Abstract

Pulsating behavior is a universal phenomenon in versatile fields. In nonlinear dissipative systems, the solitons also pulsate under proper conditions and show many interesting dynamics. However, the pulsation dynamics are generally concerned with single-soliton cases. Herein, by utilizing real-time spectroscopy technique, namely, dispersive Fourier-transform (DFT), we reveal the distinct dynamical diversity of pulsating solitons in a fiber laser. In particular, the weak to strong explosive behaviors of pulsating solitons, as well as the rogue wave generation during explosions are observed. Moreover, the concept of soliton pulsation is extended to the multi-soliton case. It is found that the simultaneous pulsations of energy, separation and relative phase difference could be observed for solitons inside the molecule, while the pulsations of each individual in a multi-soliton bunch could be regular or irregular. These findings will shed new insights into the complex nonlinear behavior of solitons in ultrafast fiber lasers as well as dissipative optical systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2019 (4)

J. Peng and H. Zeng, “Soliton collision induced explosions in a mode-locked fibre laser,” Commun. Phys. 2(1), 34 (2019).
[Crossref]

G. Wang, G. Chen, W. Li, and C. Zeng, “Real-time evolution dynamics of double-pulse mode-locking,” IEEE J. Sel. Top. Quantum Electron. 25(4), 1–4 (2019).
[Crossref]

X. Wang, Y.-G. Liu, Z. Wang, Y. Yue, J. He, B. Mao, R. He, and J. Hu, “Transient behaviors of pure soliton pulsations and soliton explosion in an L-band normal dispersion mode-locked fiber laser,” Opt. Express 27(13), 17729–17742 (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(1), 830 (2019).
[Crossref]

2018 (14)

A. E. Akosman and M. Y. Sander, “Route towards extreme optical pulsation in linear cavity ultrafast fibre lasers,” Sci. Rep. 8(1), 13385 (2018).
[Crossref]

H. Sakaguchi, D. V. Skryabin, and B. A. Malomed, “Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion,” Opt. Lett. 43(11), 2688–2691 (2018).
[Crossref]

A. Klein, G. Masri, H. Duadi, K. Sulimany, O. Lib, H. Steinberg, S. A. Kolpakov, and M. Fridman, “Ultrafast rogue wave patterns in fiber lasers,” Optica 5(7), 774–778 (2018).
[Crossref]

Z. Wang, Z. Wang, Y. Liu, R. He, J. Zhao, G. Wang, and G. Yang, “Self-organized compound pattern and pulsation of dissipative solitons in a passively mode-locked fiber laser,” Opt. Lett. 43(3), 478–481 (2018).
[Crossref]

Y. Du, Z. Xu, and X. Shu, “Spatio-spectral dynamics of the pulsating dissipative solitons in a normal-dispersion fiber laser,” Opt. Lett. 43(15), 3602–3605 (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(24), 5965–5968 (2018).
[Crossref]

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref]

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photonics Rev. 12(8), 1800009 (2018).
[Crossref]

S. Hamdi, A. Coillet, and P. Grelu, “Real-time characterization of optical soliton molecule dynamics in an ultrafast thulium fiber laser,” Opt. Lett. 43(20), 4965–4968 (2018).
[Crossref]

M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
[Crossref]

Y. Yu, Z.-C. Luo, J. Kang, and K. K. Y. Wong, “Mutually ignited soliton explosions in a fiber laser,” Opt. Lett. 43(17), 4132–4135 (2018).
[Crossref]

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (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(3), 2972–2982 (2018).
[Crossref]

H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
[Crossref]

2017 (7)

X. Wei, B. Li, Y. Yu, C. Zhang, K. K. Tsia, and K. K. Y. Wong, “Unveiling multi-scale laser dynamics through time-stretch and time-lens spectroscopies,” Opt. Express 25(23), 29098–29120 (2017).
[Crossref]

K. Krupa, K. Nithyanandan, and P. Grelu, “Vector dynamics of incoherent dissipative optical solitons,” Optica 4(10), 1239–1244 (2017).
[Crossref]

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23(1), 20–25 (2017).
[Crossref]

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Dissipative solitons with extreme spikes: bifurcation diagrams in the anomalous dispersion regime,” J. Opt. Soc. Am. B 34(7), 1542–1549 (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]

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]

2016 (5)

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
[Crossref]

J. Peng, N. Tarasov, S. Sugavanam, and D. Churkin, “Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser,” Opt. Express 24(19), 21256–21263 (2016).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10(5), 321–326 (2016).
[Crossref]

A. F. J. Runge, N. G. R. Broderick, and M. Erkinatalo, “Dynamics of soliton explosions in passively mode-locked fiber lasers,” J. Opt. Soc. Am. B 33(1), 46–53 (2016).
[Crossref]

M. Liu, A. P. Luo, Y. R. Yan, S. Hu, Y. C. Liu, H. Cui, Z. C. Luo, and W. C. Xu, “Successive soliton explosions in an ultrafast fiber laser,” Opt. Lett. 41(6), 1181–1184 (2016).
[Crossref]

2015 (3)

2013 (1)

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

2012 (3)

Z.-C. Luo, W.-J. Cao, Z.-B. Lin, Z.-R. Cai, A.-P. Luo, and W.-C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
[Crossref]

2011 (1)

2010 (1)

S. Chouli and P. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81(6), 063829 (2010).
[Crossref]

2009 (2)

2008 (4)

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008).
[Crossref]

L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, and N. Xiang, “Soliton trapping in fiber lasers,” Opt. Express 16(13), 9528–9533 (2008).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[Crossref]

2007 (1)

W. Chang, A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, “Creeping solitons in dissipative systems and their bifurcations,” Phys. Rev. E 76(1), 016607 (2007).
[Crossref]

2005 (2)

N. Akhmediev and A. Ankiewicz, “Dissipative solitons in the complex Ginzburg-Landau and Swift-Hohenberg equations,” Lect. Notes Phys. 661, 1–17 (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(1), 016616 (2005).
[Crossref]

2004 (1)

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(6), 066612 (2004).
[Crossref]

2001 (1)

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63(5), 056602 (2001).
[Crossref]

2000 (1)

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[Crossref]

1999 (1)

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999).
[Crossref]

Akhmediev, N.

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Dissipative solitons with extreme spikes: bifurcation diagrams in the anomalous dispersion regime,” J. Opt. Soc. Am. B 34(7), 1542–1549 (2017).
[Crossref]

W. Chang, J. M. Soto-Crespo, P. Vouzas, and N. Akhmediev, “Extreme soliton pulsations in dissipative systems,” Phys. Rev. E 92(2), 022926 (2015).
[Crossref]

C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

W. Chang, A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, “Creeping solitons in dissipative systems and their bifurcations,” Phys. Rev. E 76(1), 016607 (2007).
[Crossref]

N. Akhmediev and A. Ankiewicz, “Dissipative solitons in the complex Ginzburg-Landau and Swift-Hohenberg equations,” Lect. Notes Phys. 661, 1–17 (2005).
[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(6), 066612 (2004).
[Crossref]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63(5), 056602 (2001).
[Crossref]

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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).
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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(6), 066612 (2004).
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He, J.

He, J.-B.

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H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
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Hu, S.

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H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
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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).
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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).
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K. Krupa, K. Nithyanandan, and P. Grelu, “Vector dynamics of incoherent dissipative optical solitons,” Optica 4(10), 1239–1244 (2017).
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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).
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F. Amrani, M. Salhi, P. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
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A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[Crossref]

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C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
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Li, H.

M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
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G. Wang, G. Chen, W. Li, and C. Zeng, “Real-time evolution dynamics of double-pulse mode-locking,” IEEE J. Sel. Top. Quantum Electron. 25(4), 1–4 (2019).
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Lin, Z.-B.

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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(24), 5965–5968 (2018).
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M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
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M. Liu, A. P. Luo, Y. R. Yan, S. Hu, Y. C. Liu, H. Cui, Z. C. Luo, and W. C. Xu, “Successive soliton explosions in an ultrafast fiber laser,” Opt. Lett. 41(6), 1181–1184 (2016).
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X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
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Liu, Y. C.

Liu, Y.-G.

Luo, A. P.

Luo, A.-P.

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(3), 2972–2982 (2018).
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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(24), 5965–5968 (2018).
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H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
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M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
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Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23(1), 20–25 (2017).
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Z.-C. Luo, W.-J. Cao, Z.-B. Lin, Z.-R. Cai, A.-P. Luo, and W.-C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012).
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Luo, Z. C.

Luo, Z.-C.

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(3), 2972–2982 (2018).
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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(24), 5965–5968 (2018).
[Crossref]

H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
[Crossref]

M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
[Crossref]

Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23(1), 20–25 (2017).
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Z.-C. Luo, W.-J. Cao, Z.-B. Lin, Z.-R. Cai, A.-P. Luo, and W.-C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012).
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Mao, B.

Masri, G.

Merolla, J.-M.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
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M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
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Morandotti, R.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
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P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
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M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
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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).
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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).
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G. Herink, B. Jalali, C. Ropers, and D. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10(5), 321–326 (2016).
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Ryczkowski, P.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
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Sakaguchi, H.

Salhi, M.

F. Amrani, M. Salhi, P. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[Crossref]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[Crossref]

Sanchez, F.

F. Amrani, M. Salhi, P. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[Crossref]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[Crossref]

Sander, M. Y.

A. E. Akosman and M. Y. Sander, “Route towards extreme optical pulsation in linear cavity ultrafast fibre lasers,” Sci. Rep. 8(1), 13385 (2018).
[Crossref]

Shu, X.

Skryabin, D. V.

Solli, D.

G. Herink, B. Jalali, C. Ropers, and D. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10(5), 321–326 (2016).
[Crossref]

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.

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Dissipative solitons with extreme spikes: bifurcation diagrams in the anomalous dispersion regime,” J. Opt. Soc. Am. B 34(7), 1542–1549 (2017).
[Crossref]

W. Chang, J. M. Soto-Crespo, P. Vouzas, and N. Akhmediev, “Extreme soliton pulsations in dissipative systems,” Phys. Rev. E 92(2), 022926 (2015).
[Crossref]

C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

W. Chang, A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, “Creeping solitons in dissipative systems and their bifurcations,” Phys. Rev. E 76(1), 016607 (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(6), 066612 (2004).
[Crossref]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63(5), 056602 (2001).
[Crossref]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[Crossref]

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999).
[Crossref]

Steinberg, H.

Sugavanam, S.

Sulimany, K.

Sylvestre, T.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
[Crossref]

Tam, H. Y.

Tang, D. Y.

Tarasov, N.

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]

Toenger, S.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
[Crossref]

Town, G.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63(5), 056602 (2001).
[Crossref]

Tsia, K. K.

Vouzas, P.

W. Chang, J. M. Soto-Crespo, P. Vouzas, and N. Akhmediev, “Extreme soliton pulsations in dissipative systems,” Phys. Rev. E 92(2), 022926 (2015).
[Crossref]

Wang, G.

G. Wang, G. Chen, W. Li, and C. Zeng, “Real-time evolution dynamics of double-pulse mode-locking,” IEEE J. Sel. Top. Quantum Electron. 25(4), 1–4 (2019).
[Crossref]

Z. Wang, Z. Wang, Y. Liu, R. He, J. Zhao, G. Wang, and G. Yang, “Self-organized compound pattern and pulsation of dissipative solitons in a passively mode-locked fiber laser,” Opt. Lett. 43(3), 478–481 (2018).
[Crossref]

Wang, P.

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Wang, X.

Wang, Z.

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]

Wei, X.

Wei, Z.-W.

Wetzel, B.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
[Crossref]

Wong, K. K. Y.

Wu, X.

Xiang, N.

Xiao, X.

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Xu, W. C.

Xu, W.-C.

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(3), 2972–2982 (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(24), 5965–5968 (2018).
[Crossref]

M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
[Crossref]

H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
[Crossref]

Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23(1), 20–25 (2017).
[Crossref]

Z.-C. Luo, W.-J. Cao, Z.-B. Lin, Z.-R. Cai, A.-P. Luo, and W.-C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012).
[Crossref]

Xu, Z.

Yan, Y. R.

Yang, C.

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Yang, G.

Yao, J.

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(3), 2972–2982 (2018).
[Crossref]

H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
[Crossref]

Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23(1), 20–25 (2017).
[Crossref]

Yao, X.

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref]

Yu, Y.

Yue, Y.

Zeng, C.

G. Wang, G. Chen, W. Li, and C. Zeng, “Real-time evolution dynamics of double-pulse mode-locking,” IEEE J. Sel. Top. Quantum Electron. 25(4), 1–4 (2019).
[Crossref]

Zeng, H.

J. Peng and H. Zeng, “Soliton collision induced explosions in a mode-locked fibre laser,” Commun. Phys. 2(1), 34 (2019).
[Crossref]

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photonics Rev. 12(8), 1800009 (2018).
[Crossref]

Zhang, C.

Zhang, H.

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(1), 016616 (2005).
[Crossref]

Zhao, H.

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Zhao, J.

Zhao, L. M.

Commun. Phys. (1)

J. Peng and H. Zeng, “Soliton collision induced explosions in a mode-locked fibre laser,” Commun. Phys. 2(1), 34 (2019).
[Crossref]

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

G. Wang, G. Chen, W. Li, and C. Zeng, “Real-time evolution dynamics of double-pulse mode-locking,” IEEE J. Sel. Top. Quantum Electron. 25(4), 1–4 (2019).
[Crossref]

Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23(1), 20–25 (2017).
[Crossref]

IEEE Photonics J. (2)

H.-J. Chen, M. Liu, J. Yao, S. Hu, J.-B. He, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Soliton booting dynamics in an ultrafast anomalous dispersion fiber laser,” IEEE Photonics J. 10(2), 1–9 (2018).
[Crossref]

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

J. Opt. (1)

M. Liu, H. Li, A.-P. Luo, H. Cui, W.-C. Xu, and Z.-C. Luo, “Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser,” J. Opt. 20(3), 034010 (2018).
[Crossref]

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

Laser Photonics Rev. (1)

J. Peng and H. Zeng, “Build-up of dissipative optical soliton molecules via diverse soliton interactions,” Laser Photonics Rev. 12(8), 1800009 (2018).
[Crossref]

Lect. Notes Phys. (1)

N. Akhmediev and A. Ankiewicz, “Dissipative solitons in the complex Ginzburg-Landau and Swift-Hohenberg equations,” Lect. Notes Phys. 661, 1–17 (2005).
[Crossref]

Nat. Commun. (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]

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7(1), 13675 (2016).
[Crossref]

Nat. Photonics (4)

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

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10(5), 321–326 (2016).
[Crossref]

Opt. Express (7)

Opt. Lett. (10)

H. Sakaguchi, D. V. Skryabin, and B. A. Malomed, “Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion,” Opt. Lett. 43(11), 2688–2691 (2018).
[Crossref]

S. Hamdi, A. Coillet, and P. Grelu, “Real-time characterization of optical soliton molecule dynamics in an ultrafast thulium fiber laser,” Opt. Lett. 43(20), 4965–4968 (2018).
[Crossref]

L. M. Zhao, D. Y. Tang, X. Wu, H. Zhang, and H. Y. Tam, “Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM,” Opt. Lett. 34(20), 3059–3061 (2009).
[Crossref]

Z.-C. Luo, W.-J. Cao, Z.-B. Lin, Z.-R. Cai, A.-P. Luo, and W.-C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012).
[Crossref]

M. Liu, A. P. Luo, Y. R. Yan, S. Hu, Y. C. Liu, H. Cui, Z. C. Luo, and W. C. Xu, “Successive soliton explosions in an ultrafast fiber laser,” Opt. Lett. 41(6), 1181–1184 (2016).
[Crossref]

F. Amrani, M. Salhi, P. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011).
[Crossref]

Z. Wang, Z. Wang, Y. Liu, R. He, J. Zhao, G. Wang, and G. Yang, “Self-organized compound pattern and pulsation of dissipative solitons in a passively mode-locked fiber laser,” Opt. Lett. 43(3), 478–481 (2018).
[Crossref]

Y. Du, Z. Xu, and X. Shu, “Spatio-spectral dynamics of the pulsating dissipative solitons in a normal-dispersion fiber laser,” Opt. Lett. 43(15), 3602–3605 (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(24), 5965–5968 (2018).
[Crossref]

Y. Yu, Z.-C. Luo, J. Kang, and K. K. Y. Wong, “Mutually ignited soliton explosions in a fiber laser,” Opt. Lett. 43(17), 4132–4135 (2018).
[Crossref]

Optica (3)

Phys. Rev. A (3)

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78(4), 043806 (2008).
[Crossref]

S. Chouli and P. Grelu, “Soliton rains in a fiber laser: an experimental study,” Phys. Rev. A 81(6), 063829 (2010).
[Crossref]

Phys. Rev. E (5)

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

W. Chang, A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, “Creeping solitons in dissipative systems and their bifurcations,” Phys. Rev. E 76(1), 016607 (2007).
[Crossref]

W. Chang, J. M. Soto-Crespo, P. Vouzas, and N. Akhmediev, “Extreme soliton pulsations in dissipative systems,” Phys. Rev. E 92(2), 022926 (2015).
[Crossref]

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E 63(5), 056602 (2001).
[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(6), 066612 (2004).
[Crossref]

Phys. Rev. Lett. (6)

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[Crossref]

C. Lecaplain, P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
[Crossref]

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999).
[Crossref]

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008).
[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]

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref]

Sci. Rep. (1)

A. E. Akosman and M. Y. Sander, “Route towards extreme optical pulsation in linear cavity ultrafast fibre lasers,” Sci. Rep. 8(1), 13385 (2018).
[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]

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Figures (12)

Fig. 1.
Fig. 1. Schematic of (a) the fiber laser and (b) the real-time characterization of pulsating solitons.
Fig. 2.
Fig. 2. The characteristics of the single-soliton pulsation. (a) The spectrum obtained from the OSA and the average of 1500 roundtrips consecutive single-shot spectrum. (b) The RF spectrum. (c) The shot-to-shot spectra and corresponding energy evolution. (d) Pulse train.
Fig. 3.
Fig. 3. The explosive long-period pulsating soliton operation. (a) The spectrum obtained from the OSA. (b) The RF spectrum. (c) The shot-to-shot spectra and corresponding energy evolution. (d) The enlarged explosive pulsating soliton region.
Fig. 4.
Fig. 4. Irregularly pulsating dual-soliton bunch operation. (a) The spectrum obtained from the OSA. (b) The RF spectrum. (c) The pulse train. (d) The total energy evolution of the dual-soliton bunch. (e) and (g) The shot-to-shot spectra of the two solitons. (f) and (h) The energy evolutions of the two solitons.
Fig. 5.
Fig. 5. Regularly pulsating dual-soliton bunch operation. (a) The spectrum obtained from the OSA. (b) The RF spectrum. (c) The pulse train. (d) The total energy evolution of the dual-soliton bunch. (e) and (g) The shot-to-shot spectra of the two solitons. (f) and (h) The energy evolutions of the two solitons.
Fig. 6.
Fig. 6. Characteristics of periodically pulsating dual-soliton molecule. (a) The real-time spectra evolution measured with DFT, inset: the energy evolution. (b) The enlarged spectra. (c) The temporal evolution. (d) The RF spectrum. (e) The soliton separation and phase difference as a function of the roundtrips. (f) The corresponding interaction planes.
Fig. 7.
Fig. 7. Characteristics of aperiodically pulsating dual-soliton molecule. (a) The real-time spectra evolution measured with DFT, inset: the energy evolution. (b) The enlarged spectra. (c) The temporal evolution. (d) The RF spectrum. (e) The soliton separation and phase difference as a function of the roundtrips. (f) The corresponding interaction planes.
Fig. 8.
Fig. 8. Characteristics of pulsating triple-soliton molecule. (a) The real-time spectra evolution measured with DFT, inset: the energy evolution. (b) The enlarged spectra. (c) The temporal evolution. (d) The RF spectrum. (e) The soliton separation and phase difference as a function of the roundtrips. (f) The corresponding interaction planes.
Fig. 9.
Fig. 9. Optical spectra at different PC orientations. (a)–(c) Average spectra obtained from OSA. (d)–(f) Shot-to-shot spectra corresponding to the maximum pulsating soliton energy.
Fig. 10.
Fig. 10. Statistical distribution histogram of the amplitude fluctuations in explosive long-period pulsating soliton regime.
Fig. 11.
Fig. 11. Single-shot spectra of dual-soliton bunch with regular pulsation.
Fig. 12.
Fig. 12. (a) The spectrum displayed on the OSA. (b) The autocorrelation trace of the periodically pulsating soliton molecule.

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