Abstract

A theoretical model is established to study the self-similar pulses in nonlinear polarization evolution (NPE) mode-locked fiber lasers. The propagation of pulse in single mode fibers and gain fibers are described by coupled Ginzburg- Landau equation (GLE). Two wave plates and a polarizer are considered to realize the NPE mechanism in simulation. This model describes the laser completely and provides some useful pulses’ information. In our simulation the laser generates high quality self-similar pulses output. The region of steady self-similar pulses operation is found. The polarization states of different parts across the pulse are simulated along the laser cavity. It is found that polarization states across the pulse are modulated from elliptical to almost circular before the pulse passing through the polarizer.

© 2009 Optical Society of America

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  1. K. Tamura, H. A. Haus, and E. P. Ippen, "Self-starting additive pulse mode-locked erbium fiber ring laser," Electron. Lett. 28, 2226-2228 (1992).
    [CrossRef]
  2. D. Anderson, M. Desaix, M. Lisak, and M. L. Quiroga-Teixeiro, "Wave breaking in nonlinear-optical fibers," J. Opt. Soc. Am. B 9, 1358-1361 (1992).
    [CrossRef]
  3. L. E. Nelson, S. B. Fleischer, G. Lenz, and E. P. Ippen, "Efficient frequency doubling of a femtosecond fiber laser," Opt. Lett. 21, 1759-1761 (1996).
    [CrossRef] [PubMed]
  4. L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
    [CrossRef] [PubMed]
  5. A. Chong, W. H. Renninger, and F. W. Wise, "Environmentally stable all-normal-dispersion femtosecond fiber laser," Opt. Lett. 33, 1071-1073 (2008).
    [CrossRef] [PubMed]
  6. A. Chong, W. H. Renninger, and F. W. Wise, "All-normal-dispersion femtosecond fiber laser with pulse energy above 20nJ," Opt. Lett. 32, 2408-2410 (2007).
    [CrossRef] [PubMed]
  7. D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, "Wave-breaking-free pulses in nonlinear-optical fibers," J. Opt. Soc. Am. B 10, 1185- 1190 (1993).
    [CrossRef]
  8. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
    [CrossRef] [PubMed]
  9. A. Komarov, H. Leblond, and F. Sanchez, "Theoretical analysis of the operating regime of a passively-mode-locked fiber laser through nonlinear polarization rotation," Phys. Rev. A (Atomic, Molecular, and Optical Physics)  72, 063811-063817 (2005).
    [CrossRef]
  10. B. G. Bale, J. N. Kutz, and F. Wise, "Analytic theory of self-similar mode-locking," Opt. Lett. 33, 911-913 (2008).
    [CrossRef] [PubMed]
  11. K. M. Spaulding, D. H. Yong, A. D. Kim, and J. N. Kutz, "Nonlinear dynamics of mode-locking optical fiber ring lasers," J. Opt. Soc. Am. B 19, 1045-1054 (2002).
    [CrossRef]
  12. C. H. Tu, Z. Li, T. Lei, Y. N. LI, W.G. Guo, D. Wei, H. Zhu, S. G. Zhang, and F.Y. Lu, "Pulse evolution characteristics in self-similar mode-locked fiber laser," Chin. Phys. Lett. 24, 3175-3178 (2007).
    [CrossRef]
  13. A. Latkin, and S. Turitsyn, "Semi-Analytical Description of Parabolic Pulse Generation in the Normal-Dispersion Fibre Amplifiers," in Proceedings of IEEE International Conference on Transparent Optical Networks Conference (IEEE, 2006), pp. 259-262.
  14. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001), 203-209.
  15. C. R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron 23,174-176 (1987).
    [CrossRef]
  16. D. S. Kliger, and J. W. Lewis, Polarized light in optics and spectroscopy (Academic, 1990).
  17. M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
    [CrossRef]
  18. J. Wu, D. Y. Tang, L. M. Zhao, and C. C. Chan, Phys. "Soliton polarization dynamics in fiber lasers passively mode-locked by the nonlinear polarization rotation technique," Phys. Rev. E 74, 046605 (2006).
    [CrossRef]
  19. A. Komarov, H. Leblond, and F. Sanchez, "Quintic complex Ginzburg-Landau model for ring fiber lasers," Phys. Rev. E (Statistical, Nonlinear, and Soft Matter Physics)  72, 025604-025604 (2005).
    [CrossRef]

2008 (2)

2007 (2)

A. Chong, W. H. Renninger, and F. W. Wise, "All-normal-dispersion femtosecond fiber laser with pulse energy above 20nJ," Opt. Lett. 32, 2408-2410 (2007).
[CrossRef] [PubMed]

C. H. Tu, Z. Li, T. Lei, Y. N. LI, W.G. Guo, D. Wei, H. Zhu, S. G. Zhang, and F.Y. Lu, "Pulse evolution characteristics in self-similar mode-locked fiber laser," Chin. Phys. Lett. 24, 3175-3178 (2007).
[CrossRef]

2006 (2)

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

L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
[CrossRef] [PubMed]

2004 (1)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

1996 (1)

1993 (1)

1992 (2)

K. Tamura, H. A. Haus, and E. P. Ippen, "Self-starting additive pulse mode-locked erbium fiber ring laser," Electron. Lett. 28, 2226-2228 (1992).
[CrossRef]

D. Anderson, M. Desaix, M. Lisak, and M. L. Quiroga-Teixeiro, "Wave breaking in nonlinear-optical fibers," J. Opt. Soc. Am. B 9, 1358-1361 (1992).
[CrossRef]

1987 (1)

C. R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron 23,174-176 (1987).
[CrossRef]

Anderson, D.

Bale, B. G.

Buckley, J. R.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Chan, C. C.

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

Chong, A.

Clark, W. G.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Desaix, M.

Dudley, J. M.

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Ferman, M. E.

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Fleischer, S. B.

Harvey, J. D.

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Haus, H. A.

K. Tamura, H. A. Haus, and E. P. Ippen, "Self-starting additive pulse mode-locked erbium fiber ring laser," Electron. Lett. 28, 2226-2228 (1992).
[CrossRef]

Ilday, F. Ö.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Ippen, E. P.

L. E. Nelson, S. B. Fleischer, G. Lenz, and E. P. Ippen, "Efficient frequency doubling of a femtosecond fiber laser," Opt. Lett. 21, 1759-1761 (1996).
[CrossRef] [PubMed]

K. Tamura, H. A. Haus, and E. P. Ippen, "Self-starting additive pulse mode-locked erbium fiber ring laser," Electron. Lett. 28, 2226-2228 (1992).
[CrossRef]

Karlsson, M.

Kim, A. D.

Kruglov, V. I.

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Kutz, J. N.

Lei, T.

C. H. Tu, Z. Li, T. Lei, Y. N. LI, W.G. Guo, D. Wei, H. Zhu, S. G. Zhang, and F.Y. Lu, "Pulse evolution characteristics in self-similar mode-locked fiber laser," Chin. Phys. Lett. 24, 3175-3178 (2007).
[CrossRef]

Lenz, G.

Li, Z.

C. H. Tu, Z. Li, T. Lei, Y. N. LI, W.G. Guo, D. Wei, H. Zhu, S. G. Zhang, and F.Y. Lu, "Pulse evolution characteristics in self-similar mode-locked fiber laser," Chin. Phys. Lett. 24, 3175-3178 (2007).
[CrossRef]

Lisak, M.

Menyuk, C. R.

C. R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron 23,174-176 (1987).
[CrossRef]

Nelson, L. E.

Quiroga-Teixeiro, M. L.

Renninger, W. H.

Spaulding, K. M.

Tamura, K.

K. Tamura, H. A. Haus, and E. P. Ippen, "Self-starting additive pulse mode-locked erbium fiber ring laser," Electron. Lett. 28, 2226-2228 (1992).
[CrossRef]

Tang, D. Y.

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

L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
[CrossRef] [PubMed]

Thomsen, B. C.

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Tu, C. H.

C. H. Tu, Z. Li, T. Lei, Y. N. LI, W.G. Guo, D. Wei, H. Zhu, S. G. Zhang, and F.Y. Lu, "Pulse evolution characteristics in self-similar mode-locked fiber laser," Chin. Phys. Lett. 24, 3175-3178 (2007).
[CrossRef]

Wise, F.

Wise, F. W.

Wu, J.

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

L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
[CrossRef] [PubMed]

Yong, D. H.

Zhao, L. M.

L. M. Zhao, D. Y. Tang, and J. Wu, "Gain-guided soliton in a positive group-dispersion fiber laser," Opt. Lett. 31, 1788-1790 (2006).
[CrossRef] [PubMed]

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

Chin. Phys. Lett. (1)

C. H. Tu, Z. Li, T. Lei, Y. N. LI, W.G. Guo, D. Wei, H. Zhu, S. G. Zhang, and F.Y. Lu, "Pulse evolution characteristics in self-similar mode-locked fiber laser," Chin. Phys. Lett. 24, 3175-3178 (2007).
[CrossRef]

Electron. Lett. (1)

K. Tamura, H. A. Haus, and E. P. Ippen, "Self-starting additive pulse mode-locked erbium fiber ring laser," Electron. Lett. 28, 2226-2228 (1992).
[CrossRef]

IEEE J. Quantum Electron (1)

C. R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers," IEEE J. Quantum Electron 23,174-176 (1987).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (5)

Phys. Rev. E (1)

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

Phys. Rev. Lett. (2)

M. E. Ferman, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers," Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. "Self-Similar Evolution of Parabolic Pulses in a Laser," Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Other (5)

A. Komarov, H. Leblond, and F. Sanchez, "Theoretical analysis of the operating regime of a passively-mode-locked fiber laser through nonlinear polarization rotation," Phys. Rev. A (Atomic, Molecular, and Optical Physics)  72, 063811-063817 (2005).
[CrossRef]

A. Komarov, H. Leblond, and F. Sanchez, "Quintic complex Ginzburg-Landau model for ring fiber lasers," Phys. Rev. E (Statistical, Nonlinear, and Soft Matter Physics)  72, 025604-025604 (2005).
[CrossRef]

D. S. Kliger, and J. W. Lewis, Polarized light in optics and spectroscopy (Academic, 1990).

A. Latkin, and S. Turitsyn, "Semi-Analytical Description of Parabolic Pulse Generation in the Normal-Dispersion Fibre Amplifiers," in Proceedings of IEEE International Conference on Transparent Optical Networks Conference (IEEE, 2006), pp. 259-262.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001), 203-209.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of a NPE mode-locked fiber laser

Fig. 2.
Fig. 2.

Angles of polarization elements relative to the fiber fast-axis u -.

Fig. 3.
Fig. 3.

(a) The energy of a single output pulse at various angles of wave plates. (b) The value K/K 0 of output pulses at the polarizer at various angles of wave plates

Fig. 4.
Fig. 4.

(a) Temporal intensity profile (solid curve), chirp (dashed curve),and a parabolic fit (dotted curve) to the intensity profile. (b) Output power spectrum

Fig. 5.
Fig. 5.

Polarization states of the pulses at different locations: (a) after the polarizer (b) before the wave plates (c) after the 1/4 wave plate (d) after the 1/2 wave plate

Tables (1)

Tables Icon

Table 1. Parameters used in the model of NPE mode-locked fiber laser.

Equations (5)

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Axz=β1xAxtiβ222Axt2+g2Ax+ir(Ax2+AAy2)+iBγAx*Ay2 exp (2iΔβz)
Ayz=β1yAytiβ222Ayt2+g2Ay+iγ(Ay2+AAy2)+iBγAy*Ax2 exp (2iΔβz)
uz=iΔβ2uiβ222uT2+g2u+iγ(u2+23v2)u+iγ3u* v2
vz=iΔβ2viβ222vT2+g2v+iγ(v2+23u2)v+iγ3v* u2
K[ψ(z,t)]=+t2ψzt2dt(+ψzt4dt)2/(+ψzt2dt)5.

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