Abstract

The effect of stimulated Raman scattering on soliton propagation in fibers is studied for pulse durations comparable with or shorter than the molecular oscillation period. The self-frequency shift of a soliton in this interaction regime is calculated to be inversely proportional to the soliton duration and does not depend on both the characteristic frequency of the molecular oscillations and the Raman gain width of the medium.

© 1994 Optical Society of America

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  1. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  2. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).
  3. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
    [CrossRef] [PubMed]
  4. J. P. Gordon, Opt. Lett. 11, 622 (1986).
  5. A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).
  6. Y.-X. Yan, E. B. Gamble, K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
    [CrossRef]
  7. M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).
  8. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [CrossRef]
  9. V. V. Afanasyev, V. A. Vysloukh, V. N. Serkin, Opt. Lett. 15, 489 (1990).
    [CrossRef] [PubMed]
  10. G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).
  11. E. M. Dianov, A. B. Grudinin, A. M. Prokhorov, V. N. Serkin, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), p. 228.
  12. S. A. Akhmanov, V. V. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).
  13. R. J. Hawkins, C. R. Menyuk, Opt. Lett. 18, 1999 (1993).
    [CrossRef] [PubMed]

1993 (1)

1990 (2)

V. V. Afanasyev, V. A. Vysloukh, V. N. Serkin, Opt. Lett. 15, 489 (1990).
[CrossRef] [PubMed]

M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).

1987 (3)

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

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
[CrossRef] [PubMed]

1986 (2)

1985 (2)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

Y.-X. Yan, E. B. Gamble, K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

Afanasyev, V. V.

Akhmanov, S. A.

S. A. Akhmanov, V. V. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Chirkin, A. S.

S. A. Akhmanov, V. V. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Dianov, E. M.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

E. M. Dianov, A. B. Grudinin, A. M. Prokhorov, V. N. Serkin, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), p. 228.

Formichev, E. E.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

Gamble, E. B.

Y.-X. Yan, E. B. Gamble, K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

Gordon, J. P.

J. P. Gordon, Opt. Lett. 11, 622 (1986).

Grudinin, A. B.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

E. M. Dianov, A. B. Grudinin, A. M. Prokhorov, V. N. Serkin, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), p. 228.

Hasegawa, A.

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

Hawkins, R. J.

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

Khaeidarov, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

Kodama, Y.

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

Korobkin, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

Kubota, H.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).

Kurokawa, K.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).

Lamb, G. L.

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

Mamyshev, P. V.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

Nakazawa, M.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).

Nelson, K. A.

Y.-X. Yan, E. B. Gamble, K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

Prokhorov, A. M.

E. M. Dianov, A. B. Grudinin, A. M. Prokhorov, V. N. Serkin, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), p. 228.

Prokhorov, E. M.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

Serkin, V. N.

V. V. Afanasyev, V. A. Vysloukh, V. N. Serkin, Opt. Lett. 15, 489 (1990).
[CrossRef] [PubMed]

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

E. M. Dianov, A. B. Grudinin, A. M. Prokhorov, V. N. Serkin, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), p. 228.

Stelmakh, N. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

Vysloukh, V. A.

Vysloukh, V. V.

S. A. Akhmanov, V. V. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

Ya-mada, E.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).

Yan, Y.-X.

Y.-X. Yan, E. B. Gamble, K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Chem. Phys. (1)

Y.-X. Yan, E. B. Gamble, K. A. Nelson, J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

JETP Lett. (2)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, E. M. Prokhorov, V. N. Serkin, N. F. Stelmakh, E. E. Formichev, JETP Lett. 41, 294 (1985).

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, E. M. Prokhorov, V. N. Serkin, D. V. Khaeidarov, JETP Lett. 45, 260 (1987).

Opt. Lett. (5)

Phys. Rev. A (1)

M. Nakazawa, K. Kurokawa, H. Kubota, E. Ya-mada, Phys. Rev. A 65, 1881 (1990).

Other (3)

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

E. M. Dianov, A. B. Grudinin, A. M. Prokhorov, V. N. Serkin, in Optical Solitons—Theory and Experiment, J. R. Taylor, ed. (Cambridge U. Press, Cambridge, 1992), p. 228.

S. A. Akhmanov, V. V. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992).

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Figures (1)

Fig. 1
Fig. 1

Normalized soliton self-frequency shift per unit propagation length as a function of the soliton duration tp. Curve 1, the RSFS calculated with formula (11) (Gordon theory4); curve 2, the RSFS calculated with formula (12).

Equations (14)

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i Ψ ζ = 2 Ψ τ 2 + 2 | Ψ | 2 Ψ + μ Q ˜ Ψ ,
2 Q ˜ τ 2 + 2 Γ ˜ R Q ˜ τ + Ω ˜ R 2 Q ˜ = Ω ˜ R 2 | ψ | 2 .
E 0 = ( 2 n 0 | k ω ω | k n 2 t 0 2 ) 1 / 2 , Q 0 = ρ 0 | k ω ω | n 0 2 M k n 2 ( α Q ) t 0 2 Ω R 2 ,
μ = 2 π N ρ 0 n 0 n 2 M Ω R 2 ( α Q ) 2 .
Q ˜ ( τ ) = 0 d sf ( s ) | Ψ ( τ s ) | 2 ,
f ( s ) = Ω ˜ R 2 ω ˜ R exp ( Γ ˜ R s ) sin ω ˜ R s , ω ˜ R = ( Ω ˜ R 2 Γ ˜ R 2 ) 1 / 2 .
d γ d ζ = 1 2 Im d x ( i μ Ψ 0 Q ˜ ) exp ( i θ ) sech ( x ) tanh ( x ) = 1 2 μ τ p 3 d x 0 d sf ( s ) × sech 2 [ x ( s / τ p ) ] sech 2 ( x ) tanh ( x ) .
X ( Ω ) = d sf ( s ) exp ( i Ω s ) = X ( 0 ) Ω ˜ R 2 Ω ˜ R 2 Ω 2 + 2 i Γ ˜ R Ω ,
Q ˜ ( τ ) = | Ψ ( τ ) | 2 2 ( Γ ˜ R / Ω ˜ R 2 ) τ | Ψ ( τ ) | 2 + .
X ( Ω ) = X ( 0 ) ( Ω ˜ R Ω ) 2 { 1 + 2 i ( Γ ˜ R Ω ˜ R ) ( Ω ˜ R Ω ) + [ 1 4 ( Γ ˜ R Ω ˜ R ) 2 ] ( Ω ˜ R Ω ) 2 + } .
Q ˜ ( τ ) = Ω ˜ R 2 { τ d τ τ d τ | Ψ ( τ ) | 2 2 Γ ˜ R τ d τ τ d τ τ d τ | Ψ ( τ ) | 2 + } ,
d ω d z = c 1 ( 1 / t p ) 4 ,
d ω d z = c 2 ( 1 t p ) ,
c 2 = 0 . 88 μ | k ω ω | Ω R 2 1 . 76 π N ρ 0 | k ω ω | n 0 n 2 M ( α Q ) 2 .

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