Abstract

The effect of the detailed Raman cross section on the evolution of ultrashort solitons is considered. It is shown that the gain contribution leads to the self-frequency shift, whereas the phase contribution, which is usually determined by use of the Kramers–Kronig relations, has little visible effect. This result is consistent with the hypothesis that solitons are robust in the presence of Hamiltonian deformations.

© 1993 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); E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. R. Stelnakh, A. A. Formichev, Pis’ma Zh. Eksp. Teor. Fiz. 41, 242 (1985) [JETP Lett. 41, 294 (1985)].
    [CrossRef] [PubMed]
  2. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  3. M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992), App. B, pp. 176–199.
  4. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  5. K J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
    [CrossRef]
  6. R. H. Stolen, AT&T Bell Laboratories, Muray Hill, N.J. 07733 (personal communication, 1991).
  7. C. R. Menyuk, J. Opt. Soc. Am. B 10, 1585 (1993);in Guided Wave Nonlinear Optics, D. B. Ostrowsky, R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1991), pp. 457–488.
    [CrossRef]
  8. The measured Raman response function f(s) used in this study was provided by R. H. Stolen of AT&T Bell Laboratories and was reported in Ref. 4.
  9. The use of a numerical evaluation of the ZSE to measure soliton content was, to our knowledge, first reported by K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986). This technique is presented in more detail by S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992). We are grateful to K. J. Blow of British Telecom Laboratories for his help in our numerical implementation of this technique.
    [CrossRef] [PubMed]
  10. R. H. Stolen, W. J. Tomlinson, J. Opt. Soc. Am. B 9, 565 (1992).
    [CrossRef]

1993 (1)

1992 (1)

1989 (2)

1986 (3)

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986); E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. R. Stelnakh, A. A. Formichev, Pis’ma Zh. Eksp. Teor. Fiz. 41, 242 (1985) [JETP Lett. 41, 294 (1985)].
[CrossRef] [PubMed]

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

The use of a numerical evaluation of the ZSE to measure soliton content was, to our knowledge, first reported by K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986). This technique is presented in more detail by S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992). We are grateful to K. J. Blow of British Telecom Laboratories for his help in our numerical implementation of this technique.
[CrossRef] [PubMed]

Blow, K J.

K J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Blow, K. J.

The use of a numerical evaluation of the ZSE to measure soliton content was, to our knowledge, first reported by K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986). This technique is presented in more detail by S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992). We are grateful to K. J. Blow of British Telecom Laboratories for his help in our numerical implementation of this technique.
[CrossRef] [PubMed]

Gordon, J. P.

Haus, H. A.

Islam, M. N.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992), App. B, pp. 176–199.

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

Stolen, R. H.

Tomlinson, W. J.

Wood, D.

K J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

The use of a numerical evaluation of the ZSE to measure soliton content was, to our knowledge, first reported by K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986). This technique is presented in more detail by S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992). We are grateful to K. J. Blow of British Telecom Laboratories for his help in our numerical implementation of this technique.
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

K J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

The use of a numerical evaluation of the ZSE to measure soliton content was, to our knowledge, first reported by K. J. Blow, D. Wood, Opt. Commun. 58, 349 (1986). This technique is presented in more detail by S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992). We are grateful to K. J. Blow of British Telecom Laboratories for his help in our numerical implementation of this technique.
[CrossRef] [PubMed]

Opt. Lett. (2)

Other (3)

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992), App. B, pp. 176–199.

R. H. Stolen, AT&T Bell Laboratories, Muray Hill, N.J. 07733 (personal communication, 1991).

The measured Raman response function f(s) used in this study was provided by R. H. Stolen of AT&T Bell Laboratories and was reported in Ref. 4.

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Figures (5)

Fig. 1
Fig. 1

Real (dotted curve) and the imaginary (solid curve) parts of the Fourier transform of the Raman response function r(ω) and g(ω), respectively.

Fig. 2
Fig. 2

Change in the temporal position of the maximum pulse intensity as a function of propagation distance when soliton evolution is influenced by no Raman scattering and r(ω) alone (solid curve), g(ω) alone (dotted–dashed curve), and Raman scattering—both r(ω) and g(ω) (dotted curve).

Fig. 3
Fig. 3

Change in the spectral position of the maximum pulse intensity as a function of propagation distance when soliton evolution is influenced by no Raman scattering and r(ω) alone (solid curve), g(ω) alone (dotted–dashed curve), and Raman scattering—both r(ω) and g(ω) (dotted curve). The sign of the spectral axis was chosen to match that used in a similar calculation by Stolen and Tomlinson.10

Fig. 4
Fig. 4

Maximum pulse intensity as a function of propagation distance when soliton evolution is influenced by no Raman scattering (solid curve), r(ω) alone (dashed curve), g(ω) alone (dotted–dashed curve), and Raman scattering—both r(ω) and g(ω) (dotted curve).

Fig. 5
Fig. 5

Soliton energy as measured by the imaginary part of the ZSE as a function of propagation distance when soliton evolution is influenced by no Raman scattering (solid curve), r(ω) alone (dashed curve), g(ω) alone (dotted–dashed curve), and Raman scattering—both r(ω) and g(ω) (dotted curve).

Equations (4)

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i 2 π u ξ + 1 2 2 u s 2 + ( 1 α ) | u | 2 u = α u s f ( s s ) | u ( s ) | 2 d s ,
f a ( x ) = i g ( ω ) exp ( i ω s ) d ω 2 π ,
f s ( x ) = r ( ω ) exp ( i ω s ) d ω 2 π .
u 0 = A sech ( A s β ) exp ( i ϕ i ω s ) .

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