dark-bright pulse pairs of orders 2 and 4.
and 5(b) show oscilloscope traces of the 2nd and 4th order harmonics of dark-bright pulse pairs, respectively. The sensitivity to polarization in our laser may result from birefringence-induced filtering effect in the long normal-dispersion fiber spool. As [30

30. 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]

, 31

31. L. Yun, X. M. 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]

] pointed out, even in a polarization-independent laser cavity, the PC can still significantly affect the mode locking.

3.4 Dark pulses and their HML counterparts

With the pump power fixed at 72 mW, by rotating carefully the PC, a localized intensity dip in the uniform CW background could be observed as shown in Fig. 6(a)
Fig. 6 Oscilloscope traces of normalized intensity (a) and output spectrum of the dark pulse (b).
. With the appropriate laser operation conditions, the laser oscillated at a single wavelength as shown in Fig. 6(b), indicating that scalar CGLE type dark solitons had been obtained. If the laser oscillated simultaneously at two wavelengths, then due to their incoherent nonlinear coupling, the laser emission could switch between the two wavelengths, leading to the formation of vector dark domain wall solitons [16

16. H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010). [CrossRef] [PubMed]

]. Generally speaking, an authentic dark soliton would have an intensity that dropped to zero from the maximum value of the background intensity. It may be seen from Fig. 6(a) that the dark pulses which formed in our fiber laser had an intensity dip of ~14% on a strong CW background. This situation resulted from the dark pulse being partly filtered by hitting a 1 GHz bandwidth photodetector.

With increasing pump power, splitting of dark pulses was found to occur. In addition, due to the intrinsic modulation instability caused by cross phase modulation, too strong pumping also resulted in formation of new dark pulses. The new dark pulses were unstable, in that they tended to move slowly with respect to other pulses in the cavity and eventually to converge into a new harmonic component. Operation modes with the HML counterparts of dark pulse of orders 3, 4, 5 and 6 are shown in Figs. 7(a)
Fig. 7 Oscilloscope traces of the HML counterparts of dark pulse of orders 3, 4, 5 and 6. See Media 1 and Media 2.
-7(d). Media 1 and Media 2 recorded this process. Due probably to slight environmental perturbations, stable operation with harmonic trains of dark pulse could not be maintained for extended periods of time.

When the pump power was increased to 88 mW, the dark pulses and their HML counterparts became unstable. When the pump power was further increased to above 92 mW, even with careful adjustment of the polarization controller, only SSP, with no dark pulses could be observed.

4. Simulation of laser operation

The pulse propagation in a segment of fiber can be modeled well by the NLSE. However, fiber lasers have some components which cannot be modeled by the several phase modulation terms in the NLSE. For example, a fiber laser has a gain effect with a limited gain bandwidth or may also have a saturated absorber. They do not cause phase modulation but they do induce amplitude modulation in the frequency and the time domains. To take into account the amplitude modulation effects in a laser cavity properly, more terms must be added to the NLSE. The resulting differential equation is called a cubic-CGLE.

To further understand the laser behavior we performed numerical simulations with a model based on the cubic-CGLE and split-step Fourier transform algorithm. Equation (1) describes the temporal and longitudinal dependence of the slowly varying pulse envelope A (z, t) along each nonlinear element, where α is the linear loss, g0 is the small-signal gain, γ is the nonlinear parameter, β2 is the second-order dispersion and Ωg is the gain bandwidth. Higher-order nonlinear effects are neglected. The pulse-shaping mechanism in our fiber laser can be understood as a low intensity seed pulse evolving in the fiber laser which includes a weakly saturable absorber. The simulation was based on the experimental setup shown in Fig. 1. The setup modeled consisted of a segment of SMF (7 m), an Yb-doped gain fiber (1 m), and one more piece of SMF (119 m). The fiber parameters assumed were β2SMF = 20 ps2/km, β2YDF = 25 ps2/km, γ = 3 W/km.

Propagation of the pulse in the laser is described by:

Az=α2Aiβ222At2+iγ|A|2A+(g01+Epulse/Esat)(1+1Ωg22t2)A
(1)
g=g01+Epulse/Esat
(2)
T=1Rsat/[1+P/Psat]
(3)

Equation (2) which appears as a part of Eq. (1), describes the gain saturation of the doped fiber. g0 is 35 dB/m for small-signal gain, Epulse is the total energy of the pulse, and Esat = 4 nJ is the gain saturation energy. The gain bandwidth was 50 nm with a Gaussian profile. The SMF fiber sections were followed by a weakly saturable absorber which is modeled by a reflectivity function given in Eq. (3), where Rsat = 0.6 is the saturable reflectance; Psat is 1200 W, the saturable power, and P is the instantaneous pulse peak power. The extraction ratio of output coupler was 10%.

For simplicity, to generate different pulses, we assumed initial light seeds for the dark pulses and dark-bright pulse pairs to be u=u0tanh(t/t0),and u=u0tanh(t/t0)+u0sech(t/t0), respectively. In a fiber laser with fiber of weakly cavity linear birefringence, adjusting the PC has an effect similar to changing the loss of the cavity.

Numerical simulations demonstrate that stable operation of dark pulses and dark-bright pulses can be achieved in the relatively simple Yb-doped fiber laser cavity that includes a weakly saturable absorber. The SSP can provide low intensity light seeds. The loss in the cavity is considered as a controlling element. Simulation successfully reveals as shown in Figs. 8(a)
Fig. 8 A dark pulse state numerically calculated (α = 0.042/m). Evolution with time and the number of roundtrips (a), intensity profile of the dark pulse on the last roundtrip (b) and numerical spectrum (dotted curve) compared to experimental spectrum (solid curve) (c).
and 9(a)
Fig. 9 A dark-bright pulse pairs state numerically calculated (α = 0.141/m). Evolution with time and the number of roundtrips (a), intensity profile of the dark-bright pulse pairs on the last roundtrip (b) and numerical spectrum (dotted curve) compared to experimental spectrum (solid curve) (c).
, respectively, the evolution of a dark pulse and a dark-bright pulse pairs. It also shows that these pulses can propagate stably in the laser cavity as a function of time and the number of roundtrips with different loss values. The dotted curves in Figs. 8(c) and 9(c) show separately the spectra of the calculated dark pulses and dark-bright pulse pairs. The numerical spectra are qualitatively similar to the experimental spectra (solid curve).

5. Conclusion

With an intracavity polarization controller, a rich variety of nonlinear phenomena, ranging from sustained self-pulsing (SSP) to bright pulses and dark-bright pulse pairs with their HML counterparts as well as dark pulses and their HML counterparts has been observed. The results suggest that self-pulsing can provide low intensity light seeds for dark pulses and dark-bright pulse pairs on a CW background signal. The gain fiber provides pulse amplification and compensates for the laser losses. Interaction between the laser signal and the population inversion, acting as a weakly saturable absorber, can stabilize pulse operation. Numerical simulations reproduce well the results of the experimental observations. The various pulses, especially the dark pulses may find applications in high quality optical communications.

Acknowledgments

This research was supported by grants from the National Natural Science Foundation of China (11074065), the Hebei Natural Science Foundation (F2009000321, F2012205076 and A2012205023), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20101303110003) and the Technology Key Project of Colleges and Universities of Hebei Province (ZH2011107).

References and Links

1.

F. Fontana, M. Begotti, E. M. Pessina, and L. A. Lugiato, “Maxwell-Bloch modelocking instabilities in erbium-doped fiber lasers,” Opt. Commun. 114(1–2), 89–94 (1995). [CrossRef]

2.

F. Sanchez, P. Le Boudec, P.-L. François, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48(3), 2220–2229 (1993).

3.

P. Le Boudec, P. L. Francois, E. Delevaque, J.-F. Bayon, F. Sanchez, and G. M. Stephan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” Opt. Quantum Electron. 25(8), 501–507 (1993). [CrossRef]

4.

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. M. Stephan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25(5), 359–367 (1993). [CrossRef]

5.

S. Colin, E. Contesse, P. L. Boudec, G. Stephan, and F. Sanchez, “Evidence of a saturable-absorption effect in heavily erbium-doped fibers,” Opt. Lett. 21(24), 1987–1989 (1996). [CrossRef] [PubMed]

6.

L. Luo and P. L. Chu, “Suppression of self-pulsing in an erbium-doped fiber laser,” Opt. Lett. 22(15), 1174–1176 (1997). [CrossRef] [PubMed]

7.

F. Brunet, Y. Taillon, P. Galarneau, and S. LaRochelle, “A simple model describing both self-mode locking and sustained self-pulsing in ytterbium-doped ring fiber lasers,” J. Lightwave Technol. 23(6), 2131–2138 (2005). [CrossRef]

8.

J. Li, K. Ueda, M. Musha, and A. Shirakawa, “Residual pump light as a probe of self-pulsing instability in an ytterbium-doped fiber laser,” Opt. Lett. 31(10), 1450–1452 (2006). [CrossRef] [PubMed]

9.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37(5), 823–828 (1973).

10.

W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992). [CrossRef]

11.

N. Bekki and K. Nozaki, “Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation,” Phys. Lett. A 110(3), 133–135 (1985). [CrossRef]

12.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987). [CrossRef]

13.

B. Meziane, F. Sanchez, G. M. Stephan, and P. L. François, “Feedback-induced polarization switching in a Nd-doped fiber laser,” Opt. Lett. 19(23), 1970–1972 (1994). [CrossRef] [PubMed]

14.

T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002). [CrossRef] [PubMed]

15.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009). [CrossRef]

16.

H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010). [CrossRef] [PubMed]

17.

H. Yin, W. Xu, A. Luo, Z. Luo, and J. Liu, “Observation of dark pulse in a dispersion-managed fiber ring laser,” Opt. Commun. 283(21), 4338–4341 (2010). [CrossRef]

18.

S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52(4), 881–883 (2010). [CrossRef]

19.

V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14(15), 805–807 (1989). [CrossRef] [PubMed]

20.

R. Radhakrishnan and K. Aravinthan, “A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 40(43), 13023–13030 (2007). [CrossRef]

21.

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Y. S. Kivshar, and V. V. Afanasjev, “Incoherently coupled dark-bright photorefractive solitons,” Opt. Lett. 21(22), 1821–1823 (1996). [CrossRef] [PubMed]

22.

Y. Y. Lin and R. K. Lee, “Dark-bright soliton pairs in nonlocal nonlinear media,” Opt. Express 15(14), 8781–8786 (2007). [CrossRef] [PubMed]

23.

Z. H. Musslimani and J. Yang, “Transverse instability of strongly coupled dark-bright Manakov vector solitons,” Opt. Lett. 26(24), 1981–1983 (2001). [CrossRef] [PubMed]

24.

K. W. Chow and K. Nakkeeran, “Bright-dark and double-humped pulses in averaged, dispersion managed optical fiber systems,” in Optical Fibers Research Advances (Nova Science Publisher, 2007), pp. 301–313.

25.

Y. Meng, S. Zhang, H. Li, J. Du, Y. Hao, and X. Li, “Bright-dark soliton pairs in a self-mode locking fiber laser,” Opt. Eng. 51(6), 064302 (2012). [CrossRef]

26.

H. Y. Wang, W. C. Xu, W. J. Cao, L. Y. Wang, and J. L. Dong, “Experimental observation of bright-dark pulse emitting in an all-fiber ring cavity laser,” Laser Phys. 22(1), 282–285 (2012). [CrossRef]

27.

E. J. R. Kelleher, J. C. Travers, Z. Sun, A. G. Rozhin, A. C. Ferrari, S. V. Popov, and J. R. Taylor, “Nanosecond-pulse fiber lasers mode-locked with nanotubes,” Appl. Phys. Lett. 95(11), 111108 (2009). [CrossRef]

28.

X. Tian, M. Tang, P. P. Shum, Y. Gong, C. Lin, S. Fu, and T. Zhang, “High-energy laser pulse with a submegahertz repetition rate from a passively mode-locked fiber laser,” Opt. Lett. 34(9), 1432–1434 (2009). [CrossRef] [PubMed]

29.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Observation of polarization domain wall solitons in weakly birefringent cavity fiber lasers,” Phys. Rev. B 80(5), 052302 (2009). [CrossRef]

30.

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]

31.

L. Yun, X. M. 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]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.3510) Lasers and laser optics : Lasers, fiber

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 9, 2013
Revised Manuscript: February 16, 2013
Manuscript Accepted: March 17, 2013
Published: March 29, 2013

Citation
Xingliang Li, Shumin Zhang, Yichang Meng, and Yanping Hao, "Harmonic mode locking counterparts of dark pulse and dark-bright pulse pairs," Opt. Express 21, 8409-8416 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8409


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References

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