Abstract

We report the observation of nonlinear propagation of picosecond odd-symmetry dark pulses over 1-km single-mode fiber in the near infrared. The pulses are shown to propagate without distortion at the power corresponding to the fundamental dark soliton of the nonlinear Schrödinger equation. Our measurements are in quantitative agreement with numerical solutions to a modified nonlinear Schrödinger equation—including fiber loss—and constitute the first evidence to our knowledge of dark soliton propagation over fiber lengths compatible with optical telecommunication systems.

© 1993 Optical Society of America

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, 171 (1973).
    [CrossRef]
  2. L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
    [CrossRef]
  3. Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
    [CrossRef]
  4. D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
    [CrossRef] [PubMed]
  5. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
    [CrossRef] [PubMed]
  6. J. Rothenberg, Opt. Commun. 82, 107 (1991); J. Rothenberg, H. Heinrich, Opt. Lett. 17, 261 (1992).
    [CrossRef] [PubMed]
  7. W. Zhao, E. Bourkoff, J. Opt. Soc. Am. B 9, 1134 (1992).
    [CrossRef]
  8. J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
    [CrossRef]
  9. M. Lisak, D. Anderson, B. Malomed, Opt. Lett. 16, 1936 (1991).
    [CrossRef] [PubMed]
  10. W. Zhao, E. Bourkoff, Opt. Lett. 14, 1371 (1989).
    [CrossRef] [PubMed]
  11. J.-P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
    [CrossRef] [PubMed]
  12. Ph. Emplit, J.-P. Hamaide, M. Haelterman, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 248.
  13. Ph. Emplit, J.-P. Hamaide, F. Reynaud, Opt. Lett. 17, 1358 (1992).
    [CrossRef] [PubMed]
  14. B. Colombeau, M. Vampouille, C. Froehly, Opt. Commun. 19, 201 (1976).
    [CrossRef]
  15. R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
    [CrossRef]
  16. W. Zhao, E. Bourkoff, Opt. Lett. 14, 703 (1989).
    [CrossRef] [PubMed]

1992 (2)

1991 (4)

J.-P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
[CrossRef] [PubMed]

M. Lisak, D. Anderson, B. Malomed, Opt. Lett. 16, 1936 (1991).
[CrossRef] [PubMed]

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

J. Rothenberg, Opt. Commun. 82, 107 (1991); J. Rothenberg, H. Heinrich, Opt. Lett. 17, 261 (1992).
[CrossRef] [PubMed]

1990 (1)

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

1989 (2)

1988 (2)

D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

1987 (1)

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

1978 (1)

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

1976 (1)

B. Colombeau, M. Vampouille, C. Froehly, Opt. Commun. 19, 201 (1976).
[CrossRef]

1973 (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, 171 (1973).
[CrossRef]

Anderson, D.

Barthélémy, A.

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Bourkoff, E.

Colombeau, B.

B. Colombeau, M. Vampouille, C. Froehly, Opt. Commun. 19, 201 (1976).
[CrossRef]

Emplit, Ph.

Ph. Emplit, J.-P. Hamaide, F. Reynaud, Opt. Lett. 17, 1358 (1992).
[CrossRef] [PubMed]

J.-P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
[CrossRef] [PubMed]

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Ph. Emplit, J.-P. Hamaide, M. Haelterman, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 248.

Evangelides, S. G.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Froehly, C.

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

B. Colombeau, M. Vampouille, C. Froehly, Opt. Commun. 19, 201 (1976).
[CrossRef]

Giannini, J. A.

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

Giuliani, G.

D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Grischkowsky, D.

D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Haelterman, M.

J.-P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
[CrossRef] [PubMed]

Ph. Emplit, J.-P. Hamaide, M. Haelterman, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 248.

Halas, N. J.

D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Hamaide, J.-P.

Ph. Emplit, J.-P. Hamaide, F. Reynaud, Opt. Lett. 17, 1358 (1992).
[CrossRef] [PubMed]

J.-P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
[CrossRef] [PubMed]

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Ph. Emplit, J.-P. Hamaide, M. Haelterman, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 248.

Haner, M.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, 171 (1973).
[CrossRef]

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Joseph, R. I.

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Krökel, D.

D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

Leaird, D. E.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Lichtman, E.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Lin, C.

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Lisak, M.

Malomed, B.

Mollenauer, L. F.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Neubelt, M. J.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Nyman, B. M.

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

Reynaud, F.

Ph. Emplit, J.-P. Hamaide, F. Reynaud, Opt. Lett. 17, 1358 (1992).
[CrossRef] [PubMed]

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Rothenberg, J.

J. Rothenberg, Opt. Commun. 82, 107 (1991); J. Rothenberg, H. Heinrich, Opt. Lett. 17, 261 (1992).
[CrossRef] [PubMed]

Stolen, R. H.

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, 171 (1973).
[CrossRef]

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Vampouille, M.

B. Colombeau, M. Vampouille, C. Froehly, Opt. Commun. 19, 201 (1976).
[CrossRef]

Weiner, A. M.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Zhao, W.

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142, 171 (1973).
[CrossRef]

Electron. Lett. (1)

L. F. Mollenauer, M. J. Neubelt, M. Haner, E. Lichtman, S. G. Evangelides, B. M. Nyman, Electron. Lett. 27, 2055 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

J. Rothenberg, Opt. Commun. 82, 107 (1991); J. Rothenberg, H. Heinrich, Opt. Lett. 17, 261 (1992).
[CrossRef] [PubMed]

B. Colombeau, M. Vampouille, C. Froehly, Opt. Commun. 19, 201 (1976).
[CrossRef]

Ph. Emplit, J.-P. Hamaide, F. Reynaud, C. Froehly, A. Barthélémy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

R. H. Stolen, C. Lin, Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Phys. Rev. Lett. (2)

D. Krökel, N. J. Halas, G. Giuliani, D. Grischkowsky, Phys. Rev. Lett. 60, 29 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988); W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef] [PubMed]

Other (1)

Ph. Emplit, J.-P. Hamaide, M. Haelterman, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 248.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Pulse intensity profiles showing numerical simulations for (a) the shaped 5.3-ps odd-symmetry dark pulse at the fiber input; the numerical simulations for the 1-km fiber output pulses are shown under initial peak power conditions corresponding to (b) linear, (c) soliton, and (d) order-2 soliton propagations. The dotted curves in (e)–(h) are the numerical predictions of streak profiles for the signals shown in (a)–(d); the superimposed solid curves in (e)–(h) are the experimental streak profiles.

Fig. 3
Fig. 3

Spectral densities of (a) the shaped 5.3-ps odd-symmetry dark pulse at the fiber input and (b) the fiber output at high initial peak power (order-2 soliton). The dotted curves are the numerical predictions, and the solid curves are the experimental results.

Equations (1)

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A 0 ( τ ) = C - + d t A i ( τ - t ) ( rect [ t ( x ) ] × exp { i phase [ t ( x ) ] } ) ,

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