Abstract

We studied the formation of bi-soliton pairs in Kerr-type stretched pulse fiber ring laser (SPFRL). By solving the modified Ginzburg-Landau (GL) equaition, which models the SPFRL, we show that anti-phase bi-soliton can be generated robustly if a low level Gaussian pulse is injected into the ring laser in the initial set-up stage. With the help of properly selected high order nonlinear gain coefficient, the observation of anti-phase bi-soliton pairs is expected to become feasible in experiments.

© 2014 Optical Society of America

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References

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  1. A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
    [Crossref]
  2. X. Mao and A. Maruta, “Bi-soliton under the Influence of Third Order Dispersion in Dispersion Managed Optical Transmission System,” IEICE Trans. Commun. E88-B(5), 1955–1962 (2005).
    [Crossref]
  3. J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The Averaging Method for Finding Exactly Periodic Dispersion-Managed Solitons,” IEEE J. Sel. Top. Quantum Electron. 6(2), 330–336 (2000).
    [Crossref]
  4. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Stable soliton pairs in optical transmission lines and fiber lasers,” J. Opt. Soc. Am. B 15(2), 515–523 (1998).
    [Crossref]
  5. Ph. Grelu, J. Béal, and J. M. Soto-Crespo, “Soliton pairs in a fiber laser: from anomalous to normal average dispersion regime,” Opt. Express 11(18), 2238–2243 (2003).
    [Crossref] [PubMed]
  6. Y. Zhang, M. Belić, Zh. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
    [Crossref] [PubMed]
  7. Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002).
    [Crossref] [PubMed]
  8. A. Haboucha, A. Komarov, H. Leblond, and F. Sanchez, “Multiple Pulsing and Hysteresis Phenomena in Fiber Lasers: Theory and Experiment,” in Proc. ICTON’06, Paper We.B.1.2 (2006).
    [Crossref]
  9. D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
    [Crossref] [PubMed]
  10. X. Mao and A. Maruta, “Numerical Study on Multiple-Pulse Operation of Passively Modelocked Stretched Pulse Fiber Ring Laser,” Opt. Commun. 270(2), 407–413 (2007).
    [Crossref]
  11. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
    [Crossref]
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    [Crossref]
  13. D. E. Spence, J. M. Evans, W. E. Sleat, and W. Sibbett, “Regeneratively initiated self-mode-locked Ti:sapphire laser,” Opt. Lett. 16(22), 1762–1764 (1991).
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    [Crossref] [PubMed]
  15. M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
    [Crossref]
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    [Crossref]
  17. A. B. Grudinin and S. Gray, “Passive harmonic modelocking in soliton fiber lasers,” J. Opt. Soc. Am. B 14(1), 144–154 (1997).
    [Crossref]
  18. T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
    [Crossref] [PubMed]

2013 (1)

2007 (1)

X. Mao and A. Maruta, “Numerical Study on Multiple-Pulse Operation of Passively Modelocked Stretched Pulse Fiber Ring Laser,” Opt. Commun. 270(2), 407–413 (2007).
[Crossref]

2005 (3)

X. Mao and A. Maruta, “Bi-soliton under the Influence of Third Order Dispersion in Dispersion Managed Optical Transmission System,” IEICE Trans. Commun. E88-B(5), 1955–1962 (2005).
[Crossref]

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
[Crossref] [PubMed]

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
[Crossref] [PubMed]

2003 (1)

2002 (2)

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
[Crossref]

Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002).
[Crossref] [PubMed]

2000 (1)

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The Averaging Method for Finding Exactly Periodic Dispersion-Managed Solitons,” IEEE J. Sel. Top. Quantum Electron. 6(2), 330–336 (2000).
[Crossref]

1998 (1)

1997 (1)

1995 (2)

M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
[Crossref]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
[Crossref]

1994 (1)

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron. 30(1), 200–208 (1994).
[Crossref]

1991 (2)

Akhmediev, N. N.

Ankiewicz, A.

Béal, J.

Belhache, F.

Belic, M.

Doran, N. J.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The Averaging Method for Finding Exactly Periodic Dispersion-Managed Solitons,” IEEE J. Sel. Top. Quantum Electron. 6(2), 330–336 (2000).
[Crossref]

Evans, J. M.

Forysiak, W.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The Averaging Method for Finding Exactly Periodic Dispersion-Managed Solitons,” IEEE J. Sel. Top. Quantum Electron. 6(2), 330–336 (2000).
[Crossref]

Gray, S.

Grelu, Ph.

Grudinin, A. B.

Gutty, F.

Hasegawa, A.

M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
[Crossref]

Haus, H. A.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
[Crossref]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron. 30(1), 200–208 (1994).
[Crossref]

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, “Soliton Transmission Control,” Opt. Lett. 16(23), 1841–1843 (1991).
[Crossref] [PubMed]

Ikeda, H.

M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
[Crossref]

Inoue, T.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
[Crossref]

Ippen, E. P.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
[Crossref]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron. 30(1), 200–208 (1994).
[Crossref]

Kivshar, Y. S.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
[Crossref] [PubMed]

Ku, T. S.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
[Crossref] [PubMed]

Lai, Y.

Li, Y.

Lu, K.

Mao, X.

X. Mao and A. Maruta, “Numerical Study on Multiple-Pulse Operation of Passively Modelocked Stretched Pulse Fiber Ring Laser,” Opt. Commun. 270(2), 407–413 (2007).
[Crossref]

X. Mao and A. Maruta, “Bi-soliton under the Influence of Third Order Dispersion in Dispersion Managed Optical Transmission System,” IEICE Trans. Commun. E88-B(5), 1955–1962 (2005).
[Crossref]

Maruta, A.

X. Mao and A. Maruta, “Numerical Study on Multiple-Pulse Operation of Passively Modelocked Stretched Pulse Fiber Ring Laser,” Opt. Commun. 270(2), 407–413 (2007).
[Crossref]

X. Mao and A. Maruta, “Bi-soliton under the Influence of Third Order Dispersion in Dispersion Managed Optical Transmission System,” IEICE Trans. Commun. E88-B(5), 1955–1962 (2005).
[Crossref]

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
[Crossref]

Matsumoto, M.

M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
[Crossref]

Mecozzi, A.

Moores, J. D.

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
[Crossref]

Nijhof, J. H. B.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The Averaging Method for Finding Exactly Periodic Dispersion-Managed Solitons,” IEEE J. Sel. Top. Quantum Electron. 6(2), 330–336 (2000).
[Crossref]

Nonaka, Y.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
[Crossref]

Shih, M. F.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
[Crossref] [PubMed]

Sibbett, W.

Sleat, W. E.

Soto-Crespo, J. M.

Spence, D. E.

Sukhorukov, A. A.

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
[Crossref] [PubMed]

Tam, H. Y.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
[Crossref] [PubMed]

Tamura, K.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
[Crossref]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron. 30(1), 200–208 (1994).
[Crossref]

Tang, D. Y.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
[Crossref] [PubMed]

Uda, T.

M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
[Crossref]

Wu, Zh.

Yoshika, Y.

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
[Crossref]

Zhang, Y.

Zhao, B.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
[Crossref] [PubMed]

Zhao, L. M.

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
[Crossref] [PubMed]

Zheng, H.

IEEE J. Quantum Electron. (2)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-Pulse Additive Pulse Mode-Locking in Fiber Ring Laser: Theory and Experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995).
[Crossref]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive Pulse Modelocking in Fiber Lasers,” IEEE J. Quantum Electron. 30(1), 200–208 (1994).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

A. Maruta, T. Inoue, Y. Nonaka, and Y. Yoshika, “Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission,” IEEE J. Sel. Top. Quantum Electron. 8(3), 640–650 (2002).
[Crossref]

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The Averaging Method for Finding Exactly Periodic Dispersion-Managed Solitons,” IEEE J. Sel. Top. Quantum Electron. 6(2), 330–336 (2000).
[Crossref]

IEICE Trans. Commun. (1)

X. Mao and A. Maruta, “Bi-soliton under the Influence of Third Order Dispersion in Dispersion Managed Optical Transmission System,” IEICE Trans. Commun. E88-B(5), 1955–1962 (2005).
[Crossref]

J. Lightwave Technol. (1)

M. Matsumoto, H. Ikeda, T. Uda, and A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. 13(4), 658–665 (1995).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

X. Mao and A. Maruta, “Numerical Study on Multiple-Pulse Operation of Passively Modelocked Stretched Pulse Fiber Ring Laser,” Opt. Commun. 270(2), 407–413 (2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016616 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

T. S. Ku, M. F. Shih, A. A. Sukhorukov, and Y. S. Kivshar, “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94(6), 063904 (2005).
[Crossref] [PubMed]

Other (2)

A. Maruta, “Parameters Range of Bi-soliton Propagating in Dispersion Managed System,” in Proc. CLEO/Europe-EQEC’03, Paper CJ1M(2003).
[Crossref]

A. Haboucha, A. Komarov, H. Leblond, and F. Sanchez, “Multiple Pulsing and Hysteresis Phenomena in Fiber Lasers: Theory and Experiment,” in Proc. ICTON’06, Paper We.B.1.2 (2006).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 A schematic diagram of GVD and gain distribution along the fiber ring.
Fig. 2
Fig. 2 Bi-soliton circulating in the stretched pulse fiber ring laser.
Fig. 3
Fig. 3 Bi-soliton formation process from a single Gaussian pulse. Initial pulse peak is so low that it is not visible in the figure.
Fig. 4
Fig. 4 Bi-soliton in semi-log scale coordinates. The center of pulse is adjusted to 0. Particulars included in the low wing present symmetric structure.
Fig. 5
Fig. 5 Pulse spectrum evolution. Pulse center spectrum gradually converges to 0.
Fig. 6
Fig. 6 Pulse propagation in time domain when μ = 0.54. Pulse spectrum center converges to nonzero, which leads to pulse linear shift in time domain, as shown in (a). Then, spectrum center is adjusted to 0 by multiply a factor exp(jκT)to pulse in time domain, pulse center ceases to shift, as shown in (b).
Fig. 7
Fig. 7 Bi-soliton properties with respect to high order nonlinear gain coefficient μ. (a) pulse energy, (b) pulse peak power, (c) pulse spacing, (d) pulse FWHM width.
Fig. 8
Fig. 8 Pulse spectrum center with respect to high order nonlinear gain coefficient μ.
Fig. 9
Fig. 9 Examples of phase difference for symmetric and asymmetric bi-soliton. (a) and (b) show pulse phase with respect to normalized time. (c) and (d) record phase difference between two peaks for symmetric and asymmetric bi-soliton within 20 periods propagation. (e) and (f) measure pulse spacing.

Equations (7)

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i U Z b ( z ) 2 2 U T 2 + | U | 2 U = p e r t u r b a t i o n t e r m s
i U Z b ( z ) 2 2 U T 2 + | U | 2 U = i α U + i { g ( Z ) 1 + P 0 ( Z ) / P s a t ( 1 + σ 2 T 2 ) + ρ | U | 2 μ | U | 4 } U
P 0 ( Z ) = | U ( Z , T ) | 2 d T
b ( Z ) = { b 1 ( > 0 ) standard fiber b 2 ( < 0 ) gain fiber
g ( Z ) = { g 1 ( = 0 ) standard fiber g 2 ( > 0 ) gain fiber
B = b 1 l 1 + b 2 l 2 the path-averaged GVD S = b 1 l 1 + b 2 l 2 the GVD strength R = l 1 the length ratio
g 1 = 0 ( in l 1 ) , g 2 = 0.04 ( in l 2 ) , σ = 7 , ρ = 2.5 , μ = 0.58 , α = 0.55 , P s a t = 0.01

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