Abstract

We show that the generalized nonlinear Schrödinger equation admits of an analytical solution for a bright optical soliton in the presence of fourth-order dispersion. The soliton envelope is expressed as the square of a hyperbolic secant. The peak power and the duration of the soliton are uniquely defined. Numerical simulations tend to show that the temporal shape and the peak power of the soliton are stable when a weak third-order dispersion is introduced.

© 1996 Optical Society of America

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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1996 (1)

1994 (3)

1993 (2)

B. E. Lemoff, C. P. J. Barty, Opt. Lett. 18, 57 (1993).
[CrossRef] [PubMed]

M. Klauder, E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. A 47, 3844 (1993).

1990 (2)

1987 (1)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

1986 (1)

F. Salin, P. Grangier, G. Roger, A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

1985 (1)

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

1983 (2)

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1973 (1)

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

Aitchison, J. S.

Barthelemy, A.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Barty, C. P. J.

Blow, K. J.

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[CrossRef]

Brun, A.

F. Salin, P. Grangier, G. Roger, A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Chen, H. H.

P. K. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Christov, I. P.

Cummins, E.

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[CrossRef]

Doran, N. J.

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Grangier, P.

F. Salin, P. Grangier, G. Roger, A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Hasegawa, A.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

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

Huang, C. P.

Jackel, J. L.

Kapteyn, H. C.

Kasper, A.

Klauder, M.

M. Klauder, E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. A 47, 3844 (1993).

Kodama, Y.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Krausz, F.

Laedke, E. W.

M. Klauder, E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. A 47, 3844 (1993).

Laird, D. E.

Lee, Y. C.

P. K. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Lemoff, B. E.

Maneuf, S.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Mollenauer, L. F.

R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Murnane, M. M.

Oliver, M. K.

Roger, G.

F. Salin, P. Grangier, G. Roger, A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Salin, F.

F. Salin, P. Grangier, G. Roger, A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Silberberg, Y.

Smith, P. W. E.

Spatschek, K. H.

M. Klauder, E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. A 47, 3844 (1993).

Spielmann, C.

Stingl, A.

Stolen, R. H.

R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Szipöcs, R.

Taft, G.

Tappert, F.

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

Tomlinson, W. J.

Turitsyn, S. K.

M. Klauder, E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. A 47, 3844 (1993).

Vogel, E. M.

Wai, P. K.

P. K. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

Weiner, A. M.

Witte, K. J.

Zhou, J. P.

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Opt. Commun. (2)

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (2)

P. K. Wai, H. H. Chen, Y. C. Lee, Phys. Rev. A 41, 426 (1990).
[CrossRef] [PubMed]

M. Klauder, E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. A 47, 3844 (1993).

Phys. Rev. Lett. (2)

F. Salin, P. Grangier, G. Roger, A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

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Figures (4)

Fig. 1
Fig. 1

Intensity distributions of the fundamental NSE soliton (solid curves) and of the GNSE soliton with fourth-order dispersion (dashed curves) (a) on a linear scale and (b) on a logarithmic scale. The pulse durations T1 and T2 have been chosen such that the two distributions have the same full width at half-maximum, Δt.

Fig. 2
Fig. 2

Power spectra of the fundamental NSE soliton (solid curve) and of the GNSE soliton with fourth-order dispersion (dashed curve) shown in Fig. 1.

Fig. 3
Fig. 3

Evolution of the temporal intensity distribution of the GNSE soliton with (a) β3 = 0 or (b) β3 = −500 fs3/cm. All other parameters are given in the text.

Fig. 4
Fig. 4

Variation of the peak power of the GNSE soliton with propagation distance z for the values of β3 shown.

Equations (9)

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A z = i β 2 2 2 A T 2 + β 3 6 3 A T 3 + i β 4 24 4 A T 4 + i γ | A | 2 A ,
γ = n 2 ω 0 c A eff ,
A ( z , T ) = A 2 sech 2 ( T / T 2 ) exp ( i a 2 z ) .
a 2 = 24 25 β 2 2 β 4 ,
| A 2 | 2 = 9 5 β 2 2 γ β 4 ,
T 2 2 = 5 3 β 4 β 2 .
A ( z , ω ) = π 2 A 2 T 2 2 ω sinh ( ω T 2 π / 2 ) ,
β 2 ( ω ) = β 2 + β 3 3 ω + β 4 12 ω 2 ,
| β 3 | < 3 β 2 β 4 ,

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