Abstract

We report experimental measurements of structural soliton pairs in a mode-locked Yb-doped fiber laser. The quantization of the temporal separation and relative phase between the pair of dissipative solitons is clearly observed and, most interestingly, the transitions between different states as the pump power is varied show abrupt jumps. This is a clear signature of the discrete nature of the stable pair states. The typical separations are of the order of 1 ps and the separation changes are of the order of 100 fs, while the relative phase of the pulses jumps between π/2 → π/4 → π/2 as the pump power is increased.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. L. B. A. Mélo, G. F. R. Palacios, P. V. Carelli, L. H. Acioli, J. R. R. Leite, and M. H. G. de Miranda, “Deterministic chaos in an ytterbium-doped mode-locked fiber laser,” Opt. Express 26(10), 13686–13692 (2018).
    [Crossref]
  2. A. F. J. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, “Raman rogue waves in a partially mode-locked fiber laser,” Opt. Lett. 39(2), 319–322 (2014).
    [Crossref]
  3. A. F. J. Runge, N. G. R. Broderick, and M. Erkintalo, “Observation of soliton explosions in a passively mode-locked fiber laser,” Optica 2(1), 36–39 (2015).
    [Crossref]
  4. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex ginzburg-landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
    [Crossref]
  5. F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B 27(10), 2068–2077 (2010).
    [Crossref]
  6. B. A. Malomed, “Bound solitons in the nonlinear schrödinger–ginzburg-landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
    [Crossref]
  7. J. M. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28(19), 1757–1759 (2003).
    [Crossref]
  8. X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
    [Crossref]
  9. 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(1), 830 (2019).
    [Crossref]
  10. 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(6333), 50–54 (2017).
    [Crossref]
  11. K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
    [Crossref]
  12. P. Wang, X. Xiao, and C. Yang, “Quantized pulse separations of phase-locked soliton molecules in a dispersion-managed mode-locked tm fiber laser at 2μm,” Opt. Lett. 42(1), 29–32 (2017).
    [Crossref]
  13. 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(1), 158–164 (2013).
    [Crossref]
  14. B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
    [Crossref]
  15. C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
    [Crossref]
  16. B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.
  17. 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(10), 1578–1580 (2010).
    [Crossref]
  18. 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(24), 243901 (2017).
    [Crossref]
  19. A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79(3), 033807 (2009).
    [Crossref]
  20. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993).
    [Crossref]
  21. M. Olivier and M. Piché, “Origin of the bound states of pulses in the stretched-pulse fiber laser,” Opt. Express 17(2), 405–418 (2009).
    [Crossref]
  22. P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20(5), 863–870 (2003).
    [Crossref]
  23. P. 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]

2019 (2)

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(1), 830 (2019).
[Crossref]

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

2018 (1)

2017 (3)

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(24), 243901 (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(6333), 50–54 (2017).
[Crossref]

P. Wang, X. Xiao, and C. Yang, “Quantized pulse separations of phase-locked soliton molecules in a dispersion-managed mode-locked tm fiber laser at 2μm,” Opt. Lett. 42(1), 29–32 (2017).
[Crossref]

2015 (1)

2014 (3)

A. F. J. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, “Raman rogue waves in a partially mode-locked fiber laser,” Opt. Lett. 39(2), 319–322 (2014).
[Crossref]

X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
[Crossref]

B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
[Crossref]

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(1), 158–164 (2013).
[Crossref]

K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

2010 (2)

2009 (2)

A. Komarov, K. Komarov, and F. Sanchez, “Quantization of binding energy of structural solitons in passive mode-locked fiber lasers,” Phys. Rev. A 79(3), 033807 (2009).
[Crossref]

M. Olivier and M. Piché, “Origin of the bound states of pulses in the stretched-pulse fiber laser,” Opt. Express 17(2), 405–418 (2009).
[Crossref]

2003 (3)

1997 (1)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex ginzburg-landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[Crossref]

1993 (1)

1991 (1)

B. A. Malomed, “Bound solitons in the nonlinear schrödinger–ginzburg-landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
[Crossref]

Acioli, L. H.

Adams, J.

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

Aguergaray, C.

Akhmediev, N.

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(21), 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(24), 243901 (2017).
[Crossref]

Ankiewicz, A.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex ginzburg-landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[Crossref]

Béal, J.

Belhache, F.

Broderick, N. G. R.

Carelli, P. V.

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(1), 830 (2019).
[Crossref]

de Miranda, M. H. G.

Egorov, O.

Erkintalo, M.

Fu, B.

B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
[Crossref]

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Gao, B.

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

Goda, K.

K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[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(1), 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(24), 243901 (2017).
[Crossref]

P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20(5), 863–870 (2003).
[Crossref]

P. 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]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28(19), 1757–1759 (2003).
[Crossref]

Gui, L.

Gutty, F.

Haus, H. A.

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(6333), 50–54 (2017).
[Crossref]

Hua, Y.

B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
[Crossref]

Iliew, R.

Ippen, E. P.

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(6333), 50–54 (2017).
[Crossref]

K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[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(3), 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(3), 033807 (2009).
[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(24), 243901 (2017).
[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(6333), 50–54 (2017).
[Crossref]

Kutz, J. N.

Lederer, F.

Leite, J. R. R.

Li, F.

Li, X.

X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
[Crossref]

Limpert, J.

Ma, C.

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

Ma, J.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Ma, Y.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Malomed, B. A.

B. A. Malomed, “Bound solitons in the nonlinear schrödinger–ginzburg-landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
[Crossref]

Mélo, L. B. A.

Nelson, L. E.

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(1), 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(24), 243901 (2017).
[Crossref]

Olivier, M.

Ortaç, B.

Palacios, G. F. R.

Piché, M.

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(6333), 50–54 (2017).
[Crossref]

Runge, A. F. J.

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(3), 033807 (2009).
[Crossref]

Scardaci, V.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Shang, C.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

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(6333), 50–54 (2017).
[Crossref]

Soto-Crespo, J. M.

Sun, J.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Sun, Z.

B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
[Crossref]

Tamura, K.

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(1), 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(24), 243901 (2017).
[Crossref]

Tünnermann, A.

Wai, P. K. A.

Wang, C.

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

Wang, G.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Wang, P.

Wang, Y.

X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
[Crossref]

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(1), 830 (2019).
[Crossref]

Wu, G.

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

Xiao, X.

Xu, L.

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

Yang, C.

Zaviyalov, A.

Zhang, H.

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

Zhang, W.

X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
[Crossref]

Zhao, W.

X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
[Crossref]

Zhu, H.

B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
[Crossref]

Appl. Phys. Rev. (1)

C. Ma, C. Wang, B. Gao, J. Adams, G. Wu, and H. Zhang, “Recent progress in ultrafast lasers based on 2d materials as a saturable absorber,” Appl. Phys. Rev. 6(4), 041304 (2019).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

B. Fu, Y. Hua, X. Xiao, H. Zhu, Z. Sun, and C. Yang, “Broadband graphene saturable absorber for pulsed fiber lasers at 1, 1.5, and 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20, 1100705 (2014).
[Crossref]

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

Laser Phys. Lett. (1)

X. Li, Y. Wang, W. Zhang, and W. Zhao, “Experimental observation of soliton molecule evolution in yb-doped passively mode-locked fiber lasers,” Laser Phys. Lett. 11(7), 075103 (2014).
[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(1), 830 (2019).
[Crossref]

Nat. Photonics (1)

K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (2)

B. A. Malomed, “Bound solitons in the nonlinear schrödinger–ginzburg-landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
[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(3), 033807 (2009).
[Crossref]

Phys. Rev. Lett. (2)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex ginzburg-landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[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(24), 243901 (2017).
[Crossref]

Science (1)

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(6333), 50–54 (2017).
[Crossref]

Other (1)

B. Fu, J. Sun, G. Wang, C. Shang, Y. Ma, J. Ma, L. Xu, and V. Scardaci, “Solution-processed two-dimensional materials for ultrafast fiber lasers,” Nanophotonics (2020). https://doi.org/10.1515/nanoph-2019-0558.

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Figures (5)

Fig. 1.
Fig. 1. (a) Experimental setup: diode laser (DL), wavelength division multiplexing (WDM), Yb-doped fiber (YDF), quarter-waveplate ($\lambda$/4), half-waveplate ($\lambda$/2), polarizing beamsplitter (PBS), grating pair (GP), Faraday isolator (FI), GRIN collimators (C). (b) RF spectrum and (c) time series when the laser is in mode-locked regime.
Fig. 2.
Fig. 2. Average spectra recorded by the OSA: (a) - (c) Experimental data (dots) and fitting results (red lines) for different pump powers; (d) Evolution of optical spectrum with pump power.
Fig. 3.
Fig. 3. Interferometric autocorrelation for different pump powers, showing temporal separation of approximately (a) 1.09 ps, (b) 0.97 ps and (c) 0.89 ps. (d) Evolution of interferometric autocorrelation with pump power.
Fig. 4.
Fig. 4. (a) Dependence of temporal separation and (b) relative phase between solitons as function of pump power. The black circles are the experimental data and the red lines are the average values for $\tau$ (1.09 ps, 0.97 ps and 0.89 ps) and $\Delta \phi$ (0.43$\pi$, 0.22$\pi$ and 0.51$\pi$) in each pump power window.
Fig. 5.
Fig. 5. Polar representation for temporal separation and relative phase between solitons, as the pump power is varied. $\tau _1 = 1.09$ ps and $\left \langle \Delta \phi \right \rangle = 0.43\pi$ (blue), $\tau _2 = 0.97$ ps and $\left \langle \Delta \phi \right \rangle = 0.22\pi$ (red), and $\tau _3 = 0.89$ ps and $\left \langle \Delta \phi \right \rangle = 0.51\pi$ (green). The big symbols, blue diamond, red circle and green triangle are the average values of $\Delta \phi$.

Equations (3)

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E ( t ) = [ E 1 ( t ) + E 2 ( t τ ) exp ( i Δ ϕ ) ] exp ( i ω 0 t ) ,
E ( Δ ω ) = E 1 ( Δ ω ) + E 2 ( Δ ω ) exp ( i Δ ω τ ) exp ( i Δ ϕ ) ,
S ( Δ ω ) = A sech 2 ( Δ ω a ) [ 1 + b 2 + 2 b cos ( Δ ω τ + Δ ϕ ) ] ,

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