Abstract

State-of-the-art ultrafast mid-IR fiber lasers deliver optical solitons with durations of several hundred femtoseconds. The Er- or Ho-doped fluoride gain fibers generally used in these lasers have strong anomalous dispersion at ∼3 µm, which generally forces them to operate in the soliton regime. Here we report that a pulse-energy clamping effect, caused by the buildup of intracavity nonlinearities, limits the shortest obtainable pulse durations in these mid-infrared soliton fiber lasers. Excessive intra-cavity energy results in soliton instability, collapse and fragmentation into a variety of stable multi-pulse states, including phase-locked soliton molecules and harmonically mode-locked states. We report that the spectral evolution of the mid-IR laser pulses can be recorded between roundtrips through stretching their second-harmonic signal in a 25-km-length of single-mode fiber. Using a modified dispersive Fourier transform set-up, we were able to perform for the first time spectro-temporal measurements of mid-IR laser pulses both in the pulsed state and during pulse collapse and fragmentation. The results provide insight into the complex nonlinear dynamics of mid-IR soliton fiber lasers and open up new opportunities for obtaining a variety of stable multi-pulse mode-locked states at mid-IR wavelengths.

© 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]
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    [Crossref]
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    [Crossref]

2018 (4)

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]

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]

S. Tan, X. Wei, B. Li, Q. T. K. Lai, K. K. Tsia, and K. K. Y. Wong, “Ultrafast optical imaging at 2.0 µm through second-harmonic-generation-based time-stretch at 1.0 µm,” Opt. Lett. 43(16), 3822–3825 (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]

2017 (2)

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]

U. Elu, M. Baudisch, H. Pires, F. Tani, M. Frosz, F. Köttig, A. Ermolov, P. S. J. Russell, and J. Biegert, “High average power and single-cycle pulses from a mid-IR optical parametric chirped pulse amplifier,” Optica 4(9), 1024–1029 (2017).
[Crossref]

2016 (3)

S. Antipov, D. Hudson, A. Fuerbach, and S. Jackson, “High-power mid-infrared femtosecond fiber laser in the water vapor transmission window,” Optica 3(12), 1373–1376 (2016).
[Crossref]

C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (2016).
[Crossref]

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

2015 (3)

2014 (1)

D. D. Hudson, “Short pulse generation in mid-IR fiber lasers,” Opt. Fiber Technol. 20(6), 631–641 (2014).
[Crossref]

2013 (2)

2012 (3)

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

S. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).
[Crossref]

Y. Yao, A. J. Hoffman, and C. F. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6(7), 432–439 (2012).
[Crossref]

2009 (1)

2008 (1)

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1-2), 58–73 (2008).
[Crossref]

2005 (1)

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental Observation of Temporal Soliton Molecules,” Phys. Rev. Lett. 95(14), 143902 (2005).
[Crossref]

2004 (3)

P. Grelu and J. M. Soto-Crespo, “Multisoliton states and pulse fragmentation in a passively mode-locked fibre laser,” J. Opt. B: Quantum Semiclassical Opt. 6(5), S271–S278 (2004).
[Crossref]

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 70(6), 066612 (2004).
[Crossref]

F.Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-Similar Evolution of Parabolic Pulses in a Laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[Crossref]

2003 (1)

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]

1998 (1)

1997 (2)

A. Grudinin and S. Gray, “Passive harmonic mode locking in soliton fiber lasers,” J. Opt. Soc. Am. B 14(1), 144–154 (1997).
[Crossref]

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]

1994 (1)

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64(2), 149–151 (1994).
[Crossref]

1993 (3)

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62(9), 910–912 (1993).
[Crossref]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993).
[Crossref]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[Crossref]

1992 (2)

D. Noske, N. Pandit, and J. Taylor, “Source of spectral and temporal instability in soliton fiber lasers,” Opt. Lett. 17(21), 1515–1517 (1992).
[Crossref]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–808 (1992).
[Crossref]

1991 (2)

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[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: Stat., Nonlinear, Soft Matter Phys. 70(6), 066612 (2004).
[Crossref]

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

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]

Andrejco, M. J.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62(9), 910–912 (1993).
[Crossref]

Ankiewicz, A.

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]

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]

Antipov, S.

Bao, C.

C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (2016).
[Crossref]

Baudisch, M.

Belhache, F.

Bernier, M.

Biegert, J.

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]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Buckley, J. R.

F.Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-Similar Evolution of Parabolic Pulses in a Laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[Crossref]

Cankaya, H.

Chong, A.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1-2), 58–73 (2008).
[Crossref]

Chu, P. L.

Cizmeciyan, M.

Clark, W. G.

F.Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-Similar Evolution of Parabolic Pulses in a Laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[Crossref]

Coen, S.

Coillet, A.

Cui, Y.

X. Liu, X. Yao, and Y. Cui, “Real-Time Observation of the Buildup of Soliton Molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[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.

Duval, S.

Elu, U.

Emplit, P.

Ermolov, A.

Fermann, M.

Fermann, M. E.

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

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62(9), 910–912 (1993).
[Crossref]

Fortin, V.

Frosz, M.

Fuerbach, A.

Gelens, L.

Genest, J.

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]

Gmachl, C. F.

Y. Yao, A. J. Hoffman, and C. F. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6(7), 432–439 (2012).
[Crossref]

Grapinet, M.

J. M. Soto-Crespo, M. Grapinet, P. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 70(6), 066612 (2004).
[Crossref]

Gray, S.

Grelu, P.

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]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[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: Stat., Nonlinear, Soft Matter Phys. 70(6), 066612 (2004).
[Crossref]

P. Grelu and J. M. Soto-Crespo, “Multisoliton states and pulse fragmentation in a passively mode-locked fibre laser,” J. Opt. B: Quantum Semiclassical Opt. 6(5), S271–S278 (2004).
[Crossref]

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

Grudinin, A.

Haberl, F.

Haelterman, M.

Hamdi, S.

Hartl, I.

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

Haus, H.

Haus, H. A.

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64(2), 149–151 (1994).
[Crossref]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[Crossref]

Herink, G.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
[Crossref]

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

Hofer, M.

Hoffman, A. J.

Y. Yao, A. J. Hoffman, and C. F. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6(7), 432–439 (2012).
[Crossref]

Hu, T.

Hudson, D.

Hudson, D. D.

D. D. Hudson, “Short pulse generation in mid-IR fiber lasers,” Opt. Fiber Technol. 20(6), 631–641 (2014).
[Crossref]

Ilday, F.Ö.

F.Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-Similar Evolution of Parabolic Pulses in a Laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[Crossref]

Ippen, E.

Ippen, E. P.

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64(2), 149–151 (1994).
[Crossref]

Jackson, S.

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]

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

Jaramillo-Villegas, J. A.

C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (2016).
[Crossref]

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–808 (1992).
[Crossref]

Köttig, F.

Kurt, A.

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]

Lai, Q. T. K.

Leaird, D. E.

C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (2016).
[Crossref]

Leo, F.

Li, B.

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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).
[Crossref]

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M. Stratmann, T. Pagel, and F. Mitschke, “Experimental Observation of Temporal Soliton Molecules,” Phys. Rev. Lett. 95(14), 143902 (2005).
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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).
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Nelson, L.

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K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64(2), 149–151 (1994).
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M. Stratmann, T. Pagel, and F. Mitschke, “Experimental Observation of Temporal Soliton Molecules,” Phys. Rev. Lett. 95(14), 143902 (2005).
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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).
[Crossref]

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

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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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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. R. 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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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).
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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).
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M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62(9), 910–912 (1993).
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M. Stratmann, T. Pagel, and F. Mitschke, “Experimental Observation of Temporal Soliton Molecules,” Phys. Rev. Lett. 95(14), 143902 (2005).
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K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64(2), 149–151 (1994).
[Crossref]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993).
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C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (2016).
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[Crossref]

Wen, S.

Wise, F. W.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1-2), 58–73 (2008).
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F.Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-Similar Evolution of Parabolic Pulses in a Laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
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Xie, G.

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C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (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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Y. Yao, A. J. Hoffman, and C. F. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6(7), 432–439 (2012).
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[Crossref]

K. Tamura, L. E. Nelson, H. A. Haus, and E. P. Ippen, “Soliton versus nonsoliton operation of fiber ring lasers,” Appl. Phys. Lett. 64(2), 149–151 (1994).
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P. Grelu and J. M. Soto-Crespo, “Multisoliton states and pulse fragmentation in a passively mode-locked fibre laser,” J. Opt. B: Quantum Semiclassical Opt. 6(5), S271–S278 (2004).
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G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10(5), 321–326 (2016).
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M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–874 (2013).
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Optica (3)

Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. (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: Stat., Nonlinear, Soft Matter Phys. 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. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117(16), 163901 (2016).
[Crossref]

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]

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental Observation of Temporal Soliton Molecules,” Phys. Rev. Lett. 95(14), 143902 (2005).
[Crossref]

F.Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-Similar Evolution of Parabolic Pulses in a Laser,” Phys. Rev. Lett. 92(21), 213902 (2004).
[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]

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)

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Supplementary Material (3)

NameDescription
» Visualization 1       Transition from single-pulse mode-locking to pulsation state
» Visualization 2       Collapse of transient pulsation state
» Visualization 3       Buildup of phase-locked soliton pair

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Figures (10)

Fig. 1.
Fig. 1. Experimental set-up (see text for details). DM, dichroic mirror; AL, aspheric lens; FM, flip mirror; ISO, isolator; POL, polarizer.
Fig. 2.
Fig. 2. (a) Output pulse train recorded by the 33 GHz oscilloscope when the laser is mode-locked at the round-trip frequency (51.8 MHz). The dashed red line is measured using the mid-IR detector (PD 1), and the solid blue line is the second harmonic signal measured using the fast near-IR detector (PD 2). (b) FFT spectrum of the second harmonic signal. (c) and (d) Optical spectra and autocorrelation functions of the laser output pulses using 3.5-m-long gain fiber (blue) and 1.5-m-long gain fiber (red).
Fig. 3.
Fig. 3. (a), (c) and (e) Optical spectra of three soliton-molecule mode-locked states, measured by a FTIR. (b), (d) and (f) Autocorrelation traces of these three states, measured by the mid-IR autocorrelator.
Fig. 4.
Fig. 4. (a) and (b) Time-domain pulse trains and FFT spectra of the stable order 2 HML state. (c) and (d) Results of stable order 3 HML state.
Fig. 5.
Fig. 5. (a) SH-DFT set-up (see text for details). (b) and (c) Temporal and spectral evolution of a stable soliton pair, measured by the SH-DFT set-up. (d) Optical spectrum of the soliton pair in the mid-IR, measured by the FTIR.
Fig. 6.
Fig. 6. (a) Time-domain trace of the laser output measured using the mid-IR PD (panel (I)) and time-domain trace of the SH-DFT signal measured using the fast near-IR PD (panel (II)), when the laser is operating at a quasi-stable pulsation state. (b) Panel (I): Colormap of the SH-DFT signal at successive cavity roundtrips; Panel (II): Variations of the pulse energy and spectral bandwidth, estimated using the results shown in Fig. 6(a). (c) Evolution trajectory of this pulsation state in the bandwidth-energy plane.
Fig. 7.
Fig. 7. (a) Time-domain trace of the laser output measured using the mid-IR PD (panel (I)) and time-domain trace of the SH-DFT signal measured using the fast near-IR PD (panel (II)), when the laser is operating in the pulsation state with a period of 10 cavity roundtrips. (b) Panel (I): Colormap of the SH-DFT signal at successive cavity roundtrips; Panel (II): Variations of pulse energy and spectral bandwidth, estimated using the results shown in Fig. 7(a). (c) Evolution trajectory of this pulsation state in the bandwidth-energy plane.
Fig. 8.
Fig. 8. (a) Modulation of the laser pump power used to initiate soliton collapse (panel I), and a colormap of the SH-DFT signal over successive 35,000 cavity roundtrips (700 µs) during the soliton-collapse process (panel II). (b-d) Zoom-in plots (panel I) and variations of pulse energies and spectral bandwidths (panel II), at (b) single-pulse stage, (c) transient pulsation stage, and (d) pulse-collapse stage. (e) Bandwidth-energy trajectory during transition from single-pulse mode-locking to the transient pulsation state. (f) Bandwidth-energy trajectory during collapse of the transient pulsation state.
Fig. 9.
Fig. 9. (a) Modulation of the laser pump power from 2 W to 2.6 W, initiating soliton collapse (panel I), and colormap of the SH-DFT signal over successive 35,000 cavity roundtrips (700 µs) during the soliton-collapse process (panel II). (b-d) Zoom-in plots (panel I) and variations in pulse energy and spectral bandwidth (panel II), for (b) the single-pulse stage, (c) the transient pulsation stage, and (d) the pulse-collapse stage. (e) Bandwidth-energy trajectory during the transition from single-pulse mode-locking to the transient pulsation state. (f) Bandwidth-energy trajectory during collapse of the transient pulsation state.
Fig. 10.
Fig. 10. (a) Optical spectra of the quasi-stable single-pulse state (panel I) and stable soliton-pair state (panel II), measured by FTIR. (b) Colormaps of the signal from the mid-IR PD (panel I) and SH-DFT signal from the near-IR PD (panel II) over successive 10,000 cavity roundtrips (200 µs), showing the dynamics from single-pulse to soliton-pair mode-locked states. (c) Zoom into the build-up process of a soliton pair over 150 cavity roundtrips (3 µs). (d) Autocorrelation function of the SH-DFT signal, showing the evolution of the pulse separation. (e) Variations of pulse separation Δτ (panel I) and phase difference φ (panel II) between the two solitons in the pair. (f) Plot showing how φ varies over 100 cavity roundtrips (2 µs) as the number of roundtrips increases during soliton-pair buildup. Note that Δτ remains more or less constant.

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