Abstract

We report on the first experimental observation of dual wavelength domain wall type of dark solitons in a fiber laser made of all normal group velocity dispersion fibers. It was shown that this solitary wave is formed due to the cross coupling between two different wavelength laser beams and consists of localized dip structures separating the two different wavelength laser emissions.

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References

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  1. P. Emplit, J. P. Hamaide, F. Reynaud, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
    [CrossRef]
  2. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
    [CrossRef] [PubMed]
  3. Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18(5), 337–339 (1993).
    [CrossRef] [PubMed]
  4. I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991).
    [CrossRef] [PubMed]
  5. T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002).
    [CrossRef]
  6. 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]
  7. H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010).
    [CrossRef] [PubMed]
  8. M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19(2), 96–98 (1994).
    [CrossRef] [PubMed]
  9. B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994).
    [CrossRef] [PubMed]
  10. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998).
    [CrossRef]
  11. M. Haelterman and M. Badolo, “Dual-frequency wall solitary waves for nonreturn-to-zero signal transmission in W-type single-mode fibers,” Opt. Lett. 20(22), 2285–2287 (1995).
    [CrossRef] [PubMed]
  12. P. L. Boudec, C. Jaouen, P. L. François, J.-F. Bayon, F. Sanchez, P. Besnard, and G. Stéphan, “Antiphase dynamics and chaos in self-pulsing erbium-doped fiber lasers,” Opt. Lett. 18(22), 1890–1892 (1993).
    [CrossRef] [PubMed]
  13. S. Coen and T. Sylvestre, “Comment on ‘Dark pulse emission of a fiber laser’,” Phys. Rev. A 82(4), 047801 (2010).
    [CrossRef]
  14. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008).
    [CrossRef] [PubMed]
  15. C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34(14), 2096–2098 (2009).
    [CrossRef] [PubMed]

2010 (2)

H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010).
[CrossRef] [PubMed]

S. Coen and T. Sylvestre, “Comment on ‘Dark pulse emission of a fiber laser’,” Phys. Rev. A 82(4), 047801 (2010).
[CrossRef]

2009 (2)

C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34(14), 2096–2098 (2009).
[CrossRef] [PubMed]

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]

2008 (1)

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

2002 (1)

1998 (1)

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998).
[CrossRef]

1995 (1)

1994 (2)

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19(2), 96–98 (1994).
[CrossRef] [PubMed]

B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994).
[CrossRef] [PubMed]

1993 (2)

1991 (1)

1988 (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

1987 (1)

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

Badolo, M.

Barthelemy, A.

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

Bayon, J.-F.

Besnard, P.

Boudec, P. L.

Coen, S.

Emplit, P.

T. Sylvestre, S. Coen, P. Emplit, and M. Haelterman, “Self-induced modulational instability laser revisited: normal dispersion and dark-pulse train generation,” Opt. Lett. 27(7), 482–484 (2002).
[CrossRef]

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

Ferrando, A.

François, P. L.

Haelterman, M.

Hamaide, J. P.

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

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

Iii, I. N.

Jaouen, C.

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

Kivshar, Y. S.

Knize, R. J.

Leaird, D. E.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

Malomed, B. A.

B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994).
[CrossRef] [PubMed]

Milián, C.

Millot, G.

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998).
[CrossRef]

Pitois, S.

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998).
[CrossRef]

Reynaud, F.

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

Sanchez, F.

Sheppard, A. P.

Skryabin, D. V.

Stéphan, G.

Sylvestre, T.

Tang, D. Y.

H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010).
[CrossRef] [PubMed]

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

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

Turitsyn, S. K.

Wabnitz, S.

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998).
[CrossRef]

Weiner, A. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

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]

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

Zhang, H.

H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010).
[CrossRef] [PubMed]

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

Zhao, L. M.

H. Zhang, D. Y. Tang, L. M. Zhao, and R. J. Knize, “Vector dark domain wall solitons in a fiber ring laser,” Opt. Express 18(5), 4428–4433 (2010).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. A (2)

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]

S. Coen and T. Sylvestre, “Comment on ‘Dark pulse emission of a fiber laser’,” Phys. Rev. A 82(4), 047801 (2010).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

B. A. Malomed, “Optical domain walls,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(2), 1565–1571 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counter propagating laser beams,” Phys. Rev. Lett. 81(7), 1409–1412 (1998).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61(21), 2445–2448 (1988).
[CrossRef] [PubMed]

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

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Figures (5)

Fig. 1
Fig. 1

Schematics of the fiber laser. WDM: wavelength division multiplexer. EDF: erbium doped fiber. PDI: polarization dependent isolator. PCs: polarization controllers.

Fig. 2
Fig. 2

(a) Spectrum; (b) a magnified figure of the dual-wavelength DWS emission of the laser ; (c) full oscilloscope trace of dual wavelength DWS;(d) FWHM duration and total output power versus pump power.

Fig. 3
Fig. 3

(a) Wavelength resolved spectra and (b) Oscilloscope trace of the total (upper trace) and one wavelength laser emission (lower trace), measured under pump power ~260 mW.

Fig. 4
Fig. 4

(a) Spectra and (b) oscilloscope traces of the laser emission with the NLSE dark solitons appeared on emission at one of the wavelengths, measured under higher pump power ~450 mW. The upper (lower) trace corresponds to the spectrum whose longer (shorter) wavelength line is broadened.

Fig. 5
Fig. 5

Dual-wavelength DWS numerically calculated. (a) Domain wall profiles and DWS at a particular roundtrip (b) The corresponding spectrum. Evolution of the dual wavelength domain wall with the cavity roundtrips: (c) one wavelength (shorter wavelength) (d) Another wavelength (longer wavelength).

Equations (2)

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u 1 z = i β u 1 i k 2 2 u 1 t 2 + k 6 3 u 1 t 3 + i γ ( | u 1 | 2 + 2 | u 2 | 2 ) u + g 2 u 1 + g 2 Ω g 2 2 u 1 t 2 u 2 z = i β u 2 i k ' ' 2 2 u 2 t 2 + k ' ' ' 6 3 u 2 t 3 + i γ ( | u 2 | 2 + 2 | u 1 | 2 ) u 2 + g 2 u 2 + g 2 Ω g 2 2 u 2 t 2
g = G exp [ ( | u 1 | 2 + | u 2 | 2 ) d t P s a t ]

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