Abstract

The commonly used Lorentzian form of the Raman response function for studying propagation of ultrashort pulses in silica fibers does not properly account for the shoulder in the Raman gain spectrum originating from the Boson peak. We propose a more accurate form of this response function and show that its predictions for the Raman-induced frequency shift should be in better agreement with experiments.

© 2006 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 2.
  2. R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  3. F. L. Galeener, A. J. Leadbetter, and M. W. Stringfello, Phys. Rev. B 27, 1052 (1983); and references therein.
    [CrossRef]
  4. D. J. Dougherty, F. X. Kärnter, H. A. Haus, and E. P. Ippen, Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  5. A. K. Atieh, P. Myslinski, J. Chrostowski, and P. Galko, J. Lightwave Technol. 17, 216 (1999).
    [CrossRef]
  6. R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). Raman spectra are provided by R. H. Stolen.
  7. F. A. Oguama, H. Garcia, and A. M. Johnson, J. Opt. Soc. Am. B 22, 426 (2005); and references therein.
    [CrossRef]
  8. I. Mandelbaum, M. Bolshtyansky, T. F. Heinz, and A. R. H. Walker, J. Opt. Soc. Am. B 23, 621 (2006).
    [CrossRef]
  9. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  10. K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
    [CrossRef]
  11. D. Hollenbeck and C. D. Cantrell, J. Opt. Soc. Am. B 19, 2886 (2002).
    [CrossRef]
  12. V. K. Malinovsky and A. P. Sokolov, Solid State Commun. 57, 757 (1986).
    [CrossRef]
  13. V. K. Malinovskyand A. P. Sokolov, Glass Phys. Chem. 22, 152 (1996).
  14. C. McIntosh, J. Toulouse, and P. Tick, J. Non-Cryst. Solids 222, 335 (1997).
    [CrossRef]
  15. E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
    [CrossRef]
  16. V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003); and references therein.
    [CrossRef]
  17. N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
    [CrossRef]
  18. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]

2006

2005

F. A. Oguama, H. Garcia, and A. M. Johnson, J. Opt. Soc. Am. B 22, 426 (2005); and references therein.
[CrossRef]

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

2003

V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003); and references therein.
[CrossRef]

2002

2001

E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
[CrossRef]

1999

1997

C. McIntosh, J. Toulouse, and P. Tick, J. Non-Cryst. Solids 222, 335 (1997).
[CrossRef]

1996

V. K. Malinovskyand A. P. Sokolov, Glass Phys. Chem. 22, 152 (1996).

1995

1989

1986

V. K. Malinovsky and A. P. Sokolov, Solid State Commun. 57, 757 (1986).
[CrossRef]

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

1983

F. L. Galeener, A. J. Leadbetter, and M. W. Stringfello, Phys. Rev. B 27, 1052 (1983); and references therein.
[CrossRef]

1977

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 2.

Atieh, A. K.

Blow, K. J.

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

Bolshtyansky, M.

Cantrell, C. D.

Chrostowski, J.

Courtens, E.

E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
[CrossRef]

Dougherty, D. J.

Foret, M.

E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
[CrossRef]

Galeener, F. L.

F. L. Galeener, A. J. Leadbetter, and M. W. Stringfello, Phys. Rev. B 27, 1052 (1983); and references therein.
[CrossRef]

Galko, P.

Garcia, H.

Gordon, J. P.

Gurevich, V. L.

V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003); and references therein.
[CrossRef]

Haus, H. A.

Hehlen, B.

E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
[CrossRef]

Heinz, T. F.

Hellwarth, R. W.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Hiramitsu, N.

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

Hollenbeck, D.

Ikushima, A. J.

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

Ippen, E. P.

Johnson, A. M.

Kärnter, F. X.

Leadbetter, A. J.

F. L. Galeener, A. J. Leadbetter, and M. W. Stringfello, Phys. Rev. B 27, 1052 (1983); and references therein.
[CrossRef]

Malinovsky, V. K.

V. K. Malinovskyand A. P. Sokolov, Glass Phys. Chem. 22, 152 (1996).

V. K. Malinovsky and A. P. Sokolov, Solid State Commun. 57, 757 (1986).
[CrossRef]

Mandelbaum, I.

Matsushita, S.

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

McIntosh, C.

C. McIntosh, J. Toulouse, and P. Tick, J. Non-Cryst. Solids 222, 335 (1997).
[CrossRef]

Myslinski, P.

Oguama, F. A.

Parshin, D. A.

V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003); and references therein.
[CrossRef]

Saito, K.

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

Schober, H. R.

V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003); and references therein.
[CrossRef]

Shimodaira, N.

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

Sokolov, A. P.

V. K. Malinovskyand A. P. Sokolov, Glass Phys. Chem. 22, 152 (1996).

V. K. Malinovsky and A. P. Sokolov, Solid State Commun. 57, 757 (1986).
[CrossRef]

Stolen, R. H.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[CrossRef]

R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). Raman spectra are provided by R. H. Stolen.

R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). Raman spectra are provided by R. H. Stolen.

Stringfello, M. W.

F. L. Galeener, A. J. Leadbetter, and M. W. Stringfello, Phys. Rev. B 27, 1052 (1983); and references therein.
[CrossRef]

Tick, P.

C. McIntosh, J. Toulouse, and P. Tick, J. Non-Cryst. Solids 222, 335 (1997).
[CrossRef]

Tomlinson, W. J.

Toulouse, J.

C. McIntosh, J. Toulouse, and P. Tick, J. Non-Cryst. Solids 222, 335 (1997).
[CrossRef]

Vacher, R.

E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
[CrossRef]

Walker, A. R. H.

Wood, D.

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

Glass Phys. Chem.

V. K. Malinovskyand A. P. Sokolov, Glass Phys. Chem. 22, 152 (1996).

IEEE J. Quantum Electron.

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

J. Lightwave Technol.

J. Non-Cryst. Solids

C. McIntosh, J. Toulouse, and P. Tick, J. Non-Cryst. Solids 222, 335 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. B

V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B 67, 094203 (2003); and references therein.
[CrossRef]

N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushita, and A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).
[CrossRef]

F. L. Galeener, A. J. Leadbetter, and M. W. Stringfello, Phys. Rev. B 27, 1052 (1983); and references therein.
[CrossRef]

Prog. Quantum Electron.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Solid State Commun.

V. K. Malinovsky and A. P. Sokolov, Solid State Commun. 57, 757 (1986).
[CrossRef]

E. Courtens, M. Foret, B. Hehlen, and R. Vacher, Solid State Commun. 117, 187 (2001); and references therein.
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 2.

R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). Raman spectra are provided by R. H. Stolen.

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Figures (4)

Fig. 1
Fig. 1

Raman gain spectra. Blue curves with dots: experimental data[6]; dashed curve, conventional Lorentzian model; red curves, our model.

Fig. 2
Fig. 2

Decomposition of the copolarized Raman gain into its two parts, g a and g b . The dashed curve shows the fit based on the simple Lorentzian model.

Fig. 3
Fig. 3

Normalized nonlinear refractive index. Blue curve, obtained from experimental Raman spectra[6]; thin dashed curve, conventional Lorentzian model; red curve, our model.

Fig. 4
Fig. 4

RIFS rate versus soliton width T s for our model (red curve) and conventional model (dashed curve). The blue curve is based on the experimental Raman spectrum. Inset, output spectra obtained numerically for a 300 fs pulse, assumed to maintain its linear polarization.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

R i j k l ( 3 ) ( τ ) = [ ( 1 f R ) 3 ] δ ( τ ) ( δ i j δ k l + δ i k δ j l + δ i l δ j k ) + f R R a ( τ ) δ i j δ k l + ( f R 2 ) R b ( τ ) ( δ i k δ j l + δ i l δ j k ) ,
h a ( τ ) = τ 1 ( τ 1 2 + τ 2 2 ) exp ( τ τ 2 ) sin ( τ τ 1 )
h b ( τ ) = [ ( 2 τ b τ ) τ b 2 ] exp ( τ τ b ) ,
R x x x x ( 3 ) ( τ ) = ( 1 f R ) δ ( τ ) + f R [ ( f a + f c ) h a ( τ ) + f b h b ( τ ) ] ,
d ω ¯ d z = E s Ω 0 2 π A eff 0 g ( Ω ) ( Ω Ω 0 ) 3 sinh 2 ( Ω Ω 0 ) d Ω ,

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