Abstract

The evolution of soliton molecules emphasizes the complex soliton dynamics akin to matter molecules. Beyond the simplest soliton molecule—a soliton pair constituted by two bound pulses—soliton molecules with more constituents have more degrees of freedom because of the temporal pulse separations and relative phases. Here we detailedly characterize the transient dynamics of soliton triplets in fiber lasers by using the dispersive Fourier transform measurement. A particular form of leading, central, and tailing pulses is constructed to shed new light on more intriguing scenarios and fuel the molecular analogy. Especially the vibrating dynamics of the central and tailing pulses are captured near the regime of equally spaced soliton triplets, which is reminiscent of the recurrent timing jitters within multi-pulse structures. Further insights enable access into a universal form of unequally spaced soliton triplets interpreted as 2+1 soliton molecules. Different binding strengths of intramolecular and intermolecular bonds are validated with respect to the diverse internal motions involved in this soliton triplet molecule. All these findings unveil the transient dynamics with more degrees of freedom as well as highlight the possible application for all-optical bit storage.

© 2020 Chinese Laser Press

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. J. Zabusky and M. D. Kruskal, “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett. 15, 240–243 (1965).
    [Crossref]
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [Crossref]
  3. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
    [Crossref]
  4. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [Crossref]
  5. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
    [Crossref]
  6. N. Akhmediev and A. Ankiewicz, “Dissipative solitons: from optics to biology and medicine,” in Lecture Notes in Physics (Springer, 2008).
  7. G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
    [Crossref]
  8. 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]
  9. D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. Tam, “Soliton interaction in a fiber ring laser,” Phys. Rev. E 72, 016616 (2005).
    [Crossref]
  10. M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
    [Crossref]
  11. B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).
    [Crossref]
  12. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
    [Crossref]
  13. 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]
  14. L. Gui, X. Xiao, and C. Yang, “Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser,” J. Opt. Soc. Am. B 30, 158–164 (2013).
    [Crossref]
  15. J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
    [Crossref]
  16. Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
    [Crossref]
  17. Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).
  18. Y. Wang, D. Mao, X. Gan, L. Han, C. Ma, T. Xi, Y. Zhang, W. Shang, S. Hua, and J. Zhao, “Harmonic mode locking of bound-state solitons fiber laser based on MoS2 saturable absorber,” Opt. Express 23, 205–210 (2015).
    [Crossref]
  19. 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]
  20. 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]
  21. 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]
  22. M. A. Abdelalim, Y. Logvin, D. A. Khalil, and H. Anis, “Steady and oscillating multiple dissipative solitons in normal-dispersion mode-locked Yb-doped fiber laser,” Opt. Express 17, 13128–13139 (2009).
    [Crossref]
  23. A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
    [Crossref]
  24. G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
    [Crossref]
  25. J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
    [Crossref]
  26. Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
    [Crossref]
  27. X. Liu and Y. Cui, “Revealing the behavior of soliton buildup in a mode-locked laser,” Adv. Photon. 1, 016003 (2019).
    [Crossref]
  28. X. Liu, D. Popa, and N. Akhmediev, “Revealing the transition dynamics from Q switching to mode locking in a soliton laser,” Phys. Rev. Lett. 123, 093901 (2019).
    [Crossref]
  29. X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photon. Rev. 13, 1800333 (2019).
    [Crossref]
  30. J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1800009 (2018).
    [Crossref]
  31. H. J. Chen, M. Liu, J. Yao, S. Hu, J. B. He, A. P. Luo, W. C. Xu, and Z. C. Luo, “Buildup dynamics of dissipative soliton in an ultrafast fiber laser with net-normal dispersion,” Opt. Express 26, 2972–2982 (2018).
    [Crossref]
  32. A. F. J. Runge, N. G. R. Broderick, and M. Erkintalo, “Observation of soliton explosions in a passively mode-locked fiber laser,” Optica 2, 36–39 (2015).
    [Crossref]
  33. Y. Yu, Z. Luo, J. Kang, and K. K. Y. Wong, “Mutually ignited soliton explosions in a fiber laser,” Opt. Lett. 43, 4132–4135 (2018).
    [Crossref]
  34. Z. W. Wei, M. Liu, S. X. Ming, A. P. Luo, W. C. Xu, and Z. C. Luo, “Pulsating soliton with chaotic behavior in a fiber laser,” Opt. Lett. 43, 5965–5968 (2018).
    [Crossref]
  35. Y. Q. Du, Z. W. Xu, and X. W. Shu, “Spatio-spectral dynamics of the pulsating dissipative solitons in a normal-dispersion fiber laser,” Opt. Lett. 43, 3602–3605 (2018).
    [Crossref]
  36. J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
    [Crossref]
  37. M. Liu, A. Luo, Z. Luo, and W. Xu, “Dynamic trapping of a polarization rotation vector soliton in a fiber laser,” Opt. Lett. 42, 330–333 (2017).
    [Crossref]
  38. K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
    [Crossref]
  39. X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121, 023905 (2018).
    [Crossref]
  40. M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
    [Crossref]
  41. G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
    [Crossref]
  42. Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
    [Crossref]
  43. P. Grelu and N. Akhmediev, “Group interactions of dissipative solitons in a laser cavity: the case of 2+1,” Opt. Express 12, 3184–3189 (2004).
    [Crossref]

2019 (5)

Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
[Crossref]

X. Liu and Y. Cui, “Revealing the behavior of soliton buildup in a mode-locked laser,” Adv. Photon. 1, 016003 (2019).
[Crossref]

X. Liu, D. Popa, and N. Akhmediev, “Revealing the transition dynamics from Q switching to mode locking in a soliton laser,” Phys. Rev. Lett. 123, 093901 (2019).
[Crossref]

X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photon. Rev. 13, 1800333 (2019).
[Crossref]

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

2018 (9)

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121, 023905 (2018).
[Crossref]

M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
[Crossref]

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1800009 (2018).
[Crossref]

H. J. Chen, M. Liu, J. Yao, S. Hu, J. B. He, A. P. Luo, W. C. Xu, and Z. C. Luo, “Buildup dynamics of dissipative soliton in an ultrafast fiber laser with net-normal dispersion,” Opt. Express 26, 2972–2982 (2018).
[Crossref]

Y. Yu, Z. Luo, J. Kang, and K. K. Y. Wong, “Mutually ignited soliton explosions in a fiber laser,” Opt. Lett. 43, 4132–4135 (2018).
[Crossref]

Z. W. Wei, M. Liu, S. X. Ming, A. P. Luo, W. C. Xu, and Z. C. Luo, “Pulsating soliton with chaotic behavior in a fiber laser,” Opt. Lett. 43, 5965–5968 (2018).
[Crossref]

Y. Q. Du, Z. W. Xu, and X. W. Shu, “Spatio-spectral dynamics of the pulsating dissipative solitons in a normal-dispersion fiber laser,” Opt. Lett. 43, 3602–3605 (2018).
[Crossref]

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

2017 (5)

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

M. Liu, A. Luo, Z. Luo, and W. Xu, “Dynamic trapping of a polarization rotation vector soliton in a fiber laser,” Opt. Lett. 42, 330–333 (2017).
[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

2016 (2)

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
[Crossref]

2015 (2)

2013 (2)

L. Gui, X. Xiao, and C. Yang, “Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser,” J. Opt. Soc. Am. B 30, 158–164 (2013).
[Crossref]

J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
[Crossref]

2012 (1)

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

2011 (1)

G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
[Crossref]

2010 (1)

2009 (2)

M. A. Abdelalim, Y. Logvin, D. A. Khalil, and H. Anis, “Steady and oscillating multiple dissipative solitons in normal-dispersion mode-locked Yb-doped fiber laser,” Opt. Express 17, 13128–13139 (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]

2007 (2)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[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]

2005 (2)

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]

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

2004 (2)

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[Crossref]

P. Grelu and N. Akhmediev, “Group interactions of dissipative solitons in a laser cavity: the case of 2+1,” Opt. Express 12, 3184–3189 (2004).
[Crossref]

2001 (1)

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]

1999 (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref]

1997 (1)

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

1991 (1)

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

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

1965 (1)

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett. 15, 240–243 (1965).
[Crossref]

Abdelalim, M. A.

Akhmediev, N.

X. Liu, D. Popa, and N. Akhmediev, “Revealing the transition dynamics from Q switching to mode locking in a soliton laser,” Phys. Rev. Lett. 123, 093901 (2019).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[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]

P. Grelu and N. Akhmediev, “Group interactions of dissipative solitons in a laser cavity: the case of 2+1,” Opt. Express 12, 3184–3189 (2004).
[Crossref]

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[Crossref]

N. Akhmediev and A. Ankiewicz, “Dissipative solitons: from optics to biology and medicine,” in Lecture Notes in Physics (Springer, 2008).

Akhmediev, N. N.

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

Andral, U.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Anis, H.

Ankiewicz, A.

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

N. Akhmediev and A. Ankiewicz, “Dissipative solitons: from optics to biology and medicine,” in Lecture Notes in Physics (Springer, 2008).

Barland, S.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Broderick, N.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Broderick, N. G. R.

Chen, H. J.

Cheng, J.

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Churkin, D. V.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Coillet, A.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

Cui, H.

M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
[Crossref]

Cui, Y.

X. Liu and Y. Cui, “Revealing the behavior of soliton buildup in a mode-locked laser,” Adv. Photon. 1, 016003 (2019).
[Crossref]

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121, 023905 (2018).
[Crossref]

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]

Drummond, P. D.

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]

Du, Y. Q.

Egorov, O.

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]

Erkintalo, M.

Fu, S.

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Gan, X.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

Grapinet, M.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[Crossref]

Grelu, P.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[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]

P. Grelu and N. Akhmediev, “Group interactions of dissipative solitons in a laser cavity: the case of 2+1,” Opt. Express 12, 3184–3189 (2004).
[Crossref]

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[Crossref]

Gui, L.

Han, L.

He, J. B.

He, W.

M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
[Crossref]

Herink, G.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

Hu, S.

Hua, S.

Iliew, R.

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]

Jalali, B.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Jiang, X.

M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
[Crossref]

Kang, J.

Khalil, D. A.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Krupa, K.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Kruskal, M. D.

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett. 15, 240–243 (1965).
[Crossref]

Kurtz, F.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

Lederer, F.

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]

Li, H.

M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
[Crossref]

Li, L.

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Limpert, J.

Liu, A. Q.

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]

Liu, B.

Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
[Crossref]

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Liu, D.

Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
[Crossref]

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Liu, M.

Liu, T.

Liu, X.

X. Liu, D. Popa, and N. Akhmediev, “Revealing the transition dynamics from Q switching to mode locking in a soliton laser,” Phys. Rev. Lett. 123, 093901 (2019).
[Crossref]

X. Liu and Y. Cui, “Revealing the behavior of soliton buildup in a mode-locked laser,” Adv. Photon. 1, 016003 (2019).
[Crossref]

X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photon. Rev. 13, 1800333 (2019).
[Crossref]

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121, 023905 (2018).
[Crossref]

Logvin, Y.

Luo, A.

M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
[Crossref]

M. Liu, A. Luo, Z. Luo, and W. Xu, “Dynamic trapping of a polarization rotation vector soliton in a fiber laser,” Opt. Lett. 42, 330–333 (2017).
[Crossref]

Luo, A. P.

Luo, S.

J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
[Crossref]

Luo, Y.

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Luo, Y. Y.

Luo, Z.

Luo, Z. C.

Ma, C.

Mahjoubfar, A.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Malomed, B. A.

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

Man, W. S.

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]

Mao, D.

Mei, J. W.

G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
[Crossref]

Ming, S. X.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

Nielsen, C. K.

Nithyanandan, K.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Ortaç, B.

Pang, M.

X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photon. Rev. 13, 1800333 (2019).
[Crossref]

M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
[Crossref]

Peng, J.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1800009 (2018).
[Crossref]

J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
[Crossref]

Popa, D.

X. Liu, D. Popa, and N. Akhmediev, “Revealing the transition dynamics from Q switching to mode locking in a soliton laser,” Phys. Rev. Lett. 123, 093901 (2019).
[Crossref]

Qin, Y.

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Ropers, C.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Runge, A. F. J.

Russell, P. St. J.

M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
[Crossref]

Segev, M.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref]

Shang, W.

Shen, Q.

J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
[Crossref]

Shu, X. W.

Shum, P.

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Shum, P. P.

Solli, D. R.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Sorokina, M.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

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]

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[Crossref]

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

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

Sugavanam, S.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

Sun, Q.

Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
[Crossref]

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

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 72, 016616 (2005).
[Crossref]

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]

Tang, D.

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Tang, D. Y.

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]

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

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]

Tang, X.

Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
[Crossref]

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Tarasov, N.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

Tchofo-Dinda, P.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

Tünnermann, A.

Turitsyn, S. K.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

Wang, Y.

Wang, Z. Q.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

Wei, Z. W.

Wong, K. K. Y.

Xi, T.

Xia, R.

Xiang, Y.

Y. Y. Luo, Y. Xiang, T. Liu, B. Liu, R. Xia, Z. Yan, X. Tang, D. Liu, Q. Sun, and P. P. Shum, “Real-time access to the coexistence of soliton singlets and molecules in an all-fiber laser,” Opt. Lett. 44, 4263–4266 (2019).
[Crossref]

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

Xiao, X.

Xiao, X. S.

G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
[Crossref]

Xu, W.

M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
[Crossref]

M. Liu, A. Luo, Z. Luo, and W. Xu, “Dynamic trapping of a polarization rotation vector soliton in a fiber laser,” Opt. Lett. 42, 330–333 (2017).
[Crossref]

Xu, W. C.

Xu, Z. W.

Yan, Z.

Yang, C.

Yang, C. X.

G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
[Crossref]

Yao, J.

Yao, X.

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121, 023905 (2018).
[Crossref]

Yu, Y.

Zabusky, N. J.

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett. 15, 240–243 (1965).
[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]

Zeng, H.

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1800009 (2018).
[Crossref]

Zhan, L.

J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
[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 72, 016616 (2005).
[Crossref]

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]

Zhao, G. Z.

G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
[Crossref]

Zhao, J.

Zhao, L.

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Zhao, L. M.

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]

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

Adv. Photon. (1)

X. Liu and Y. Cui, “Revealing the behavior of soliton buildup in a mode-locked laser,” Adv. Photon. 1, 016003 (2019).
[Crossref]

Chin. Phys. Lett. (1)

G. Z. Zhao, X. S. Xiao, J. W. Mei, and C. X. Yang, “Multiple dissipative solitons in a long-cavity normal-dispersion mode-locked Yb-doped fiber laser,” Chin. Phys. Lett. 29, 034207 (2011).
[Crossref]

Commun. Phys. (1)

J. Peng, M. Sorokina, S. Sugavanam, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and H. Zeng, “Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers,” Commun. Phys. 1, 20 (2018).
[Crossref]

IEEE Photon. J. (1)

Y. Luo, Y. Xiang, B. Liu, Y. Qin, Q. Sun, X. Tang, and P. Shum, “Manipulation of dispersion-managed soliton molecules in a near zero-dispersion fiber laser,” IEEE Photon. J. 10, 7105210 (2018).

IEEE Photonics Technol. Lett. (1)

J. Peng, L. Zhan, S. Luo, and Q. Shen, “Generation of soliton molecules in a normal-dispersion fiber laser,” IEEE Photonics Technol. Lett. 25, 948–951 (2013).
[Crossref]

J. Opt. (1)

M. Liu, H. Li, A. Luo, H. Cui, W. Xu, and Z. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20, 034010 (2018).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (2)

X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photon. Rev. 13, 1800333 (2019).
[Crossref]

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photon. Rev. 12, 1800009 (2018).
[Crossref]

Nat. Commun. (1)

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10, 830 (2019).
[Crossref]

Nat. Photonics (4)

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

M. Pang, W. He, X. Jiang, and P. St. J. Russell, “All-optical bit storage in a fibre laser by optomechanically bound states of solitons,” Nat. Photonics 10, 454–458 (2016).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[Crossref]

Nature (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (6)

Optica (1)

Phys. Rev. A (4)

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. 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]

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

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]

Phys. Rev. E (3)

D. Y. Tang, B. Zhao, L. M. Zhao, and H. Y. 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]

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[Crossref]

Phys. Rev. Lett. (6)

X. Liu, D. Popa, and N. Akhmediev, “Revealing the transition dynamics from Q switching to mode locking in a soliton laser,” Phys. Rev. Lett. 123, 093901 (2019).
[Crossref]

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

N. J. Zabusky and M. D. Kruskal, “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett. 15, 240–243 (1965).
[Crossref]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901 (2017).
[Crossref]

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121, 023905 (2018).
[Crossref]

Sci. Rep. (1)

Y. Luo, J. Cheng, B. Liu, Q. Sun, L. Li, S. Fu, D. Tang, L. Zhao, and D. Liu, “Group-velocity-locked vector soliton molecules in fiber lasers,” Sci. Rep. 7, 2369 (2017).
[Crossref]

Science (2)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref]

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356, 50–54 (2017).
[Crossref]

Other (1)

N. Akhmediev and A. Ankiewicz, “Dissipative solitons: from optics to biology and medicine,” in Lecture Notes in Physics (Springer, 2008).

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 (7)

Fig. 1.
Fig. 1. (a) Schematic diagram of the NPR-based mode-locked fiber laser and the real-time characterization setup; (b) graphical representation of leading, central, and tailing pulses; (c) sketch of the temporal distribution, spectral interferograms, and first-order autocorrelation traces for the equally spaced soliton triplet, vibrating soliton triplet, and unequally spaced soliton triplet. DFT, dispersive Fourier transform; FFT, fast Fourier transform.
Fig. 2.
Fig. 2. Stationary equally spaced soliton triplet. (a) Averaged DFT spectrum (black line) and OSA-measured spectrum (red line); (b), (c) pulse trains before and after DFT; (d) 2D contour plot of the shot-to-shot spectra, and the inset shows the close-up; (e) 2D contour plot of the shot-to-shot first-order autocorrelation traces; (f), (g) retrieved temporal separations and relative phases of the central pulse and tailing pulse.
Fig. 3.
Fig. 3. Vibrating equally spaced soliton triplet. (a) 2D contour plot of the shot-to-shot spectra; (b) 2D contour plot of the shot-to-shot first-order autocorrelation traces; (c), (d) close-ups of the spectra and autocorrelation traces; (e) retrieved temporal separations of the central pulse and tailing pulse; (f), (g) trajectories of (τ12, φ12) and (τ13, φ13) in the interaction spaces.
Fig. 4.
Fig. 4. Vibrating equally spaced soliton triplet. (a) 2D contour plot of the shot-to-shot spectra; (b) 2D contour plot of the shot-to-shot first-order autocorrelation traces; (c), (d) close-ups of the spectra and autocorrelation traces; (e) retrieved relative phases of the central pulse (top panel) and tailing pulse (bottom panel); (f) retrieved temporal separation of the central pulse.
Fig. 5.
Fig. 5. Unequally spaced soliton triplet with oscillating phase. (a) 2D contour plot of the shot-to-shot spectra; (b), (c) close-ups of the spectra with different magnifications; (d) 2D contour plot of the shot-to-shot first-order autocorrelation traces; (e) retrieved relative phases of φ12, φ23, and φ13, and the insets show the close-ups; (f) trajectories in the interaction plane; (g) trajectories of (τ12, φ12) and (τ13, φ13) in the interaction space; (h) oscillatory frequency of the phase evolution for the shaking soliton molecule.
Fig. 6.
Fig. 6. Unequally spaced soliton triplet with stepping phase evolution. (a) 2D contour plot of the shot-to-shot spectra; (b) 2D contour plot of the shot-to-shot first-order autocorrelation traces; (c) retrieved temporal separations of τ12, τ23, and τ13; (d) retrieved relative phases of φ12, φ23, and φ13; (e) trajectories of (τ12, φ12) and (τ13, φ13) in the interaction space.
Fig. 7.
Fig. 7. Analytical fit for the soliton triplet with stepping phase evolution. (a) Evolution of the temporal separations and (b) the relative phases between constituents of the triplet; (c) temporal distribution; (d) corresponding evolution of the spectral intensity profile; (e) corresponding first-order autocorrelation trace.

Equations (1)

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

φ13=cos(z)+z1,