Abstract

We have numerically solved an extended version of the nonlinear Schrödinger equation, taking into account higher-order dispersion, the shock (self-steepening) term, and a term describing the Raman self-pumping of an ultrashort pulse. It is shown that the Raman effect is dominant on a femtosecond time scale and leads to the decay of higher-order solitons. For the case of the N = 2 soliton an intense pulse at a distinctly Stokes-shifted frequency is created. This pulse eventually shapes into a fundamental soliton, and its further evolution is governed by the combination of dispersion, self-phase modulation, and the soliton self-frequency shift.

© 1987 Optical Society of America

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  1. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  2. P. K. A. Wai, C. R. Menyuk, Y. C. Lee, H. H. Chen, Opt. Lett. 11, 464 (1986).
    [Crossref] [PubMed]
  3. E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).
  4. L. F. Mollenauer, R. H. Stolen, Opt. Lett. 9, 13 (1984).
    [Crossref] [PubMed]
  5. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [Crossref] [PubMed]
  6. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [Crossref] [PubMed]
  7. L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
    [Crossref]
  8. R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
    [Crossref]
  9. R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1972).
    [Crossref]
  10. P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
    [Crossref]
  11. B. Zysset, P. Beaud, W. Hodel, Appl. Phys. Lett. 50, 1027 (1987).
    [Crossref]
  12. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

1987 (2)

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[Crossref]

B. Zysset, P. Beaud, W. Hodel, Appl. Phys. Lett. 50, 1027 (1987).
[Crossref]

1986 (4)

1985 (2)

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

1984 (1)

1980 (1)

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

1975 (1)

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[Crossref]

1972 (1)

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1972).
[Crossref]

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[Crossref]

B. Zysset, P. Beaud, W. Hodel, Appl. Phys. Lett. 50, 1027 (1987).
[Crossref]

Bischel, W. K.

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[Crossref]

Chen, H. H.

Dianov, E. M.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Fisher, R. A.

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[Crossref]

Fomichev, A. A.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Golovchenko, E. A.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).

Gordon, J. P.

J. P. Gordon, Opt. Lett. 11, 662 (1986).
[Crossref] [PubMed]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

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

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[Crossref]

B. Zysset, P. Beaud, W. Hodel, Appl. Phys. Lett. 50, 1027 (1987).
[Crossref]

Ippen, E. P.

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1972).
[Crossref]

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Lee, Y. C.

Mamyshev, P. V.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
[Crossref] [PubMed]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

L. F. Mollenauer, R. H. Stolen, Opt. Lett. 9, 13 (1984).
[Crossref] [PubMed]

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

Prokhorov, A. M.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).

Stel'makh, M. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, Opt. Lett. 9, 13 (1984).
[Crossref] [PubMed]

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

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1972).
[Crossref]

Wai, P. K. A.

Weber, H. P.

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[Crossref]

Zysset, B.

B. Zysset, P. Beaud, W. Hodel, Appl. Phys. Lett. 50, 1027 (1987).
[Crossref]

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[Crossref]

Appl. Phys. Lett. (2)

R. H. Stolen, E. P. Ippen, Appl. Phys. Lett. 22, 276 (1972).
[Crossref]

B. Zysset, P. Beaud, W. Hodel, Appl. Phys. Lett. 50, 1027 (1987).
[Crossref]

IEEE J. Quantum Electron. (2)

P. Beaud, W. Hodel, B. Zysset, H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[Crossref]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[Crossref]

J. Appl. Phys. (1)

R. A. Fisher, W. K. Bischel, J. Appl. Phys. 46, 4921 (1975).
[Crossref]

JETP Lett. (2)

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel'makh, A. A. Fomichev, JETP Lett. 41, 294 (1985).

Opt. Lett. (4)

Phys. Rev. Lett. (1)

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

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Figures (3)

Fig. 1
Fig. 1

The spectral evolution along the fiber of a 100-fsec N = 2 soliton under the influence of third-order dispersion, the shock term, and the Raman term. The actual fiber length is normalized to the soliton period of the input pulse: z/z0 = 0 (a), 0.5 (b), 1 (c), 1.5 (d), 2 (e), and 2.5 (f). The spectral intensity (plotted against ν0ν) is in arbitrary units, but the scale is the same for all traces except (a).

Fig. 2
Fig. 2

The frequency shift ν0ν (a) and the corresponding pulse duration (b) of the Stokes pulse as a function of the normalized fiber length.

Fig. 3
Fig. 3

The temporal evolution of the soliton as a function of the normalized fiber length: z/z0 = 0 (a), 0.25 (b), 0.5 (c), 0.75 (d), and 1 (e). The pulse intensity is normalized to the input-pulse peak intensity.

Equations (3)

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i A / z ½ k 0 2 A / t 2 + n 2 k 0 A | A | 2 = 0 ,
i A / z ½ k 0 2 A / t 2 + n 2 k 0 A | A | 2 = i / 6 k 0 3 A / t 3 2 i n 2 / c ( A | A | 2 ) / t + c R A | A | 2 / t .
E = const . λ 3 D ( λ ) A eff ( λ ) / T ,

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