Abstract

Raman effects cause a continuous downshift of the mean frequency of pulses propagating in optical fibers. For solitons in silica fibers, the effect varies roughly with the inverse fourth power of the pulse width. At 1.5-μm wavelength in a fiber with 15 psec/nm/km time-of-flight dispersion, a soliton of 250-fsec duration is predicted to shift by its own spectral width after about 100m of propagation. The theory agrees well with recent measurements.

© 1986 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).
    [CrossRef] [PubMed]
  2. For a more complete discussion of the soliton units, see the L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986), Appendix.
    [CrossRef]
  3. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [CrossRef]
  4. E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, V. N. Serkin, JETP Lett. 42, 87 (1985).
  5. R. H. Stolen, M. A. Bösch, Phys. Rev. Lett. 48, 805 (1982).
    [CrossRef]
  6. R. H. Stolen, C. Lee, R. K. Jain, J. Opt. Soc. Am. B 1, 652 (1984).
    [CrossRef]
  7. A. Hasegawa, Y. Kodama, AT&T Bell Laboratories, Murray Hill, N.J. 07974 (personal communication).

1986

For a more complete discussion of the soliton units, see the L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986), Appendix.
[CrossRef]

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

1985

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

1984

1982

R. H. Stolen, M. A. Bösch, Phys. Rev. Lett. 48, 805 (1982).
[CrossRef]

1981

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Bösch, M. A.

R. H. Stolen, M. A. Bösch, Phys. Rev. Lett. 48, 805 (1982).
[CrossRef]

Dianov, E. M.

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

Golovchenko, E. A.

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

Gordon, J. P.

For a more complete discussion of the soliton units, see the L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986), Appendix.
[CrossRef]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

A. Hasegawa, Y. Kodama, AT&T Bell Laboratories, Murray Hill, N.J. 07974 (personal communication).

Islam, M. N.

For a more complete discussion of the soliton units, see the L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986), Appendix.
[CrossRef]

Jain, R. K.

Kodama, Y.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

A. Hasegawa, Y. Kodama, AT&T Bell Laboratories, Murray Hill, N.J. 07974 (personal communication).

Lee, C.

Mitschke, F. M.

Mollenauer, L. F.

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

For a more complete discussion of the soliton units, see the L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986), Appendix.
[CrossRef]

Prokhorov, A. M.

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

Serkin, V. N.

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

Stolen, R. H.

R. H. Stolen, C. Lee, R. K. Jain, J. Opt. Soc. Am. B 1, 652 (1984).
[CrossRef]

R. H. Stolen, M. A. Bösch, Phys. Rev. Lett. 48, 805 (1982).
[CrossRef]

IEEE J. Quantum Electron.

For a more complete discussion of the soliton units, see the L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986), Appendix.
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

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

Opt. Lett.

Phys. Rev. Lett.

R. H. Stolen, M. A. Bösch, Phys. Rev. Lett. 48, 805 (1982).
[CrossRef]

Proc. IEEE

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Other

A. Hasegawa, Y. Kodama, AT&T Bell Laboratories, Murray Hill, N.J. 07974 (personal communication).

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Figures (2)

Fig. 1
Fig. 1

h(τ) for silica-core fibers, numerically computed from Eqs. (21) and (22).

Fig. 2
Fig. 2

Soliton frequency shifts δν0 versus τ, for various unit lengths of (lossless) fiber having D = 15 psec/nm/km, and for λ = 1.5 μm, as computed from Eq. (20) and the h(τ) of Fig. 1. The pulse bandwidth (FWHM) is shown for comparison.

Equations (27)

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- i u z = 1 2 2 u t 2 + u 2 u
u = sech ( t ) exp ( i z / 2 )
t c 2 / z c = - 2 k ω 2 = λ 2 D / 2 π c ,
P c z c = λ A eff / 2 π n 2 .
τ = 1.763 t c .
u ( t ) = d Ω u ˜ ( Ω ) exp ( - i Ω t )
u ˜ = ½ sech ( π Ω / 2 ) ,
P ( t ) = u 2 = sech 2 ( t )
W ( Ω ) = 2 π u ˜ 2 = π 2 sech 2 ( π Ω / 2 ) .
W ( 0 ) = π 2 P c t c 2 = λ 3 8 π ( A eff D / n 2 ) ,
u 2 u u ( t ) d s f ( s ) u ( t - s ) 2 ,
- i u ˜ ( Ω ) z = - 1 2 Ω 2 u ˜ ( Ω ) + d Ω χ ( Ω ) u ˜ ( Ω - Ω ) × d Ω u ˜ * ( Ω ) u ˜ ( Ω + Ω ) ,
χ ( Ω ) = d s f ( s ) exp ( i Ω s )
z u ˜ s ( Ω ) 2 = - 2 χ ( Ω - Ω p ) u p 2 u ˜ s ( Ω ) 2 ,             Ω Ω p ,
α R ( Ω ) = 2 χ ( Ω ) .
Ω = π d Ω Ω u ˜ 2 .
d Ω d z = - π d Ω α R ( Ω ) d Ω Ω u ˜ * ( Ω ) u ˜ ( Ω ) × d Ω u ˜ * ( Ω ) u ˜ ( Ω + Ω ) .
d x sech ( x + a / 2 ) sech ( x - a / 2 ) = 2 a / sinh a ,
d ω 0 d z = - π 8 d Ω Ω 3 α R ( Ω ) / sinh 2 ( π Ω / 2 ) ,
α R ( Ω ) = ( z c P c / A eff ) G ( ν ) = ( λ / 2 π n 2 ) G ( ν ) ,
α R ( Ω ) = R ( Ω / 2 π t c ) ,
d ν 0 d z ( THz / km ) = - 10 5 λ 2 D 16 π c t c 3 0 d Ω Ω 3 R ( Ω / 2 π t c ) / sinh 2 ( π Ω / 2 ) ,
d ν 0 / d z ( THz / km ) = 0.0436 / τ 4 .
d ν 0 / d z = 0.0436 h ( τ ) / τ 4 ,
h ( τ ) = 496 t c 0 d Ω Ω 3 R ( Ω / 2 π t c ) / sinh 2 ( π Ω / 2 )
R ( ν ) = 10 - 2 ν [ 1.02 + 2.73 ν 2 + 0.66 exp ( - 20 ν 2 ) + 0.72 exp ( - 100 ν 2 ) ] ,
u { u 2 - c 1 u 2 / t + ½ c 2 2 u 2 / t 2 - } ,

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