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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 10 — May. 12, 2008
  • pp: 7169–7174
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Observation of central wavelength dynamics in erbium-doped fiber ring laser

Huiwen Xu, Dajun Lei, Shuangchun Wen, Xiquan Fu, Jinggui Zhang, Yufeng Shao, Lifu Zhang, Hua Zhang, and Dianyuan Fan  »View Author Affiliations


Optics Express, Vol. 16, Issue 10, pp. 7169-7174 (2008)
http://dx.doi.org/10.1364/OE.16.007169


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Abstract

We report on the observation of central wavelength dynamics in an erbium-doped fiber ring laser by using the nonlinear polarization rotating technique. The evolution of central wavelength with the laser operation state was observed experimentally. Numerical simulations confirmed the experimental observation and further demonstrated that the dynamics of wavelength evolution is due to the combined effects of fiber birefringence, fiber nonlinearity, and cavity filter.

© 2008 Optical Society of America

1. Introduction

Passively mode-locked fiber lasers have attracted intensive attention due to their many potential applications. With the net abnormal fiber dispersion, many operation regimes have been found in the lasers, such as continuous wave [1

1. D. Y. Tang, W. S. Man, and H. Y. Tam, “Stimulated soliton pulse formation and its mechanism in a passively mode-locked soliton laser,” Opt. Commun. 165, 189–194 (1999). [CrossRef]

], single-soliton [2

2. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992). [CrossRef]

, 3

3. M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1328 (1993). [CrossRef]

], bound-soliton [4–7

4. B. A. Malomed, “Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation,” Phys. Rev. A 44, 6954–6957 (1991). [CrossRef] [PubMed]

], and noise-like soliton emission states [8–10

8. M. Horowitz, Y. Barad, and Y. Silberberg, “Noise-like pulses with a broadband spectrum generated from an erbium-doped fiber laser,” Opt. Lett. 22, 799–801 (1997). [CrossRef] [PubMed]

]. Experimentally, the operation state of the laser can vary from one to another by simply tuning the polarization controllers in the cavity. The laser always operates in the CW regime at low pump power level and can immediately achieve soliton operation as the pump power increased beyond a certain threshold.

As early as in 1992, Matsas et al. [2

2. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992). [CrossRef]

] reported the central wavelength tunability of mode-locked solitons. The mechanism for the tunability, however, was not argued. In 2000, Man et al. found a 6 nm continuously tuning range by adjusting the polarization controllers in the laser cavity [11

11. W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000). [CrossRef]

]. The mechanism for the central wavelength tunability is due to the effect of cavity birefringence. To the best of our knowledge, the entire dynamics of central wavelength evolution corresponding to the change of laser operation state has not been studied. In this paper, we present the experimental results of central wavelength dynamics in the fiber ring laser for the first time. We show the experimental observation that, far away from the central wavelength of the amplified spontaneous emission (ASE) spectrum of the Erbium doped fiber, central wavelength of mode-locked solitons always generated at the long wavelength side of the ASE spectrum. Moreover, we obtain a dual-wavelength emission state by tuning the polarization controllers (PCs). In this case, continuously adjusting the PCs leads to an energy transfer between the two spectral components. Soliton operation is eventually achieved by further rotating the PCs when the CW of the long wavelength side becomes strong enough. Based on the analysis by the linear transmission model and the simulation results, we attribute the dynamics of wavelength evolution to the combined effects of the fiber birefringence, fiber nonlinearity, and cavity filtering of the fiber laser.

2. Experimental setup and results

The schematic experimental setup of our fiber laser is shown in Fig. 1. It is an erbium-doped fiber ring laser made of pure abnormal dispersion fibers. The laser has a 3 m erbium-doped fiber (EDF) with a GVD of -10 ps2/km at 1550 nm and a mode-field diameter (MFD) of 9.8 µm. All other fibers are single-mode fiber (SMF) with a GVD of -18 ps2/km and a MFD of 9.3 µm. The total cavity length is about 9 m. Mode-locking is achieved through nonlinear polarization rotating technique. A polarization dependent isolator, which plays the dual roles of a polarizer and an isolator, is placed between the two PCs. A WDM coupler is used to couple the pump light and a 10% coupler is used for light output. The laser is pumped by a 980 nm ALD98-500-B_FA pump laser and the output of the laser is analyzed with a commercial optical spectrum analyzer.

Fig. 1. Schematic design of a fiber laser passively mode locked by nonlinear polarizationrotation. WDM is the wavelength division multiplexing coupler.

To study the central wavelength evolution in the fiber laser, we start by analyzing the ASE of the EDF. By disconnecting the isolator, shown in Fig. 1, and increasing the pump power, we obtain the spectrum of ASE as shown in Fig. 2(a). It can be seen that the optical spectrum exhibits an asymmetry with the central wavelength at 1532 nm. Reconnecting the isolator, we obtain the self-started soliton operation through appropriately tuning the PCs and increasing the pump power. Fig. 2(b) shows the typical spectrum of the mode-locked solitons. We surprisingly find that far away from the central wavelength of the ASE, the mode-locked pulses are always generated with the central wavelength of about 1558 nm, indicating that there might be some wavelength-dependent mechanism for achieving soliton operation from the CW emission state.

Fig. 2. Typical optical spectra of the ASE and mode-locked solitons. (a) shows the typical spectrum of the ASE for the central wavelength of 1532 nm. (b) shows the typical spectrum of the mode-locked solitons for the central wavelength of 1558 nm.
Fig. 3. Optical spectra under different PC rotating orientation. The pump power is 325 mW. (a) Spectrum of ASE. (b)–(h) Spectral shaping corresponding to the PC rotation.

To get more information on the central wavelength dynamics, we further observe the optical spectral evolution corresponding to the emission state variation by rotating the PCs. Fig. 3 shows the experimental results. For the purpose of comparison, Fig. 3(a) presents the typical spectrum of ASE. Fig. 3(b) shows the optical spectrum for the case that only one peak is visible at 1532 nm. This optical spectrum has a very similar shape to that in Fig. 3(a), suggesting that the laser cavity has a little effect on the light propagation. Figs. 3(c)–(f) show the spectral evolution as the PCs are continuously tuned. As the PCs are rotated, the optical spectrum collapses and the power for the long-wavelength side increases gradually. In this case, a dual-wavelength emission state is realized. We also note that, as the PCs are further tuned, an exchange of power between the two wavelengths will take place. Eventually, we obtain a new CW emission state with only one spectral peak at 1558 nm after the energy transfer, as shown in Fig. 3(g). From Fig. 3(h) we see that the soliton spectrum is generated immediately by further rotating the PCs. The sidebands are clearly visible, indicating that mode-locking is achieved [12

12. S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average,” Electron. Lett. 28, 806–808 (1992). [CrossRef]

]. Note that the pump power is not changed during the PC tuning process. Enlighten from the soliton generation process from the CW state, we believe that the cavity effect is strongly dependent on the PC rotating orientation and the light wavelength.

3. Numerical simulations

To verify the experimental results we conduct numerical simulations to study the effect of PC on the wavelength dynamics. We use exactly the same model and simulation techniques as described in [13

13. J. Wu, D. Y. Tang, L. M. Zhao, and C. C. Chan, “Soliton polarization dynamics in fiber lasers passively mode-locked by the nonlinear polarization rotation technique,” Phys. Rev. E 74, 046605 (2006). [CrossRef]

]. In order to closely simulate the experimental situations, we use the following parameters for the laser. The GVD parameters of the EDF and the SMF are -18 ps2/km and -10 ps2/km, respectively, the nonlinear parameter γ=3W-1km-1, the third order dispersion β‴=0.1ps3/km, the gain bandwidth Ωg=30nm, the gain saturation energy Esat=1000pJ, and the cavity length L=3SMF+3EDF+3SMF=9m. The orientation of the intra-cavity polarizer to the fiber fast birefringent axis Ψ=0.125π, and the small signal gain coefficient G=500. We did not measure the exact birefringence in the laser cavity. Although most of the laser cavity is constructed with standard single-mode fiber that has an intrinsic beat length of about 10 m, there is strong birefringence from the wave plates, the winding of fibers and the nonuniformities of the EDFA in the laser cavity [11

11. W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000). [CrossRef]

]. So we choose the fiber beat length Lb=L/10 as the typical value that gives a good qualitative agreement between the experimental and simulation results.

Fig. 4. Numerically calculated spectra under different linear phase delay bias for a small signal gain of 500, in which (a) and (c) show the spectra as linear phase delay is 0.5π and -0.7π; respectively, while (b) shows the spectra as linear phase delay is 0.2π, 0.18π, and 0.12π respectively.

Figure 4 shows the calculated results. Like the experimental observations, the spectral profile strongly depends on the linear phase delay bias, which experimentally corresponds to changing the orientations of the PCs. From Fig. 4(a) we see that a CW emission state is generated at 1548 nm as the linear phase delay bias is set to 0.5π. In this case, as we decrease the linear phase delay bias, the power of the CW state decreases correspondingly. Fig. 4(b) shows the case when the phase delay is biased at 0.2π, 0.18π and 0.12π, respectively. A weak spectral component appears at 1558 nm as the linear phase delay is set to 0.2π. As we continue to decrease the linear phase delay, the weak component grows up immediately and a dual-wavelength CW emission state is obtained. We note that the interval between the two wavelengths is much shorter than the experimental observation. We believe that this difference mainly arise from the parabolic approximation of the gain spectrum in our model. Fig. 4(c) shows the case when soliton spectrum is generated with the central wavelength of 1558 nm, as the linear phase delay is set to -0.7π. The sidebands can be seen clearly, indicating that the mode-locking is achieved. We have used different birefringence and gain bandwidth with the parabolic profile approximation for the further simulations. We found that, although the interval and the location of the peaks vary with different parameters, the wavelength shows similar evolution dynamics. Hence, the calculated soliton spectrum exhibits exactly the same characteristics as the experimental observation.

4. Analysis of the mechanism of wavelength dynamics

For better understanding the physical origins of the wavelength dynamics, we use the linear transmission model [14

14. C. J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton fiber ring laser,” Opt. Lett. 17, 417–419 (1992). [CrossRef] [PubMed]

, 15

15. 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, 043816 (2005). [CrossRef]

] to determine the cavity transmission coefficient of the laser cavity. Based on this model, many intrinsic features have been well illuminated, such as multi-soliton operation, wavelength tunability, energy quantization and sideband asymmetry [11

11. W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000). [CrossRef]

, 15

15. 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, 043816 (2005). [CrossRef]

]. The transmission coefficient can be expressed as T2=sin2θsin2φ+cos2θcos2φ+12sin(2θ)sin(2φ)cos(ΔΦ), , where ΔϕϕPCϕLBϕNL is the net phase delay between the fast and slow axes of the fiber, ΔϕPC is the PC induced phase delay, ΔϕNL=2γLP cos(2θ)/3 is the fiber induced nonlinear phase change [13

13. J. Wu, D. Y. Tang, L. M. Zhao, and C. C. Chan, “Soliton polarization dynamics in fiber lasers passively mode-locked by the nonlinear polarization rotation technique,” Phys. Rev. E 74, 046605 (2006). [CrossRef]

], and ΔϕLB=2πLBm/λ is the phase delay caused by the linear fiber birefringence. θ is the angle between the fast axis of the fiber and the axis of the polarizer, and φ is the angle between the axis of the analyzer and the fast axis of the fiber. We note that ΔϕLB depends on the wavelength, indicating that the net phase delay Δϕ is also varying with the wavelength, and the short wavelength will lead to larger phase delay than the long wavelength. Fig. 5 shows the transmission coefficient versus the phase delay for θ=π/8 and ϕ=θ+π/2. It is seen that the cavity generates a cavity filter effect, namely, as the light propagates in the cavity the loss it experiences is strongly dependent on the net phase delay. Note that the similar filter effect still exists even with the different θ and ϕ. When the phase delay is biased between (2n+1)π and 2(n+1)π, the cavity will generate a positive feedback, as the actual cavity transmission increases under the effect of the nonlinear polarization rotation. On the contrary, the cavity will generate a negative feedback if the phase delay is located in the range from 2 to (2n+1)π [15

15. 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, 043816 (2005). [CrossRef]

].

We assume that the net phase delay is located at “A” which is in the negative feedback range. A stable CW emission state should be obtained in this range as a larger peak power of the light will lead to a smaller cavity transmission coefficient in this range. The wavelength of the CW should be at the short-wavelength side as it experiences lower loss than the longwavelength side. As the phase delay is decreased to “B” by the PCs adjustment, the power for both short-wavelength and long-wavelength sides will still be maintained but the power for the mid-wavelength band will be suppressed due to the cavity loss dispersion. Hence, the two spectral components are sufficiently separated and the dual-wavelength emission state is obtained. If the net phase delay is slightly shifted through the PC rotation, the cavity loss of the long wavelength component will increase (decrease) and the one of the short wavelength component will decrease (increase), and thus the energy transfer will take place. The phase delay will be biased at “C” as we further tune the PCs. The short-wavelength side of the spectrum will experience more lose than the long-wavelength side. In this case, the cavity will amplify the power of long-wavelength side but suppress the one of short-wavelength side. Hence, the central wavelength is biased at the long-wavelength side. Eventually, mode-locked solitons will be generated as the power becomes large enough. As a consequence, the wavelength dynamics corresponding to the variation of the operation state is due to the combined effects of the fiber birefringence, nonlinearity, and cavity filter of the laser.

Fig. 5. Relationship between system transmission coefficient and phase delay. “A”, “B” and “C” show typical linear phase delay offset ranges corresponding to the different PC rotating orientation, respectively.

The above analysis is based on the assumption that the nonlinear phase delay bias is negative. In fact, the nonlinear phase delay can be either negative or positive, depending on θ. As θ is in the range from π/4 to π/2, the nonlinear phase delay bias will become positive, and relatively, the positive feed back range will be biased between 2 and (2n+1)π. Therefore, the opposite wavelength evolution process can also be obtained with solitons generated at the short wavelength side of the gain bandwidth. This process has also been demonstrated in both our experimental and numerical results that confirm the theoretical results well.

5. Summary

In conclusion, we have experimentally observed the dynamics of the central wavelength evolution corresponding to the variation of the laser emission state. We find the mode-locked solitons is always generated at the central wavelength of 1558 nm, which is 26 nm away from the central wavelength of the ASE of the EDF. A dual-wavelength emission state is also observed with the wavelengths of 1532 and 1558 nm as the PCs are rotated to a certain orientation. Mode-locking is achieved eventually at the central wavelength of 1558 nm when the PCs are further tuned. Confirmed by the simulation results and analyzed by the linear transmission model, we attribute the dynamics of wavelength evolution to the combined effects of the fiber birefringence, fiber nonlinearity, and cavity filter of the fiber laser.

Acknowledgment

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 10576012, 10776008, and 60538010).

References and links

1.

D. Y. Tang, W. S. Man, and H. Y. Tam, “Stimulated soliton pulse formation and its mechanism in a passively mode-locked soliton laser,” Opt. Commun. 165, 189–194 (1999). [CrossRef]

2.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992). [CrossRef]

3.

M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1328 (1993). [CrossRef]

4.

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation,” Phys. Rev. A 44, 6954–6957 (1991). [CrossRef] [PubMed]

5.

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett 80, 4657–4660 (1998). [CrossRef]

6.

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, 033806 (2002). [CrossRef]

7.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively mode-locked fiber laser,” Phys. Rev. A 64, 033814 (2001). [CrossRef]

8.

M. Horowitz, Y. Barad, and Y. Silberberg, “Noise-like pulses with a broadband spectrum generated from an erbium-doped fiber laser,” Opt. Lett. 22, 799–801 (1997). [CrossRef] [PubMed]

9.

D. Y. Tang, L. M. Zhao, and B. Zhao, “Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser,” Opt. Express 13, 2289–2294 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-7-2289 [CrossRef] [PubMed]

10.

M. Horowitz and Y. Silberberg, “Control of noise-like pulse generation in Erbium-doped fiber lasers,” IEEE Photon. Technol. Lett. 10, 1389–1391 (1998). [CrossRef]

11.

W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000). [CrossRef]

12.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average,” Electron. Lett. 28, 806–808 (1992). [CrossRef]

13.

J. Wu, D. Y. Tang, L. M. Zhao, and C. C. Chan, “Soliton polarization dynamics in fiber lasers passively mode-locked by the nonlinear polarization rotation technique,” Phys. Rev. E 74, 046605 (2006). [CrossRef]

14.

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton fiber ring laser,” Opt. Lett. 17, 417–419 (1992). [CrossRef] [PubMed]

15.

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, 043816 (2005). [CrossRef]

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.3510) Lasers and laser optics : Lasers, fiber
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 3, 2008
Revised Manuscript: April 20, 2008
Manuscript Accepted: April 23, 2008
Published: May 2, 2008

Citation
Huiwen Xu, Dajun Lei, Shuangchun Wen, Xiquan Fu, Jinggui Zhang, Yufeng Shao, Lifu Zhang, Hua Zhang, and Dianyuan Fan, "Observation of central wavelength dynamics in erbium-doped fiber ring laser," Opt. Express 16, 7169-7174 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7169


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References

  1. D. Y. Tang, W. S. Man, and H. Y. Tam, "Stimulated soliton pulse formation and its mechanism in a passively mode-locked soliton laser," Opt. Commun. 165, 189-194 (1999). [CrossRef]
  2. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, "Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation," Electron. Lett. 28, 1391-1393 (1992). [CrossRef]
  3. M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, "Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation," Electron. Lett. 29, 1327-1328 (1993). [CrossRef]
  4. B. A. Malomed, "Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation," Phys. Rev. A 44, 6954-6957 (1991). [CrossRef] [PubMed]
  5. M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett 80, 4657-4660 (1998). [CrossRef]
  6. 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, 033806 (2002). [CrossRef]
  7. D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, "Observation of bound states of solitons in a passively mode-locked fiber laser," Phys. Rev. A 64, 033814 (2001). [CrossRef]
  8. M. Horowitz, Y. Barad, and Y. Silberberg, "Noise-like pulses with a broadband spectrum generated from an erbium-doped fiber laser," Opt. Lett. 22, 799-801 (1997). [CrossRef] [PubMed]
  9. D. Y. Tang, L. M. Zhao, and B. Zhao, "Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser," Opt. Express 13, 2289-2294 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-7-2289 [CrossRef] [PubMed]
  10. M. Horowitz and Y. Silberberg, "Control of noise-like pulse generation in Erbium-doped fiber lasers," IEEE Photon. Technol. Lett. 10, 1389-1391 (1998). [CrossRef]
  11. W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, "Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser," J. Opt. Soc. Am. B 17, 28-33 (2000). [CrossRef]
  12. S. M. J. Kelly, "Characteristic sideband instability of periodically amplified average," Electron. Lett. 28, 806-808 (1992). [CrossRef]
  13. J. Wu, D. Y. Tang, L. M. Zhao, and C. C. Chan, "Soliton polarization dynamics in fiber lasers passively mode-locked by the nonlinear polarization rotation technique," Phys. Rev. E 74, 046605 (2006). [CrossRef]
  14. C. J. Chen, P. K. A. Wai, and C. R. Menyuk, "Soliton fiber ring laser," Opt. Lett. 17, 417-419 (1992). [CrossRef] [PubMed]
  15. 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, 043816 (2005). [CrossRef]

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