Abstract

Dark soliton formation and soliton dynamics in all-normal dispersion cavity fiber ring lasers without an anti-saturable absorber in cavity is studied both theoretically and numerically. It is shown that under suitable conditions the dark solitons formed could be described by the nonlinear Schrödinger equation. The dark soliton formation in an all-normal-dispersion cavity erbium-doped fiber ring laser without an anti-saturable absorber in cavity is first experimentally demonstrated. Individual dark solitons are experimentally identified. Excellent agreement between theory and experiment is observed.

© 2014 Optical Society of America

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References

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  1. Y. S. Kivishar and G. Agrawal, Optical Solitons: From fiber to photonic crystals, Academic Press, 2003.
  2. Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
    [CrossRef] [PubMed]
  3. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
    [CrossRef]
  4. P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. 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]
  9. H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
    [CrossRef]
  10. D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
    [CrossRef]
  11. M. J. Ablowitz, T. P. Horikis, S. D. Nixon, and D. J. Frantzeskakis, “Dark solitons in mode-locked lasers,” Opt. Lett. 36(6), 793–795 (2011).
    [CrossRef] [PubMed]
  12. V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).
  13. S. A. Gredeskul and Y. S. Kivshar, “Generation of dark solitons in optical fibers,” Phys. Rev. Lett. 62(8), 977 (1989).
    [CrossRef] [PubMed]
  14. S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
    [CrossRef]

2013

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

2012

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

2011

2009

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
[CrossRef]

2005

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]

1992

1991

1989

S. A. Gredeskul and Y. S. Kivshar, “Generation of dark solitons in optical fibers,” Phys. Rev. Lett. 62(8), 977 (1989).
[CrossRef] [PubMed]

1987

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

1986

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

1980

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[CrossRef]

1973

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Ablowitz, M. J.

Assanto, G.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

Barthelemy, A.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

Blow, K. J.

Chen, C. J.

Chen, Z. G.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Christodoulides, D. N.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Doran, N. J.

Emplit, P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

Frantzeskakis, D. J.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[CrossRef]

Gredeskul, S. A.

S. A. Gredeskul and Y. S. Kivshar, “Generation of dark solitons in optical fibers,” Phys. Rev. Lett. 62(8), 977 (1989).
[CrossRef] [PubMed]

Groehly, C.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

Hamaide, J. P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

Horikis, T. P.

Iii, I. N.

Kelly, S. M. J.

Kivshar, Y. S.

S. A. Gredeskul and Y. S. Kivshar, “Generation of dark solitons in optical fibers,” Phys. Rev. Lett. 62(8), 977 (1989).
[CrossRef] [PubMed]

Li, L.

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

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]

Menyuk, C. R.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[CrossRef]

Nixon, S. D.

Reynaud, F.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

Seaton, C. T.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

Segev, M.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Shen, D. Y.

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

Smith, K.

Song, Y. F.

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

Stegeman, G. I.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

Stolen, R. H.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[CrossRef]

Tang, D. Y.

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
[CrossRef]

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]

Trillo, S.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

Wai, P. K. A.

Wu, X.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Zhang, H.

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
[CrossRef]

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.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
[CrossRef]

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. Lett.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, “Experimental observation of polarization instability in a birefringent optical fiber,” Appl. Phys. Lett. 49(19), 1224–1226 (1986).
[CrossRef]

Opt. Commun.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Groehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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]

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A 80(4), 045803 (2009).
[CrossRef]

D. Y. Tang, L. Li, Y. F. Song, H. Zhang, and D. Y. Shen, “Evidence of dark solitons in all-normal dispersion fiber lasers,” Phys. Rev. A 88(1), 013849 (2013).
[CrossRef]

Phys. Rev. Lett.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980).
[CrossRef]

S. A. Gredeskul and Y. S. Kivshar, “Generation of dark solitons in optical fibers,” Phys. Rev. Lett. 62(8), 977 (1989).
[CrossRef] [PubMed]

Rep. Prog. Phys.

Z. G. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Sov. Phys. JETP

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

Other

Y. S. Kivishar and G. Agrawal, Optical Solitons: From fiber to photonic crystals, Academic Press, 2003.

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Figures (5)

Fig. 1
Fig. 1

Normalized intensity of the dark solitons calculated from Eq. (4) with different values ofϕ.

Fig. 2
Fig. 2

Numerically simulated dark soliton formation initialed by a dip of A2 = 0.02W, B = 1, C = 0.25. (a) Contour plot under Es = 0.9pJ. (b) Intensity and phase profiles of the dark solitons at the round trip of 1200.

Fig. 3
Fig. 3

Schematic configuration of the fiber laser. WDM: wavelength division multiplexer. DSF: dispersion shifted fiber. EDF: erbium doped fiber. PC: polarization controller.

Fig. 4
Fig. 4

Dark pulse emission of the fiber laser experimentally observed. (a) A measured oscilloscope trace; (b) the corresponding optical spectrum.

Fig. 5
Fig. 5

The laser emission over 4 consecutive cavity roundtrips (a) the overall laser emission in 200 ns; (b) Zoom-in of a small segment in the four roundtrips.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

i u z β 2 2 2 u t 2 +γ | u | 2 ui gα 2 ui g 2 Ω g 2 2 u t 2 =0
g= g 0 1+ | u | 2 dt / E s
i U ξ η 2 2 U τ 2 + | U | 2 Ui (GL) 2 Ui G 2 Ω 2 2 U τ 2 =0
U( ξ,τ )= u 0 [cosϕtanh( u 0 cosϕ( τ u 0 ξsinϕ ) )+isinϕ]exp( i u 0 2 ξ )

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