Abstract

Fission of optical solitons in a glass fiber induced by the stimulated Raman effect is demonstrated by a theory, simulations, and experiments. The solitons born by fission retain the amplitudes predicted by inverse-scattering calculations. For n = 2 solitons, fission occurs within a distance of 15 km for an initial pulse width of 10 psec.

© 1988 Optical Society of America

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References

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  1. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986); Opt. Lett. 12, 355 (1987).
    [CrossRef] [PubMed]
  2. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  3. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [CrossRef]
  4. Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
    [CrossRef] [PubMed]
  5. W. Hodel, H. P. Weber, Opt. Lett. 12, 924 (1987).
    [CrossRef] [PubMed]
  6. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  7. J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]
  8. R. H. Stolen, Proc. IEEE 68, 1232 (1980).
    [CrossRef]
  9. Strictly speaking, the Raman term does not allow momentum conservation in a slow time scale. However, during the short time of fission the momentum conservation approximately holds.
  10. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); K. Tai, A. Tomita, Appl. Phys. Lett. 48, 1033 (1986).
    [CrossRef] [PubMed]

1987 (3)

1986 (2)

1980 (2)

R. H. Stolen, Proc. IEEE 68, 1232 (1980).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); K. Tai, A. Tomita, Appl. Phys. Lett. 48, 1033 (1986).
[CrossRef] [PubMed]

1974 (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Gordon, J. P.

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

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); K. Tai, A. Tomita, Appl. Phys. Lett. 48, 1033 (1986).
[CrossRef] [PubMed]

Hasegawa, A.

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

Hodel, W.

Kodama, Y.

Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
[CrossRef] [PubMed]

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

Mitschke, F. M.

Mollenauer, L. F.

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986); Opt. Lett. 12, 355 (1987).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); K. Tai, A. Tomita, Appl. Phys. Lett. 48, 1033 (1986).
[CrossRef] [PubMed]

Nozaki, K.

Satsuma, J.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Stolen, R. H.

R. H. Stolen, Proc. IEEE 68, 1232 (1980).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); K. Tai, A. Tomita, Appl. Phys. Lett. 48, 1033 (1986).
[CrossRef] [PubMed]

Weber, H. P.

Yajima, N.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

IEEE J. Quantum Electron. (1)

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

Opt. Lett. (4)

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980); L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. J. Tomlinson, Opt. Lett. 8, 289 (1983); R. H. Stolen, L. F. Mollenauer, W. J. Tomlinson, Opt. Lett. 8, 186 (1983); K. Tai, A. Tomita, Appl. Phys. Lett. 48, 1033 (1986).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. H. Stolen, Proc. IEEE 68, 1232 (1980).
[CrossRef]

Prog. Theor. Phys. Suppl. (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (1)

Strictly speaking, the Raman term does not allow momentum conservation in a slow time scale. However, during the short time of fission the momentum conservation approximately holds.

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Figures (3)

Fig. 1
Fig. 1

(a) Amplitude pulse shape at Z = 10. (b) Contour plot of pulse trajectory for an initial condition of Q(T, 0) = 2 sech(T). β3 = 1.1 × 10−3.

Fig. 2
Fig. 2

(a) Amplitude pulse shape at Z = 20. (b) Contour plot of pulse trajectory for an initial condition of Q(T, 0) = 3 sech(T). β3 = 1.1 × 10−3. The crossings in (b) are due to the periodic boundary condition.

Fig. 3
Fig. 3

(a) Experimental and (b) numerical autocorrelation traces, (c) Contour plot of pulse trajectory, Γ = 4 × 10−2 and β3 = 2.5 × 10−3 were used in the calculation.

Equations (8)

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i ( q z + k q t + γ q ) 1 2 k 2 q t 2 + ν q | q | 2 + i a 2 | q | 2 t = 0 ,
Im a 2 = γ R / Δ ω ,
d f d z = 4 15 n 2 E m 4 Im a 2 k λ = 2 . 56 π 2 λ k Im a 2 n 2 τ 4 ,
( π n 2 ) 1 / 2 E m τ = 1 . 76 ( λ k ) 1 / 2 .
d f d z = 0 . 082 [ τ ( psec ) ] 4 ( THz km ) .
Δ t = d z υ g ( ω + Δ ω ) d z υ g ( ω ) = k Δ ω d z = 1 . 67 [ z ( km ) ] 2 ( d f / d z ) ( THz / km ) [ λ ( μ m ) ] 2 × D ( psec / nm km ) ( psec ) ,
( k λ ) 1 / 2 = 2 . 3 × 10 5 [ λ ( μ m ) ] 3 / 2 × [ D ( psec / nm km ) ] 1 / 2 ( psec ) .
i Q Z + 1 2 2 Q T 2 + | Q | 2 + i ( Γ Q + β 3 Q | Q | 2 T ) = 0 ,

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