Abstract

We found two kinds of soliton explosions based on the complex Ginzburg-Landau equation without nonlinearity saturation and high-order effects, demonstrating the soliton explosions as an intrinsic property of the dissipative systems. The two kinds of soliton explosions are caused by the dual-pulsing instability and soliton erupting, respectively. The transformation and relationship between the two kinds of soliton explosions are discussed. The parameter space for the soliton explosion in a mode-locked laser cavity is found numerically. Our results can help one to obtain or avoid the soliton explosions in mode-locked fiber lasers and understand the nonlinear dynamics of the dissipative systems.

© 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]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (3)

2016 (5)

2015 (1)

2013 (2)

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–875 (2013).
[Crossref]

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

2012 (1)

C. Cartes, O. Descalzi, and H. R. Brand, “Noise can induce explosions for dissipative solitons,” Phys. Rev. E 85(1), 015205 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (2)

S. C. V. Latas and M. F. S. Ferreira, “Soliton explosion control by higher-order effects,” Opt. Lett. 35(11), 1771–1773 (2010).
[Crossref] [PubMed]

X. M. Liu, “Pulse evolution without wave-breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010).
[Crossref]

2007 (1)

D. Turaev, A. G. Vladimirov, and S. Zelik, “Chaotic bound state of localized structures in the complex Ginzburg-Landau equation,” Phys. Rev. E 75(4), 045601 (2007).
[Crossref] [PubMed]

2005 (1)

E. Podivilov and V. L. Kalashinkov, “Heavily chirped solitary pulses in the normal dispersion region: new solitons of the cubic-quintic complex Ginzburg-Landau equation,” JEPT Lett. 82(8), 524–528 (2005).

2004 (1)

N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E 70(3), 036613 (2004).
[Crossref] [PubMed]

2003 (1)

N. Akhmediev and J. M. Soto-Crespo, “Exploding solitons and Shil’nikov’s theorem,” Phys. Lett. A 317(3-4), 287–292 (2003).
[Crossref]

2002 (2)

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
[Crossref] [PubMed]

I. S. Aranson and L. Kramer, “The world of complex Ginzburg-Landau equation,” Rev. Mod. Phys. 71(1), 99–143 (2002).
[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] [PubMed]

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] [PubMed]

1996 (1)

V. V. Afanasjev, N. Akhmediev, and J. M. Soto-Crespo, “Three forms of localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53(2), 1931–1940 (1996).

Afanasjev, V. V.

V. V. Afanasjev, N. Akhmediev, and J. M. Soto-Crespo, “Three forms of localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53(2), 1931–1940 (1996).

Akhmediev, N.

N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E 70(3), 036613 (2004).
[Crossref] [PubMed]

N. Akhmediev and J. M. Soto-Crespo, “Exploding solitons and Shil’nikov’s theorem,” Phys. Lett. A 317(3-4), 287–292 (2003).
[Crossref]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

V. V. Afanasjev, N. Akhmediev, and J. M. Soto-Crespo, “Three forms of localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53(2), 1931–1940 (1996).

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] [PubMed]

Aranson, I. S.

I. S. Aranson and L. Kramer, “The world of complex Ginzburg-Landau equation,” Rev. Mod. Phys. 71(1), 99–143 (2002).
[Crossref]

Brand, H. R.

C. Cartes, O. Descalzi, and H. R. Brand, “Noise can induce explosions for dissipative solitons,” Phys. Rev. E 85(1), 015205 (2012).
[Crossref] [PubMed]

Broderick, N. G. R.

Cartes, C.

C. Cartes and O. Descalzi, “Periodic exploding dissipative solitons,” Phys. Rev. A 93(3), 031801 (2016).
[Crossref]

C. Cartes, O. Descalzi, and H. R. Brand, “Noise can induce explosions for dissipative solitons,” Phys. Rev. E 85(1), 015205 (2012).
[Crossref] [PubMed]

Christodoulides, D. N.

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Cui, H.

Cundiff, S. T.

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
[Crossref] [PubMed]

Descalzi, O.

C. Cartes and O. Descalzi, “Periodic exploding dissipative solitons,” Phys. Rev. A 93(3), 031801 (2016).
[Crossref]

C. Cartes, O. Descalzi, and H. R. Brand, “Noise can induce explosions for dissipative solitons,” Phys. Rev. E 85(1), 015205 (2012).
[Crossref] [PubMed]

Du, Y. Q.

Erkintalo, M.

Fermann, M. E.

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–875 (2013).
[Crossref]

Ferreira, M. F. S.

Goda, K.

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

Grelu, P.

Hartl, I.

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–875 (2013).
[Crossref]

Hu, S.

Jalali, B.

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

Kalashinkov, V. L.

E. Podivilov and V. L. Kalashinkov, “Heavily chirped solitary pulses in the normal dispersion region: new solitons of the cubic-quintic complex Ginzburg-Landau equation,” JEPT Lett. 82(8), 524–528 (2005).

Karupa, K.

Kramer, L.

I. S. Aranson and L. Kramer, “The world of complex Ginzburg-Landau equation,” Rev. Mod. Phys. 71(1), 99–143 (2002).
[Crossref]

Latas, S. C. V.

Liu, M.

Liu, X. M.

X. M. Liu, “Pulse evolution without wave-breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010).
[Crossref]

Liu, Y. C.

Luo, A. P.

Luo, Z. C.

Nithyanandan, K.

Podivilov, E.

E. Podivilov and V. L. Kalashinkov, “Heavily chirped solitary pulses in the normal dispersion region: new solitons of the cubic-quintic complex Ginzburg-Landau equation,” JEPT Lett. 82(8), 524–528 (2005).

Runge, A. F. J.

Shu, X. W.

Soto-Crespo, J. M.

N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E 70(3), 036613 (2004).
[Crossref] [PubMed]

N. Akhmediev and J. M. Soto-Crespo, “Exploding solitons and Shil’nikov’s theorem,” Phys. Lett. A 317(3-4), 287–292 (2003).
[Crossref]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

V. V. Afanasjev, N. Akhmediev, and J. M. Soto-Crespo, “Three forms of localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53(2), 1931–1940 (1996).

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] [PubMed]

Turaev, D.

D. Turaev, A. G. Vladimirov, and S. Zelik, “Chaotic bound state of localized structures in the complex Ginzburg-Landau equation,” Phys. Rev. E 75(4), 045601 (2007).
[Crossref] [PubMed]

Vladimirov, A. G.

D. Turaev, A. G. Vladimirov, and S. Zelik, “Chaotic bound state of localized structures in the complex Ginzburg-Landau equation,” Phys. Rev. E 75(4), 045601 (2007).
[Crossref] [PubMed]

Wise, F. W.

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Wright, L. G.

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Xu, W. C.

Yan, Y. R.

Yao, J.

Zelik, S.

D. Turaev, A. G. Vladimirov, and S. Zelik, “Chaotic bound state of localized structures in the complex Ginzburg-Landau equation,” Phys. Rev. E 75(4), 045601 (2007).
[Crossref] [PubMed]

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

JEPT Lett. (1)

E. Podivilov and V. L. Kalashinkov, “Heavily chirped solitary pulses in the normal dispersion region: new solitons of the cubic-quintic complex Ginzburg-Landau equation,” JEPT Lett. 82(8), 524–528 (2005).

Nat. Photonics (2)

M. E. Fermann and I. Hartl, “Ultrafast fibre lasers,” Nat. Photonics 7(11), 868–875 (2013).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (4)

Optica (2)

Phys. Lett. A (1)

N. Akhmediev and J. M. Soto-Crespo, “Exploding solitons and Shil’nikov’s theorem,” Phys. Lett. A 317(3-4), 287–292 (2003).
[Crossref]

Phys. Rev. A (2)

C. Cartes and O. Descalzi, “Periodic exploding dissipative solitons,” Phys. Rev. A 93(3), 031801 (2016).
[Crossref]

X. M. Liu, “Pulse evolution without wave-breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81(5), 053819 (2010).
[Crossref]

Phys. Rev. E (5)

D. Turaev, A. G. Vladimirov, and S. Zelik, “Chaotic bound state of localized structures in the complex Ginzburg-Landau equation,” Phys. Rev. E 75(4), 045601 (2007).
[Crossref] [PubMed]

V. V. Afanasjev, N. Akhmediev, and J. M. Soto-Crespo, “Three forms of localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53(2), 1931–1940 (1996).

C. Cartes, O. Descalzi, and H. R. Brand, “Noise can induce explosions for dissipative solitons,” Phys. Rev. E 85(1), 015205 (2012).
[Crossref] [PubMed]

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] [PubMed]

N. Akhmediev and J. M. Soto-Crespo, “Strongly asymmetric soliton explosions,” Phys. Rev. E 70(3), 036613 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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] [PubMed]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88(7), 073903 (2002).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

I. S. Aranson and L. Kramer, “The world of complex Ginzburg-Landau equation,” Rev. Mod. Phys. 71(1), 99–143 (2002).
[Crossref]

Science (1)

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Supplementary Material (3)

NameDescription
» Visualization 1       this is a visualization of the pulse dynamics related to Fig. 3 in our submitted manuscript.
» Visualization 2       this is a visualization of the pulse dynamics related to Fig. 4 in our submitted manuscript.
» Visualization 3       this is a visualization of the pulse dynamics related to Fig. 5 in our submitted manuscript.

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Figures (9)

Fig. 1
Fig. 1 Schematic of the fiber laser in our simulation. LD:laser diode, WDM:wavelength division multiplexer, OC: output coupler, SA: saturable absorber, EDF: Er-doped fiber, SMF: single mode fiber.
Fig. 2
Fig. 2 Pulse characteristics with 1020pJ pump strength, 70% modulation depth and 0.091ps2 net-dispersion: (a) pulse evolution in temporal domain, (b) pulse evolution in spectral domain, (c) pulse energy evolution, (d) evolution of frequency width of the soliton, (e) pulse intensity profiles at different stages, (f) pulse spectra at different stages.
Fig. 3
Fig. 3 Pulse characteristics with 1180pJ pump strength, 70% modulation depth and 0.091ps2 net-dispersion: (a) pulse evolution in temporal domain (see Visualization 1), (b) pulse evolution in spectral domain (see Visualization 1), (c) pulse energy evolution, (d) evolution of frequency width of the soliton, (e) pulse intensity profiles at different stages, (f) pulse spectra at different stages.
Fig. 4
Fig. 4 Pulse characteristics with 1800pJ pump strength, 70% modulation depth and 0.1ps2 net-dispersion: (a) pulse evolution in temporal domain (see Visualization 2), (b) pulse evolution in spectral domain (see Visualization 2), (c) pulse energy evolution, (d) evolution of frequency width of the soliton, (e) pulse intensity profiles at different stages, (f) pulse spectra at different stages.
Fig. 5
Fig. 5 Pulse characteristics with 2400pJ pump strength, 70% modulation depth and 0.1ps2 net-dispersion: (a) pulse evolution in temporal domain (see Visualization 3), (b) pulse evolution in spectral domain (see Visualization 3), (c) pulse intensity profiles at different stages, (d) pulse spectra at different stages, (e) pulse energy evolution.
Fig. 6
Fig. 6 Pulse characteristics with 10000pJ pump strength, 70% modulation depth and 0.1ps2 net-dispersion: (a) pulse evolution in temporal domain, (b) pulse evolution in spectral domain, (c) pulse intensity profiles at different stages, (d) pulse spectra at different stages, (e) pulse energy evolution.
Fig. 7
Fig. 7 Pulse evolutions (normalized) with 70% modulation depth and 0.091ps2 net-dispersion under different pump strength: (a) 1180pJ, (b) 1190pJ, (c) 1200pJ.
Fig. 8
Fig. 8 Upper and lower limits of the pump strength for the soliton explosion happening with 70% modulation depth under different net-dispersion.
Fig. 9
Fig. 9 Pulse evolutions with 70% modulation depth, 0.1ps2 net-dispersion, 1700pJ pump strength under different spectral filtering: (a) and (d) without BPF, (b) and (e) 10nm(FWHM) BPF, (c) and (f) 5nm BPF.

Equations (3)

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u z = 1 2 i β 2 2 u T 2 + i γ | u | 2 u + 1 2 g ( 1 + 1 Ω 2 2 T 2 ) u
g = g 0 exp ( | u | 2 d t / E s )
T = 1 α / ( 1 + P / P 0 )

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