Abstract

Bound solitons with various phase differences and pulse separations were observed in a net-anomalous-dispersion erbium fiber laser mode-locked by carbon nanotubes, including two-soliton bound states with phase differences close to π (out of phase), 0 (in phase), and ±π/2, as well as triple-soliton bound states. To our knowledge, this is the first time that in-phase two-soliton bound states have been obtained experimentally in fiber lasers. Evolution of bound states with change of pump power was investigated, and stability of different bound states was compared. Mechanisms why and how various bound states appeared in the same fiber laser are discussed and analyzed.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Tang, B. Zhao, L. Zhao, and H. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
    [CrossRef]
  2. A. Grudinin and S. Gray, “Passive harmonic mode locking in soliton fiber lasers,” J. Opt. Soc. Am. B 14, 144–154 (1997).
    [CrossRef]
  3. N. Seong and D. Kim, “Experimental observation of stable bound solitons in a figure-eight fiber laser,” Opt. Lett. 27, 1321–1323 (2002).
    [CrossRef]
  4. S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17, 11776–11781 (2009).
    [CrossRef]
  5. S. Chouli and P. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81, 063829 (2010).
    [CrossRef]
  6. M. Grapinet and P. Grelu, “Vibrating soliton pairs in a mode-locked laser cavity,” Opt. Lett. 31, 2115–2117 (2006).
    [CrossRef]
  7. B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35, 1578–1580 (2010).
    [CrossRef]
  8. M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
    [CrossRef]
  9. A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79, 033807 (2009).
    [CrossRef]
  10. J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
    [CrossRef]
  11. A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Multi-soliton complexes in mode-locked fiber lasers,” Appl. Phys. B 104, 513–521 (2011).
    [CrossRef]
  12. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
    [CrossRef]
  13. M. Olivier, and M. Piché, “Origin of the bound states of pulses in the stretched-pulse fiber laser,” Opt. Express 17, 405–418 (2009).
    [CrossRef]
  14. B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).
    [CrossRef]
  15. B. A. Malomed, “Bound solitons in coupled nonlinear Schrödinger equations,” Phys. Rev. A 45, R8321–R8323 (1992).
    [CrossRef]
  16. N. Akhmediev, A. Ankiewicz, and J. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
    [CrossRef]
  17. D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
    [CrossRef]
  18. P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27, 966–968 (2002).
    [CrossRef]
  19. L. Zhao, D. Tang, X. Wu, D. Lei, and S. Wen, “Bound states of gain-guided solitons in a passively mode-locked fiber laser,” Opt. Lett. 32, 3191–3193 (2007).
    [CrossRef]
  20. B. Ortaç, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ilday, “Generation of parabolic bound pulses from a Yb-fiber laser,” Opt. Express 14, 6075–6083 (2006).
    [CrossRef]
  21. P. Grelu, J. Béal, and J. Soto-Crespo, “Soliton pairs in a fiber laser: from anomalous to normal average dispersion regime,” Opt. Express 11, 2238–2243 (2003).
    [CrossRef]
  22. C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.
  23. X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
    [CrossRef]
  24. X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
    [CrossRef]
  25. P. Grelu, F. Belhache, F. Gutty, and J. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
    [CrossRef]
  26. L. Gui, X. Yang, G. Zhao, X. Yang, X. Xiao, J. Zhu, and C. Yang, “Suppression of continuous lasing in a carbon nanotube polyimide film mode-locked erbium-doped fiber laser,” Appl. Opt. 50, 110–115 (2011).
    [CrossRef]
  27. L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”
  28. N. Kagi, A. Oyobe, and K. Nakamura, “Temperature dependence of the gain in erbium-doped fibers,” J. Lightwave Technol. 9, 261–265 (1991).
    [CrossRef]
  29. M. Bolshtyansky, P. Wysocki, and N. Conti, “Model of temperature dependence for gain shape of erbium-doped fiber amplifier,” J. Lightwave Technol. 18, 1533–1540 (2000).
    [CrossRef]
  30. S. Cundiff, B. Collings, and W. Knox, “Polarization locking in an isotropic, modelocked soliton Er/Yb fiber laser,” Opt. Express 1, 12–21 (1997).
    [CrossRef]
  31. J. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).
    [CrossRef]
  32. R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
    [CrossRef]
  33. A. Pilipetskii, E. Golovchenko, and C. Menyuk, “Acoustic effect in passively mode-locked fiber ring lasers,” Opt. Lett. 20, 907–909 (1995).
    [CrossRef]
  34. J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
    [CrossRef]
  35. A. Zaviyalov, P. Grelu, and F. Lederer, “Impact of slow gain dynamics on soliton molecules in mode-locked fiber lasers,” Opt. Lett. 37, 175–177 (2012).
    [CrossRef]
  36. B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
    [CrossRef]

2012 (2)

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

A. Zaviyalov, P. Grelu, and F. Lederer, “Impact of slow gain dynamics on soliton molecules in mode-locked fiber lasers,” Opt. Lett. 37, 175–177 (2012).
[CrossRef]

2011 (4)

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
[CrossRef]

L. Gui, X. Yang, G. Zhao, X. Yang, X. Xiao, J. Zhu, and C. Yang, “Suppression of continuous lasing in a carbon nanotube polyimide film mode-locked erbium-doped fiber laser,” Appl. Opt. 50, 110–115 (2011).
[CrossRef]

A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Multi-soliton complexes in mode-locked fiber lasers,” Appl. Phys. B 104, 513–521 (2011).
[CrossRef]

2010 (2)

2009 (4)

S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17, 11776–11781 (2009).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
[CrossRef]

M. Olivier, and M. Piché, “Origin of the bound states of pulses in the stretched-pulse fiber laser,” Opt. Express 17, 405–418 (2009).
[CrossRef]

A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79, 033807 (2009).
[CrossRef]

2007 (2)

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
[CrossRef]

L. Zhao, D. Tang, X. Wu, D. Lei, and S. Wen, “Bound states of gain-guided solitons in a passively mode-locked fiber laser,” Opt. Lett. 32, 3191–3193 (2007).
[CrossRef]

2006 (2)

2005 (2)

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

D. Tang, B. Zhao, L. Zhao, and H. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
[CrossRef]

2004 (1)

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

2003 (4)

2002 (2)

2000 (1)

1998 (1)

J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[CrossRef]

1997 (3)

1995 (1)

1992 (1)

B. A. Malomed, “Bound solitons in coupled nonlinear Schrödinger equations,” Phys. Rev. A 45, R8321–R8323 (1992).
[CrossRef]

1991 (2)

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

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature dependence of the gain in erbium-doped fibers,” J. Lightwave Technol. 9, 261–265 (1991).
[CrossRef]

Akhmediev, N.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
[CrossRef]

J. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[CrossRef]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, and J. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[CrossRef]

Béal, J.

Bekker, A.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Belhache, F.

Bergman, K.

J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[CrossRef]

Bolshtyansky, M.

Brunel, M.

B. Ortaç, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ilday, “Generation of parabolic bound pulses from a Yb-fiber laser,” Opt. Express 14, 6075–6083 (2006).
[CrossRef]

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

Chartier, T.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

Chédot, C.

Chouli, S.

S. Chouli and P. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81, 063829 (2010).
[CrossRef]

S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17, 11776–11781 (2009).
[CrossRef]

Collings, B.

J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[CrossRef]

S. Cundiff, B. Collings, and W. Knox, “Polarization locking in an isotropic, modelocked soliton Er/Yb fiber laser,” Opt. Express 1, 12–21 (1997).
[CrossRef]

Conti, N.

Cundiff, S.

Devine, N.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
[CrossRef]

Du, J.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Egorov, O.

A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Multi-soliton complexes in mode-locked fiber lasers,” Appl. Phys. B 104, 513–521 (2011).
[CrossRef]

B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35, 1578–1580 (2010).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Fischer, B.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Gat, O.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Golovchenko, E.

Grapinet, M.

Gray, S.

Grelu, P.

A. Zaviyalov, P. Grelu, and F. Lederer, “Impact of slow gain dynamics on soliton molecules in mode-locked fiber lasers,” Opt. Lett. 37, 175–177 (2012).
[CrossRef]

S. Chouli and P. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81, 063829 (2010).
[CrossRef]

S. Chouli and P. Grelu, “Rains of solitons in a fiber laser,” Opt. Express 17, 11776–11781 (2009).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
[CrossRef]

M. Grapinet and P. Grelu, “Vibrating soliton pairs in a mode-locked laser cavity,” Opt. Lett. 31, 2115–2117 (2006).
[CrossRef]

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

J. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).
[CrossRef]

P. Grelu, F. Belhache, F. Gutty, and J. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
[CrossRef]

P. Grelu, J. Béal, and J. Soto-Crespo, “Soliton pairs in a fiber laser: from anomalous to normal average dispersion regime,” Opt. Express 11, 2238–2243 (2003).
[CrossRef]

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

Grudinin, A.

Gui, L.

L. Gui, X. Yang, G. Zhao, X. Yang, X. Xiao, J. Zhu, and C. Yang, “Suppression of continuous lasing in a carbon nanotube polyimide film mode-locked erbium-doped fiber laser,” Appl. Opt. 50, 110–115 (2011).
[CrossRef]

L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”

Gutty, F.

Hao, Y.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Hideur, A.

B. Ortaç, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ilday, “Generation of parabolic bound pulses from a Yb-fiber laser,” Opt. Express 14, 6075–6083 (2006).
[CrossRef]

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

Hohmuth, R.

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Ilday, F.

Iliew, R.

A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Multi-soliton complexes in mode-locked fiber lasers,” Appl. Phys. B 104, 513–521 (2011).
[CrossRef]

B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35, 1578–1580 (2010).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Kagi, N.

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature dependence of the gain in erbium-doped fibers,” J. Lightwave Technol. 9, 261–265 (1991).
[CrossRef]

Kim, D.

Knox, W.

J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[CrossRef]

S. Cundiff, B. Collings, and W. Knox, “Polarization locking in an isotropic, modelocked soliton Er/Yb fiber laser,” Opt. Express 1, 12–21 (1997).
[CrossRef]

Komarov, A.

A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79, 033807 (2009).
[CrossRef]

Komarov, K.

A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79, 033807 (2009).
[CrossRef]

Kutz, J.

J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[CrossRef]

Leblond, H.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

Lederer, F.

A. Zaviyalov, P. Grelu, and F. Lederer, “Impact of slow gain dynamics on soliton molecules in mode-locked fiber lasers,” Opt. Lett. 37, 175–177 (2012).
[CrossRef]

A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Multi-soliton complexes in mode-locked fiber lasers,” Appl. Phys. B 104, 513–521 (2011).
[CrossRef]

B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35, 1578–1580 (2010).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Lei, D.

Li, H.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Li, X.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”

Limpert, J.

B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35, 1578–1580 (2010).
[CrossRef]

B. Ortaç, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ilday, “Generation of parabolic bound pulses from a Yb-fiber laser,” Opt. Express 14, 6075–6083 (2006).
[CrossRef]

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Lu, C.

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Luan, X.

X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
[CrossRef]

Malomed, B. A.

B. A. Malomed, “Bound solitons in coupled nonlinear Schrödinger equations,” Phys. Rev. A 45, R8321–R8323 (1992).
[CrossRef]

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

Man, W.

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Meng, Y.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Menyuk, C.

Mitschke, F.

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

Nakamura, K.

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature dependence of the gain in erbium-doped fibers,” J. Lightwave Technol. 9, 261–265 (1991).
[CrossRef]

Nielsen, C. K.

B. Ortaç, A. Zaviyalov, C. K. Nielsen, O. Egorov, R. Iliew, J. Limpert, F. Lederer, and A. Tünnermann, “Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser,” Opt. Lett. 35, 1578–1580 (2010).
[CrossRef]

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Olivier, M.

Ortac, B.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Ortaç, B.

Oyobe, A.

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature dependence of the gain in erbium-doped fibers,” J. Lightwave Technol. 9, 261–265 (1991).
[CrossRef]

Pagel, T.

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

Piché, M.

Pilipetskii, A.

Richter, W.

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Sanchez, F.

A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79, 033807 (2009).
[CrossRef]

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

Schreiber, T.

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Seong, N.

Shen, D.

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Smulakovsky, V.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Soto-Crespo, J.

Soto-Crespo, J. M.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
[CrossRef]

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

Stratmann, M.

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

Tam, H.

D. Tang, B. Zhao, L. Zhao, and H. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
[CrossRef]

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Tang, D.

X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
[CrossRef]

L. Zhao, D. Tang, X. Wu, D. Lei, and S. Wen, “Bound states of gain-guided solitons in a passively mode-locked fiber laser,” Opt. Lett. 32, 3191–3193 (2007).
[CrossRef]

D. Tang, B. Zhao, L. Zhao, and H. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
[CrossRef]

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Tunnermann, A.

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

Tünnermann, A.

Weill, R.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Wen, S.

Wu, X.

X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
[CrossRef]

L. Zhao, D. Tang, X. Wu, D. Lei, and S. Wen, “Bound states of gain-guided solitons in a passively mode-locked fiber laser,” Opt. Lett. 32, 3191–3193 (2007).
[CrossRef]

Wysocki, P.

Xiao, X.

L. Gui, X. Yang, G. Zhao, X. Yang, X. Xiao, J. Zhu, and C. Yang, “Suppression of continuous lasing in a carbon nanotube polyimide film mode-locked erbium-doped fiber laser,” Appl. Opt. 50, 110–115 (2011).
[CrossRef]

L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”

Yang, C.

L. Gui, X. Yang, G. Zhao, X. Yang, X. Xiao, J. Zhu, and C. Yang, “Suppression of continuous lasing in a carbon nanotube polyimide film mode-locked erbium-doped fiber laser,” Appl. Opt. 50, 110–115 (2011).
[CrossRef]

L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”

Yang, X.

Yang, Z.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Zaviyalov, A.

Zavyalov, A.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Zhang, Q.

X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
[CrossRef]

Zhang, S.

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Zhao, B.

D. Tang, B. Zhao, L. Zhao, and H. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
[CrossRef]

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Zhao, G.

Zhao, L.

Zhu, H.

L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”

Zhu, J.

Appl. Opt. (1)

Appl. Phys. B (1)

A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Multi-soliton complexes in mode-locked fiber lasers,” Appl. Phys. B 104, 513–521 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Kutz, B. Collings, K. Bergman, and W. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34, 1749–1757 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, “Generation of bound states of three ultrashort pulses with a passively mode-locked high-power Yb-doped double-clad fiber laser,” IEEE Photon. Technol. Lett. 16, 1274–1276 (2004).
[CrossRef]

J. Lightwave Technol. (2)

N. Kagi, A. Oyobe, and K. Nakamura, “Temperature dependence of the gain in erbium-doped fibers,” J. Lightwave Technol. 9, 261–265 (1991).
[CrossRef]

M. Bolshtyansky, P. Wysocki, and N. Conti, “Model of temperature dependence for gain shape of erbium-doped fiber amplifier,” J. Lightwave Technol. 18, 1533–1540 (2000).
[CrossRef]

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

Laser Phys. (1)

X. Li, S. Zhang, Y. Meng, Y. Hao, H. Li, J. Du, and Z. Yang, “Observation of soliton bound states in a graphene mode locked erbium-doped fiber laser,” Laser Phys. 22, 774–777 (2012).
[CrossRef]

Opt. Commun. (1)

X. Wu, D. Tang, X. Luan, and Q. Zhang, “Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber,” Opt. Commun. 284, 3614–3618 (2011).
[CrossRef]

Opt. Express (5)

Opt. Lett. (8)

Phys. Rev. A (7)

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[CrossRef]

A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79, 033807 (2009).
[CrossRef]

S. Chouli and P. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81, 063829 (2010).
[CrossRef]

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

B. A. Malomed, “Bound solitons in coupled nonlinear Schrödinger equations,” Phys. Rev. A 45, R8321–R8323 (1992).
[CrossRef]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers,” Phys. Rev. A 80, 043829 (2009).
[CrossRef]

D. Tang, B. Zhao, D. Shen, C. Lu, W. Man, and H. Tam, “Compound pulse solitons in a fiber ring laser,” Phys. Rev. A 68, 013816 (2003).
[CrossRef]

Phys. Rev. E (2)

D. Tang, B. Zhao, L. Zhao, and H. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
[CrossRef]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[CrossRef]

Other (2)

C. K. Nielsen, B. Ortac, T. Schreiber, J. Limpert, R. Hohmuth, W. Richter, and A. Tunnermann, “Single pulse and bound state operation of a self-starting self-similar all-PM Yb-doped fiber laser,” in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds. (SPIE, 2006), pp. 10217.

L. Gui, X. Li, X. Xiao, H. Zhu, and C. Yang, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China, are preparing a manuscript to be called “Widely-spaced bound states in a soliton fiber laser with graphene saturable absorber.”

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Spectra of two-soliton bound states with θ1= (a) π, (b) 0, (c) π/2, and (d) π/2 according to Eq. (2). Blue dotted curve is for single soliton (unbound), and black solid curve is for bound solitons. For all figures, 0.8 ps chirp-free sech-shaped pulses with center wavelength 1560 nm and pulse separation 6 ps were used.

Fig. 2.
Fig. 2.

Spectrum of a triple-soliton bound state with θ1=π and θ2=0 according to Eq. (5). Blue dotted curve is for single soliton (unbound), and black solid curve is for bound solitons. Here 0.8 ps chirp-free sech-shaped pulses with center wavelength 1560 nm and pulse separation t1=4ps were used.

Fig. 3.
Fig. 3.

Schematic of the laser cavity setup.

Fig. 4.
Fig. 4.

(a) Experimental spectrum (black solid curve) of an out-of-phase two-soliton bound state and (b) corresponding autocorrelation trace, (a) also gives fitting results for the bound state (red dashed curve) and its envelope (unbound).

Fig. 5.
Fig. 5.

In-phase two-soliton bound states: (a) experimental optical spectrum and fitting results with sech-shaped pulses, (b) experimental optical spectrum and fitting results with Gaussian-shaped pulses, and (c) corresponding autocorrelation trace. (d) Optical spectra of another in-phase bound state. Sech-profiled pulses were used for fitting if no special explanation is given in this paper.

Fig. 6.
Fig. 6.

(a) Experimental and fitting spectra of a π/2 phase-difference two-soliton bound state. (b) Experimental and fitting spectra of a π/2 phase-difference two-soliton bound state. Fitting spectra of the envelope (unbound) are also presented.

Fig. 7.
Fig. 7.

Spectral evolution of bound states with decreasing pump power. (a) Triple-soliton bound state when pump=139mW. Black solid curve is for experimental spectrum, red dashed curve is for fitting spectrum with parameters marked in the figure, and blue dotted curve is for fitting spectrum of a single soliton (unbound). (b) Two-soliton bound state when pump=128mW. (c) Two-soliton bound state when pump=118mW. Modulation period and calculated pulse separation are marked in (b) and (c).

Fig. 8.
Fig. 8.

Sequential spectral evolution from (a) to (d) of a two-soliton bound state under the lab environment without intentional change of experimental conditions. Evolution from (a) to (c) took several minutes, and (d) was stable for at least half an hour. Modulation period, pulse separation, and phase difference are marked in the figures.

Fig. 9.
Fig. 9.

Spectral evolution of a two-soliton bound state with phase difference from π/2 to 0.

Fig. 10.
Fig. 10.

All observed two-soliton bound states in our experiments.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

F(ν)+F(ν)exp(j2πνt1)exp(jθ1)=F(ν)exp[j(πνt1θ12)]·2cos(πνt1θ12).
|F(ν)+F(ν)exp(j2πνt1)exp(jθ1)|2=2|F(ν)|2·[1+cos(2πνt1θ1)].
Ik(Ik1+Ik+1)/2(k=2,3,),
F(ν)+F(ν)exp(j2πνt1)exp(jθ1)+F(ν)exp[j2πν·(2t1)]exp(jθ2)=F(ν)exp[j(2πνt1θ22)]·{2cos(2πνt1θ22)+exp[j(θ1θ22)]}.
|F(ν)|2·[2cos(2πνt1)1]2=|F(ν)|2·[2cos(4πνt1)4cos(2πνt1)+3].

Metrics