Abstract

Ultra-fast soliton dynamics is one of the most attractive phenomena in the mode-locked fiber laser. However, the formation and breakup of solitons are difficult to observe, due to the transient nature of the process. Using the time-stretch technique, we are able to trace the real-time evolution of the soliton bound state formation and mode-locking build-up. Q-switched instabilities exist in both booting processes. Moreover, we find that the evolving patterns of soliton bound states are highly dependent on their initial conditions. Here, two types of soliton pairs are observed in the cavity and their typical forming dynamics are recorded and analyzed. Our findings uncover a diverse set of soliton dynamics in a mode-locked fiber laser and thus promote our understandings about complex dynamics in nonlinear optical systems. These results also provide a valuable reference for further theoretical studies.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  39. M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
    [Crossref]

2018 (3)

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] [PubMed]

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

2017 (5)

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 (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] [PubMed]

Y. Wang, F. Leo, J. Fatome, M. Erkintalo, S. G. Murdoch, and S. Coen, “Universal mechanism for the binding of temporal cavity solitons,” Optica 4(8), 855–863 (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] [PubMed]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (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. Photon. 10, 321 (2016).

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

2015 (2)

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]

M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
[Crossref]

2013 (2)

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[Crossref]

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–874 (2013).
[Crossref]

2012 (1)

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

2009 (1)

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Discrete Family of Dissipative Soliton Pairs in Mode-Locked Fiber Lasers,” Phys. Rev. A 79(5), 1744–1747 (2009).
[Crossref]

2008 (2)

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[Crossref]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

2007 (1)

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

2006 (1)

C. K. Nielsen, “Mode Locked Fiber Lasers: Theoretical and Experimental Developments,” IEEE J. Sel. Top. Quantum Electron. 10, 129–136 (2006).

2005 (1)

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(4), 043816 (2005).
[Crossref]

2004 (1)

2003 (2)

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Y. Han and B. Jalali, “Photonic Time-Stretched Analog-to-Digital Converter: Fundamental Concepts and Practical Considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

2001 (2)

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 Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[Crossref] [PubMed]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Mechanisms of spectral shift in ultrashort-pulse laser oscillators,” J. Opt. Soc. Am. B 18(11), 1732–1741 (2001).
[Crossref]

1999 (2)

1997 (2)

N. N. Akhmediev, A. Ankiewicz, and J. M. Sotocrespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[Crossref]

M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, “Fiber-lasers for ultrafast optics,” Appl. Phys. B 65(2), 259–275 (1997).
[Crossref]

1995 (1)

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

1994 (2)

K. J. Weingarten, B. Braun, and U. Keller, “In situ small-signal gain of solid-state lasers determined from relaxation oscillation frequency measurements,” Opt. Lett. 19(15), 1140–1142 (1994).
[Crossref] [PubMed]

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30(6), 1469–1477 (1994).
[Crossref]

1992 (2)

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992).
[Crossref]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–807 (1992).
[Crossref]

1991 (1)

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
[Crossref] [PubMed]

1990 (1)

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

1986 (1)

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[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 Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[Crossref] [PubMed]

Akhmediev, N. N.

N. N. Akhmediev, A. Ankiewicz, and J. M. Sotocrespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[Crossref]

Alsous, M. B.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Anderson, D.

Andonovic, I.

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992).
[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] [PubMed]

Ankiewicz, A.

N. N. Akhmediev, A. Ankiewicz, and J. M. Sotocrespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[Crossref]

Apostolopoulos, G.

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(6), 341–351 (2017).
[Crossref]

Billet, C.

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]

Blow, K. J.

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992).
[Crossref]

Braun, B.

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(6), 341–351 (2017).
[Crossref]

Broderick, N. G. R.

Brovelli, L. R.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

Calasso, I. G.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

Chen, H. J.

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Churkin, D. V.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

Coen, S.

Y. Wang, F. Leo, J. Fatome, M. Erkintalo, S. G. Murdoch, and S. Coen, “Universal mechanism for the binding of temporal cavity solitons,” Optica 4(8), 855–863 (2017).
[Crossref]

M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[Crossref]

Craig-Ryan, S. P.

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Däweritz, L.

Dennis, M. L.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30(6), 1469–1477 (1994).
[Crossref]

Dudley, 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).
[Crossref]

Duling, I. N.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30(6), 1469–1477 (1994).
[Crossref]

Egorov, O.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Discrete Family of Dissipative Soliton Pairs in Mode-Locked Fiber Lasers,” Phys. Rev. A 79(5), 1744–1747 (2009).
[Crossref]

Erkintalo, M.

Fatome, J.

Fermann, M. E.

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–874 (2013).
[Crossref]

M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, “Fiber-lasers for ultrafast optics,” Appl. Phys. B 65(2), 259–275 (1997).
[Crossref]

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Friedland, K. J.

Galvanauskas, A.

M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, “Fiber-lasers for ultrafast optics,” Appl. Phys. B 65(2), 259–275 (1997).
[Crossref]

Genty, G.

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]

George, J.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Glas, P.

Grange, R.

Grelu, P.

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] [PubMed]

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

Gupta, P. K.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Haberl, F.

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Han, Y.

Harter, D.

M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, “Fiber-lasers for ultrafast optics,” Appl. Phys. B 65(2), 259–275 (1997).
[Crossref]

Hartl, I.

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–874 (2013).
[Crossref]

He, J. B.

Herfort, J.

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] [PubMed]

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. Photon. 10, 321 (2016).

Hofer, M.

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

Hönninger, C.

Hsieh, W. F.

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

Hsu, C. C.

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

Hu, S.

Iliew, R.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Discrete Family of Dissipative Soliton Pairs in Mode-Locked Fiber Lasers,” Phys. Rev. A 79(5), 1744–1747 (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(6333), 50–54 (2017).
[Crossref] [PubMed]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 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. Photon. 10, 321 (2016).

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Y. Han and B. Jalali, “Photonic Time-Stretched Analog-to-Digital Converter: Fundamental Concepts and Practical Considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

Jang, J. K.

M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[Crossref]

Kaertner, F. X.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

Kalashnikov, V. L.

Kamp, M.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

Keller, U.

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–807 (1992).
[Crossref]

Knappe, R.

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[Crossref]

Kopf, D.

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

Kostial, H.

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] [PubMed]

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] [PubMed]

L’Huillier, J. A.

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[Crossref]

Lederer, F.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Discrete Family of Dissipative Soliton Pairs in Mode-Locked Fiber Lasers,” Phys. Rev. A 79(5), 1744–1747 (2009).
[Crossref]

Leitner, M.

Leo, F.

Li, B.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

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 (2017).
[Crossref]

Lin, J. H.

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

Lin, K. H.

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

Lisak, M.

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(4), 043816 (2005).
[Crossref]

Liu, M.

Luo, A. P.

Luo, K.

M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
[Crossref]

Luo, Z. 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(6), 341–351 (2017).
[Crossref]

Malomed, B. A.

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
[Crossref] [PubMed]

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).
[Crossref]

Morier-Genoud, F.

Moser, M.

Mukhopadhyay, P. K.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Murdoch, S. G.

Y. Wang, F. Leo, J. Fatome, M. Erkintalo, S. G. Murdoch, and S. Coen, “Universal mechanism for the binding of temporal cavity solitons,” Optica 4(8), 855–863 (2017).
[Crossref]

M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[Crossref]

Närhi, 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).
[Crossref]

Nathan, T. P. S.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Nielsen, C. K.

C. K. Nielsen, “Mode Locked Fiber Lasers: Theoretical and Experimental Developments,” IEEE J. Sel. Top. Quantum Electron. 10, 129–136 (2006).

Nithyanandan, 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] [PubMed]

Paschotta, R.

Ranganathan, K.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Riedel, A.

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] [PubMed]

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. Photon. 10, 321 (2016).

Runge, A. F. J.

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).
[Crossref]

Sandrock, T.

Schlatter, A.

Sharma, S. K.

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Smith, N. J.

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992).
[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] [PubMed]

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. Photon. 10, 321 (2016).

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Sorokin, E.

Sorokina, I. T.

Sotocrespo, J. M.

N. N. Akhmediev, A. Ankiewicz, and J. M. Sotocrespo, “Multisoliton Solutions of the Complex Ginzburg-Landau Equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[Crossref]

Soto-Crespo, J. M.

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 Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[Crossref] [PubMed]

Sucha, G.

M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, “Fiber-lasers for ultrafast optics,” Appl. Phys. B 65(2), 259–275 (1997).
[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(4), 043816 (2005).
[Crossref]

Tchofo-Dinda, P.

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] [PubMed]

Theobald, C.

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[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 Stat. Nonlin. Soft Matter Phys. 63(5), 056602 (2001).
[Crossref] [PubMed]

Tsia, K. K.

Turitsyn, S. K.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

Wallenstein, R.

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[Crossref]

Wang, Y.

Wei, X.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

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 (2017).
[Crossref]

Wei, Y.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

Weingarten, K. J.

Weitz, M.

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[Crossref]

Wong, K. K. Y.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

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 (2017).
[Crossref]

Wrage, M.

Xu, W. C.

Yang, W. H.

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

Yao, J.

Yu, Y.

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

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 (2017).
[Crossref]

Zavyalov, A.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Discrete Family of Dissipative Soliton Pairs in Mode-Locked Fiber Lasers,” Phys. Rev. A 79(5), 1744–1747 (2009).
[Crossref]

Zeller, S. C.

Zhang, C.

Zhao, B.

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(4), 043816 (2005).
[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(4), 043816 (2005).
[Crossref]

Appl. Phys. B (2)

M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, “Fiber-lasers for ultrafast optics,” Appl. Phys. B 65(2), 259–275 (1997).
[Crossref]

C. Theobald, M. Weitz, R. Knappe, R. Wallenstein, and J. A. L’Huillier, “Stable Q-switch mode-locking of Nd:YVO4 lasers with a semiconductor saturable absorber,” Appl. Phys. B 92(1), 1–3 (2008).
[Crossref]

Appl. Phys. Lett. (1)

Y. Wei, B. Li, X. Wei, Y. Yu, and K. K. Y. Wong, “Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser,” Appl. Phys. Lett. 112(8), 081104 (2018).
[Crossref]

Electron. Lett. (2)

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–807 (1992).
[Crossref]

M. E. Fermann, M. Hofer, F. Haberl, and S. P. Craig-Ryan, “Femtosecond fibre laser,” Electron. Lett. 26(20), 1737–1738 (1990).
[Crossref]

IEEE J. Quantum Electron. (1)

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30(6), 1469–1477 (1994).
[Crossref]

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

C. K. Nielsen, “Mode Locked Fiber Lasers: Theoretical and Experimental Developments,” IEEE J. Sel. Top. Quantum Electron. 10, 129–136 (2006).

J. Lightwave Technol. (2)

Y. Han and B. Jalali, “Photonic Time-Stretched Analog-to-Digital Converter: Fundamental Concepts and Practical Considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. 10(10), 1329–1333 (1992).
[Crossref]

J. Opt. Soc. Am. B (4)

Laser Phys. Lett. (1)

J. H. Lin, K. H. Lin, C. C. Hsu, W. H. Yang, and W. F. Hsieh, “Supercontinuum generation in a microstructured optical fiber by picosecond self Q-switched mode-locked Nd:GdVO 4 laser,” Laser Phys. Lett. 4(6), 413–417 (2007).
[Crossref]

Nat. Photon. (1)

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. Photon. 10, 321 (2016).

Nat. Photonics (6)

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]

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–874 (2013).
[Crossref]

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

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7(8), 657–663 (2013).
[Crossref]

New J. Phys. (1)

M. Erkintalo, K. Luo, J. K. Jang, S. Coen, and S. G. Murdoch, “Bunching of temporal cavity solitons via forward Brillouin scattering,” New J. Phys. 17(11), 115009 (2015).
[Crossref]

Opt. Commun. (1)

P. K. Mukhopadhyay, M. B. Alsous, K. Ranganathan, S. K. Sharma, P. K. Gupta, J. George, and T. P. S. Nathan, “Simultaneous Q-switching and mode-locking in an intracavity frequency doubled diode-pumped Nd:YVO4/KTP green laser with Cr4+:YAG,” Opt. Commun. 222(1-6), 399–404 (2003).
[Crossref]

Opt. Eng. (1)

F. X. Kaertner, L. R. Brovelli, D. Kopf, M. Kamp, I. G. Calasso, and U. Keller, “Control of solid state laser dynamics by semiconductor devices,” Opt. Eng. 34(7), 2024–2036 (1995).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optica (2)

Phys. Rev. A (3)

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation,” Phys. Rev. A 44(10), 6954–6957 (1991).
[Crossref] [PubMed]

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(4), 043816 (2005).
[Crossref]

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, “Discrete Family of Dissipative Soliton Pairs in Mode-Locked Fiber Lasers,” Phys. Rev. A 79(5), 1744–1747 (2009).
[Crossref]

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

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Phys. Rev. Lett. (2)

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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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).
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Other (1)

A. Mahjoubfar, C. L. Chen, and B. Jalali, Artificial Intelligence in Label-free Microscopy; Biological Cell Classification by Time Stretch (Springer, 2017).

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Figures (6)

Fig. 1
Fig. 1 (i) Experimental setup of DFT technique. The output pulse of the fiber laser is stretched by 10-km dispersion compensation fiber (DCF) and its spectrum is mapped into the temporal domain. The stretched pulse is acquired by a high-speed photodetector and monitored in a real-time oscilloscope. The mode-locked fiber laser used in our experiment is a commercial PriTel femtosecond fiber laser with a ring cavity. A 980 nm laser diode (LD) is served as the pump source. All fibers in the cavity are polarization maintaining fibers (PMF), including the 100-cm-long Er-doped fiber (EDF). Terms shown in the figure are abbreviated as follows: WDM: wavelength division multiplexer, TF: tunable filter, SESAM: semiconductor saturable absorber mirror, OC: optical coupler, ISO: isolator. (ii) The evolution of soliton dynamics with the increasing of pump power. (a) Quasi-cw Q-switched bursts emerge at low pump level and produce a noise-like fluctuation under a Q-switched envelope. (b) Increased pump current stimulates transient soliton molecules. They evolve from quasi-cw Q-switched bursts and fade out rapidly. (c) If the pump power is further increased, the transient soliton explosion will convert into a stable mode-locked pulse train. (d) The transition from a single soliton operation to a soliton molecule regime has to undergo a transient period of Q-switched instabilities.
Fig. 2
Fig. 2 Q-switched instabilities before the stable mode locking. (a) Q-switched bursts under relative low pump power usually possess Gaussian-like envelopes and fixed Q-switched period. (b) As the pump power increases, the Q-switched period (blue) and temporal width (red) of the Q-switched bursts reduce gradually. This can be explained by the increased relaxation oscillations frequency under high pump power. (c) Temporal evolution of one Q-switched burst under 260 mA without dispersion. Multiple pulses coexist in the cavity with an uneven power distribution. (d) Meanwhile, we record the same Q-switched burst via insertion of a 10-km DCF (dispersion value is ~1486 ps/nm). These pulses do not present any temporal stretch compared with the data set without dispersion, indicating that the bandwidth of these fluctuations is quite narrow. Moreover, their relative timing is not altered by the dispersion, implying that all these pulses origin from a single wavelength. (e) Q-switched bursts under pump currents from 320 mA to 350 mA. Double-burst with higher power and larger temporal width can be observed in this regime. (f) The real-time evolution of a typical double-burst measured by using DFT technique. One dominant pulse explodes in power and bandwidth after the depletion of background fluctuations. (g) The Fourier transform of the real-time spectrum represents the autocorrelation of its temporal waveform. The autocorrelation traces indicate that a four-pulse soliton is created in the Q-switched burst.
Fig. 3
Fig. 3 The build-up of stable mode locking in real time. All the results are recorded at ~360 mA. (a-c) Real-time spectral evolution from Q-switched instabilities to stable mode locking is resolved using DFT method. One seed pulse outbursts from a background fluctuations, with a suddenly broadening bandwidth and a rapidly-evolving fringe pattern. A stable mode locking is established gradually at the end of the Q-switched burst. (d) The blue line shows the power evolution of the background and dominant pulses in the mode-locking build-up event. The red line illustrates the 3dB bandwidth of the dominant fluctuation. (e) We trace the central wavelength variation of the dominant pulse and observe a spectral blue shift. The central wavelength of mode-locked pulses is ~0.7 nm shorter than that of the dominant pulse before mode locking.
Fig. 4
Fig. 4 The formation dynamics of soliton molecule above 460 mA. (a) The optical spectral evolution recorded by an OSA before entering soliton molecule regime. A cw sideband emerges at high pump power. (b) The recorded transient regime from single pulse regime to the soliton bound state over a time-window of 4 s, in which a ~1.2 s Q-switched mode-locking regime is illustrated. The results are measured by time-stretch technique, so the relative low peak power of single pulse operation mainly results from its large bandwidth. (c) Experimental real-time spectral evolution of the formation of a soliton molecule from the Q-switched mode-locking burst. (d) The Fourier transform of the measured real-time spectrum, representing the autocorrelation of its temporal waveform. (e) The autocorrelation of the 1500th roundtrip. The inset shows the position relation of the three solitons. (f) The separation and relative phase as a function of roundtrips over roundtrips from 2000 to 5000, illustrating a decaying fluctuation before entering the stable bound state.
Fig. 5
Fig. 5 Formation dynamics of another soliton bound state above 460 mA. (a) The data set recorded after a dispersive element. The formation process takes about 6 ms to achieve a stable bound state. (b) Real-time spectral evolution at the beginning of bound state. (c) The synchronously recorded data set without dispersion shows the starting dynamics in temporal domain. Two solitons with ~700 ps separation emerge simultaneously in the cavity. (d) Spectral evolution from ~3.8 ms to ~6.8 ms. In this period, the two solitons are close enough so that the spectral patterns can be resolved by our oscilloscope. (e) Fourier transform of the real-time spectrum shown in (d). It represents the autocorrelation of the temporal waveform. The turn-back trace is caused by the under-sampling of the spectral information. Actually, the soliton separation is decreasing monotonously, until achieving a stable state at ~50 ps separation.
Fig. 6
Fig. 6 The formation of large separation bound state above 460 mA. (a) Real-time evolution of the starting dynamics of two solitons after time-stretch. (b) The synchronously measured temporal evolution. (c) The separation variation in the whole record range of ~8 ms, showing a slight decreasing tendency. (d) The spectra of single soliton operation (under 360 mA) and two soliton pairs (under 465 mA).

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