Abstract

Pulse generation in birefringent fibers by four-wave mixing in the presence of Raman scattering is theoretically modeled by a set of coupled nonlinear Schrödinger equations that are solved numerically. We discuss phase matching in the positive group-velocity dispersion regime for the split-pump configuration, which places the parametric frequency shift within the Raman band, and derive the combined initial gain. It is found that for shorter fiber lengths the symmetry-breaking roles of Raman–Stokes gain and Raman–anti-Stokes loss is balanced by four-wave mixing, resulting in a common effective power gain for both components. The importance of the relative phase of the four participating pulses as a switching parameter for the direction of the energy flow is demonstrated. It is further shown that, as a result of pulse walk-off, Raman scattering becomes the dominant process for longer fiber lengths. Theoretical results are compared with experimental cross-correlation pulse shapes.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics (Quantum Electronics—Principles and Applications), (Academic, San Diego, 1989).
  2. R. H. Stolen, Ch. Lin, and R. K. Jain, "A time-dispersion tuned fiber Raman oscillator," Appl. Phys. Lett. 30, 341 (1977).
    [CrossRef]
  3. M. N. Islam, L. F. Mollenauer, and R. H. Stolen, "Amplifier/compressor fiber Raman lasers," Opt. Lett. 12, 814 (1987).
    [CrossRef] [PubMed]
  4. R. H. Stolen, "Phase matching in birefringent fibers," Opt. Lett. 6, 213 (1981).
    [CrossRef] [PubMed]
  5. J. K. Chee and J. M. Liu, "Polarization-dependent parametric and Raman processes in a birefringent optical fiber," IEEE J. Quantum Electron. 26, 541 (1990).
    [CrossRef]
  6. M. Kuckartz, R. Schulz, and H. Harde, "Operation of a fibergrating compressor in the Raman regime," J. Opt. Soc. Am. B 5, 1353 (1988).
    [CrossRef]
  7. M. Kuckartz, R. Schulz, and H. Harde, "Nonlinear propagation effects in birefringent fibers," in Nonlinear Optical Materials, G. Roosen, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 234 (1988).
    [CrossRef]
  8. R. W. Hellwarth, "Third order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  9. M. Kuckartz, R. Schulz, and H. Harde, "Theoretical and experimental studies of combined self-phase modulation and stimulated Raman scattering in single-mode fibers," Opt. Quantum Electron. 19, 237 (1987).
    [CrossRef]
  10. D. Schadt, B. Jaskorzynska, and U. Österberg, "Numerical study on combined stimulated Raman scattering and selfphase modulation in optical fibers influenced by walk-off between pump and Stokes pulses," J. Opt. Soc. Am. B 3, 1057 (1986).
    [CrossRef]
  11. R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062 (1982).
    [CrossRef]
  12. A. Vatarescu, "Light conversion in nonlinear monomode optical fibers," IEEE J. Lightwave Technol. LT-5, 6 (1987).
  13. H. G. Park, J. D. Park, and S. S. Lee, "Pump-intensity-dependent frequency shift in Stokes and anti-Stokes spectra generated by stimulated four-photon mixing in birefringent fiber," Appl. Opt. 26, 2974 (1987).
    [CrossRef] [PubMed]
  14. K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  15. P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
    [CrossRef]
  16. J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682 (1990).
    [CrossRef] [PubMed]
  17. Yijiang Chen, "Combined process of stimulated Raman scattering and four-wave-mixing in optical fibers," J. Opt. Soc. Am. B 7, 43 (1990).
    [CrossRef]
  18. E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
    [CrossRef]
  19. J. K. Chee and J. M. Liu, "Raman-assisted parametric frequency and polarization conversion in a birefringent fiber," Opt. Lett. 14, 820 (1989).
    [CrossRef] [PubMed]
  20. E. Golovchenko and A. N. Pilipetskii, "Theoretical analysis of spectrum generation by modulational instability and Raman amplification in high-birefringent fibers," Sov. Lightwave Commun. 1, 271 (1991).
  21. S. Trillo and S. Wabnitz, "Parametric and Raman amplification in birefringent fibers," J. Opt. Soc. Am. B 9, 1061 (1992).
    [CrossRef]
  22. A. Hasegawa, Optical Solitons in Fibers, Vol. 116 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1989).
    [CrossRef]
  23. R. K. Jain and K. Stenersen, "Phase-matched four-photon mixing processes in birefringent fibers," Appl. Phys. B 35, 49 (1984).
    [CrossRef]
  24. R. Hellwarth, J. Cherlow, and T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964 (1975).
    [CrossRef]
  25. R. H. Stolen and E. P. Ippen, "Raman gain in glass optical fibers," Appl. Phys. Lett. 22, 276 (1973).
    [CrossRef]
  26. A. R. Chraplyvy, D. Marcuse, and D. S. Henry, "Carrierinduced phase noise in angle-modulated optical-fiber systems," IEEE J. Lightwave Technol. LT-2, 6 (1984).
    [CrossRef]
  27. J. K. Chee and J. M. Liu, "Compression of Stokes pulses generated through a parametric four-photon mixing process in a birefringent fiber," Opt. Lett. 14, 1074 (1989).
    [CrossRef] [PubMed]
  28. S. Schulz, M. Kuckartz, and H. Harde, "A fiber grating Raman laser generating subpicosecond pulses," Opt. Commun. 70, 239 (1989).
    [CrossRef]
  29. J. Mostowski and M. G. Raymer, "The buildup of stimulated Raman scattering from spontaneous Raman scattering," Opt. Commun. 36, 237 (1981).
    [CrossRef]
  30. M. G. Raymer and J. Mostowski, "Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation," Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  31. J. Auyeung and A. Yariv, "Spontaneous and stimulated Raman scattering in long low loss fibers," IEEE J. Quantum Electron. QE-14, 347 (1978).
    [CrossRef]
  32. Neglect of the XPM terms should not cause any major changes for the calculated pulse profiles or the energy conversion. Only some smaller deviations in the U-shaped region of the pump and in the wings of the Stokes pulse may be expected.
  33. The development and the evolution of the chirps and the compressibility of the pulses will be the subject of a future paper.

1992 (1)

1991 (1)

E. Golovchenko and A. N. Pilipetskii, "Theoretical analysis of spectrum generation by modulational instability and Raman amplification in high-birefringent fibers," Sov. Lightwave Commun. 1, 271 (1991).

1990 (5)

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

Yijiang Chen, "Combined process of stimulated Raman scattering and four-wave-mixing in optical fibers," J. Opt. Soc. Am. B 7, 43 (1990).
[CrossRef]

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

J. K. Chee and J. M. Liu, "Polarization-dependent parametric and Raman processes in a birefringent optical fiber," IEEE J. Quantum Electron. 26, 541 (1990).
[CrossRef]

1989 (3)

1988 (1)

1987 (4)

M. N. Islam, L. F. Mollenauer, and R. H. Stolen, "Amplifier/compressor fiber Raman lasers," Opt. Lett. 12, 814 (1987).
[CrossRef] [PubMed]

M. Kuckartz, R. Schulz, and H. Harde, "Theoretical and experimental studies of combined self-phase modulation and stimulated Raman scattering in single-mode fibers," Opt. Quantum Electron. 19, 237 (1987).
[CrossRef]

A. Vatarescu, "Light conversion in nonlinear monomode optical fibers," IEEE J. Lightwave Technol. LT-5, 6 (1987).

H. G. Park, J. D. Park, and S. S. Lee, "Pump-intensity-dependent frequency shift in Stokes and anti-Stokes spectra generated by stimulated four-photon mixing in birefringent fiber," Appl. Opt. 26, 2974 (1987).
[CrossRef] [PubMed]

1986 (2)

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

D. Schadt, B. Jaskorzynska, and U. Österberg, "Numerical study on combined stimulated Raman scattering and selfphase modulation in optical fibers influenced by walk-off between pump and Stokes pulses," J. Opt. Soc. Am. B 3, 1057 (1986).
[CrossRef]

1984 (2)

R. K. Jain and K. Stenersen, "Phase-matched four-photon mixing processes in birefringent fibers," Appl. Phys. B 35, 49 (1984).
[CrossRef]

A. R. Chraplyvy, D. Marcuse, and D. S. Henry, "Carrierinduced phase noise in angle-modulated optical-fiber systems," IEEE J. Lightwave Technol. LT-2, 6 (1984).
[CrossRef]

1982 (1)

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062 (1982).
[CrossRef]

1981 (3)

R. H. Stolen, "Phase matching in birefringent fibers," Opt. Lett. 6, 213 (1981).
[CrossRef] [PubMed]

J. Mostowski and M. G. Raymer, "The buildup of stimulated Raman scattering from spontaneous Raman scattering," Opt. Commun. 36, 237 (1981).
[CrossRef]

M. G. Raymer and J. Mostowski, "Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation," Phys. Rev. A 24, 1980 (1981).
[CrossRef]

1978 (1)

J. Auyeung and A. Yariv, "Spontaneous and stimulated Raman scattering in long low loss fibers," IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

1977 (2)

R. H. Stolen, Ch. Lin, and R. K. Jain, "A time-dispersion tuned fiber Raman oscillator," Appl. Phys. Lett. 30, 341 (1977).
[CrossRef]

R. W. Hellwarth, "Third order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

1975 (1)

R. Hellwarth, J. Cherlow, and T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964 (1975).
[CrossRef]

1973 (1)

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical fibers," Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Quantum Electronics—Principles and Applications), (Academic, San Diego, 1989).

Auyeung, J.

J. Auyeung and A. Yariv, "Spontaneous and stimulated Raman scattering in long low loss fibers," IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062 (1982).
[CrossRef]

Chee, J. K.

Chen, Yijiang

Cherlow, J.

R. Hellwarth, J. Cherlow, and T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964 (1975).
[CrossRef]

Chraplyvy, A. R.

A. R. Chraplyvy, D. Marcuse, and D. S. Henry, "Carrierinduced phase noise in angle-modulated optical-fiber systems," IEEE J. Lightwave Technol. LT-2, 6 (1984).
[CrossRef]

Dianov, E. M.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Drummond, P. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

Dudley, J. M.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

Golovchenko, E.

E. Golovchenko and A. N. Pilipetskii, "Theoretical analysis of spectrum generation by modulational instability and Raman amplification in high-birefringent fibers," Sov. Lightwave Commun. 1, 271 (1991).

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Harde, H.

S. Schulz, M. Kuckartz, and H. Harde, "A fiber grating Raman laser generating subpicosecond pulses," Opt. Commun. 70, 239 (1989).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Operation of a fibergrating compressor in the Raman regime," J. Opt. Soc. Am. B 5, 1353 (1988).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Theoretical and experimental studies of combined self-phase modulation and stimulated Raman scattering in single-mode fibers," Opt. Quantum Electron. 19, 237 (1987).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Nonlinear propagation effects in birefringent fibers," in Nonlinear Optical Materials, G. Roosen, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 234 (1988).
[CrossRef]

Harvey, J. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

A. Hasegawa, Optical Solitons in Fibers, Vol. 116 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1989).
[CrossRef]

Hellwarth, R.

R. Hellwarth, J. Cherlow, and T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964 (1975).
[CrossRef]

Hellwarth, R. W.

R. W. Hellwarth, "Third order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Henry, D. S.

A. R. Chraplyvy, D. Marcuse, and D. S. Henry, "Carrierinduced phase noise in angle-modulated optical-fiber systems," IEEE J. Lightwave Technol. LT-2, 6 (1984).
[CrossRef]

Ippen, E. P.

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical fibers," Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

Islam, M. N.

Jain, R. K.

R. K. Jain and K. Stenersen, "Phase-matched four-photon mixing processes in birefringent fibers," Appl. Phys. B 35, 49 (1984).
[CrossRef]

R. H. Stolen, Ch. Lin, and R. K. Jain, "A time-dispersion tuned fiber Raman oscillator," Appl. Phys. Lett. 30, 341 (1977).
[CrossRef]

Jaskorzynska, B.

D. Schadt, B. Jaskorzynska, and U. Österberg, "Numerical study on combined stimulated Raman scattering and selfphase modulation in optical fibers influenced by walk-off between pump and Stokes pulses," J. Opt. Soc. Am. B 3, 1057 (1986).
[CrossRef]

Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

Kuckartz, M.

S. Schulz, M. Kuckartz, and H. Harde, "A fiber grating Raman laser generating subpicosecond pulses," Opt. Commun. 70, 239 (1989).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Operation of a fibergrating compressor in the Raman regime," J. Opt. Soc. Am. B 5, 1353 (1988).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Theoretical and experimental studies of combined self-phase modulation and stimulated Raman scattering in single-mode fibers," Opt. Quantum Electron. 19, 237 (1987).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Nonlinear propagation effects in birefringent fibers," in Nonlinear Optical Materials, G. Roosen, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 234 (1988).
[CrossRef]

Lee, S. S.

Leonhardt, R.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

Lin, Ch.

R. H. Stolen, Ch. Lin, and R. K. Jain, "A time-dispersion tuned fiber Raman oscillator," Appl. Phys. Lett. 30, 341 (1977).
[CrossRef]

Liu, J. M.

Mamyshev, P. V.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Marcuse, D.

A. R. Chraplyvy, D. Marcuse, and D. S. Henry, "Carrierinduced phase noise in angle-modulated optical-fiber systems," IEEE J. Lightwave Technol. LT-2, 6 (1984).
[CrossRef]

Mollenauer, L. F.

Mostowski, J.

J. Mostowski and M. G. Raymer, "The buildup of stimulated Raman scattering from spontaneous Raman scattering," Opt. Commun. 36, 237 (1981).
[CrossRef]

M. G. Raymer and J. Mostowski, "Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation," Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Österberg, U.

D. Schadt, B. Jaskorzynska, and U. Österberg, "Numerical study on combined stimulated Raman scattering and selfphase modulation in optical fibers influenced by walk-off between pump and Stokes pulses," J. Opt. Soc. Am. B 3, 1057 (1986).
[CrossRef]

Park, H. G.

Park, J. D.

Pilipetskii, A. N.

E. Golovchenko and A. N. Pilipetskii, "Theoretical analysis of spectrum generation by modulational instability and Raman amplification in high-birefringent fibers," Sov. Lightwave Commun. 1, 271 (1991).

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

Raymer, M. G.

J. Mostowski and M. G. Raymer, "The buildup of stimulated Raman scattering from spontaneous Raman scattering," Opt. Commun. 36, 237 (1981).
[CrossRef]

M. G. Raymer and J. Mostowski, "Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation," Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Rothenberg, J. E.

J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

Schadt, D.

D. Schadt, B. Jaskorzynska, and U. Österberg, "Numerical study on combined stimulated Raman scattering and selfphase modulation in optical fibers influenced by walk-off between pump and Stokes pulses," J. Opt. Soc. Am. B 3, 1057 (1986).
[CrossRef]

Schulz, R.

M. Kuckartz, R. Schulz, and H. Harde, "Operation of a fibergrating compressor in the Raman regime," J. Opt. Soc. Am. B 5, 1353 (1988).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Theoretical and experimental studies of combined self-phase modulation and stimulated Raman scattering in single-mode fibers," Opt. Quantum Electron. 19, 237 (1987).
[CrossRef]

M. Kuckartz, R. Schulz, and H. Harde, "Nonlinear propagation effects in birefringent fibers," in Nonlinear Optical Materials, G. Roosen, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 234 (1988).
[CrossRef]

Schulz, S.

S. Schulz, M. Kuckartz, and H. Harde, "A fiber grating Raman laser generating subpicosecond pulses," Opt. Commun. 70, 239 (1989).
[CrossRef]

Stenersen, K.

R. K. Jain and K. Stenersen, "Phase-matched four-photon mixing processes in birefringent fibers," Appl. Phys. B 35, 49 (1984).
[CrossRef]

Stolen, R. H.

M. N. Islam, L. F. Mollenauer, and R. H. Stolen, "Amplifier/compressor fiber Raman lasers," Opt. Lett. 12, 814 (1987).
[CrossRef] [PubMed]

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062 (1982).
[CrossRef]

R. H. Stolen, "Phase matching in birefringent fibers," Opt. Lett. 6, 213 (1981).
[CrossRef] [PubMed]

R. H. Stolen, Ch. Lin, and R. K. Jain, "A time-dispersion tuned fiber Raman oscillator," Appl. Phys. Lett. 30, 341 (1977).
[CrossRef]

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical fibers," Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Trillo, S.

Vatarescu, A.

A. Vatarescu, "Light conversion in nonlinear monomode optical fibers," IEEE J. Lightwave Technol. LT-5, 6 (1987).

Wabnitz, S.

Yang, T.

R. Hellwarth, J. Cherlow, and T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964 (1975).
[CrossRef]

Yariv, A.

J. Auyeung and A. Yariv, "Spontaneous and stimulated Raman scattering in long low loss fibers," IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

R. K. Jain and K. Stenersen, "Phase-matched four-photon mixing processes in birefringent fibers," Appl. Phys. B 35, 49 (1984).
[CrossRef]

Appl. Phys. Lett. (2)

R. H. Stolen and E. P. Ippen, "Raman gain in glass optical fibers," Appl. Phys. Lett. 22, 276 (1973).
[CrossRef]

R. H. Stolen, Ch. Lin, and R. K. Jain, "A time-dispersion tuned fiber Raman oscillator," Appl. Phys. Lett. 30, 341 (1977).
[CrossRef]

IEEE J. Lightwave Technol. (2)

A. Vatarescu, "Light conversion in nonlinear monomode optical fibers," IEEE J. Lightwave Technol. LT-5, 6 (1987).

A. R. Chraplyvy, D. Marcuse, and D. S. Henry, "Carrierinduced phase noise in angle-modulated optical-fiber systems," IEEE J. Lightwave Technol. LT-2, 6 (1984).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. Auyeung and A. Yariv, "Spontaneous and stimulated Raman scattering in long low loss fibers," IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062 (1982).
[CrossRef]

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Mutual influence of the parametric effects and stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

J. K. Chee and J. M. Liu, "Polarization-dependent parametric and Raman processes in a birefringent optical fiber," IEEE J. Quantum Electron. 26, 541 (1990).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (3)

S. Schulz, M. Kuckartz, and H. Harde, "A fiber grating Raman laser generating subpicosecond pulses," Opt. Commun. 70, 239 (1989).
[CrossRef]

J. Mostowski and M. G. Raymer, "The buildup of stimulated Raman scattering from spontaneous Raman scattering," Opt. Commun. 36, 237 (1981).
[CrossRef]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, "Cross-phase modulational instability in high-birefringence fibers," Opt. Commun. 78, 137 (1990).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

M. Kuckartz, R. Schulz, and H. Harde, "Theoretical and experimental studies of combined self-phase modulation and stimulated Raman scattering in single-mode fibers," Opt. Quantum Electron. 19, 237 (1987).
[CrossRef]

Phys. Rev. A (2)

J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

M. G. Raymer and J. Mostowski, "Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation," Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Phys. Rev. B (1)

R. Hellwarth, J. Cherlow, and T. Yang, "Origin and frequency dependence of nonlinear optical susceptibilities of glasses," Phys. Rev. B 11, 964 (1975).
[CrossRef]

Phys. Rev. Lett. (1)

K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

R. W. Hellwarth, "Third order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Sov. Lightwave Commun. (1)

E. Golovchenko and A. N. Pilipetskii, "Theoretical analysis of spectrum generation by modulational instability and Raman amplification in high-birefringent fibers," Sov. Lightwave Commun. 1, 271 (1991).

Other (5)

G. P. Agrawal, Nonlinear Fiber Optics (Quantum Electronics—Principles and Applications), (Academic, San Diego, 1989).

M. Kuckartz, R. Schulz, and H. Harde, "Nonlinear propagation effects in birefringent fibers," in Nonlinear Optical Materials, G. Roosen, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1017, 234 (1988).
[CrossRef]

A. Hasegawa, Optical Solitons in Fibers, Vol. 116 of Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 1989).
[CrossRef]

Neglect of the XPM terms should not cause any major changes for the calculated pulse profiles or the energy conversion. Only some smaller deviations in the U-shaped region of the pump and in the wings of the Stokes pulse may be expected.

The development and the evolution of the chirps and the compressibility of the pulses will be the subject of a future paper.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic of split-pump pulse coupling and parametric pulse generation in a birefringent fiber. The angle θ is input polarization with respect to the fast axis, A refers to the anti-Stokes pulse, and S refers to the Stokes pulse.

Fig. 2
Fig. 2

Combined FWM and perpendicular/parallel SRS gain coefficient for the Raman–Stokes component on the slow axis for an input cw intensity of 760 MW/cm2 and δn = 0.0003 (fiber 1).

Fig. 3
Fig. 3

Semilogarithmic parametric energies normalized to the total pump input energy as a function of fiber length.

Fig. 4
Fig. 4

Evolution of (a) the pump pulses and (b) the parametric pulses in fiber 1 near z = zc for I0 = 760 MW/cm2, T0 = 85 ps, and θ = 45°.

Fig. 5
Fig. 5

Evolution of the relative phase ϕr. The parameters are the same as those for Fig. 4. The line starting at t/T0 = 0 indicates the position of the maximum pump-pulse overlap.

Fig. 6
Fig. 6

(a) Evolution of pump pulses P1 and P2 and ordinary 13-THz Raman pulse and (b) parametric Raman–Stokes pulse with the parameters of fiber 2 for I0 = 1.1 GW/cm2, T0 = 70 ps, and θ = 27°.

Fig. 7
Fig. 7

Schematic of the experimental setup.

Fig. 8
Fig. 8

Cross-correlation traces of (a) pump pulses and (b) parametric pulses after 30 m of fiber 1.

Fig. 9
Fig. 9

Cross-correlation traces of (a) pump pulses on the fast axis and (b) Raman–Stokes pulse on the slow axis after 300 m of fiber 2.

Equations (22)

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

E ^ ( z , t ) = 1 2 j e ^ j A j ( z , t ) exp [ i ( ω j t - β j z ) ] + c . c . ,
P r ( 3 ) = ³ / 0 [ ½ χ ( 3 ) A r 2 + χ ( 3 ) A s 2 + χ ( 3 ) A t 2 + χ ( 3 ) A u 2 ] A r + ³ / 0 χ ( 3 ) A s A t A u * exp ( ± i Δ β z ) ± i ³ / 0 j = s , t , u χ , ( 3 ) A j 2 A r ,
Δ β = Δ ω 2 β 2 - δ n Δ ω c
Δ ω = δ n β 2 c ,
A P 1 z = - i 2 β 2 2 A P 1 t 2 - α 2 A P 1 + i ρ χ ( 3 ) × ( ½ A P 1 2 + A A 2 + A P 2 2 + A S 2 ) A P 1 × i ρ χ ( 3 ) A S A A A P 2 * exp ( - i Δ β z ) + ρ [ - χ ( 3 ) ( Δ ω ) A S 2 + χ ( 3 ) ( Δ ω ) A A 2 ] A P 1 ,
A P 2 z = Δ β 1 , P 2 A P 2 t - i 2 β 2 2 A P 2 t 2 - α 2 A P 2 + i ρ χ ( 3 ) × ( ½ A P 2 2 + A S 2 + A P 1 2 + A A 2 ) A P 2 × i ρ χ ( 3 ) A S A A A P 1 * exp ( - i Δ β z ) + ρ [ - χ ( 3 ) ( Δ ω ) A S 2 + χ ( 3 ) ( Δ ω ) A A 2 ] A P 2 ,
A S z = Δ β 1 , S A S t - i 2 β 2 2 A S t 2 - α 2 A S + i ρ χ ( 3 ) × ( ½ A S 2 + A P 2 2 + A P 1 2 + A A 2 ) A S × i ρ χ ( 3 ) A P 1 A P 2 A A * exp ( i Δ β z ) + ρ [ χ ( 3 ) ( Δ ω ) A P 2 2 + χ ( 3 ) ( Δ ω ) A P 1 2 + χ ( 3 ) ( 2 Δ ω ) A A 2 ] A S ,
A A z = Δ β 1 , A A A t - i 2 β 2 2 A A t 2 - α 2 A A + i ρ χ ( 3 ) × ( ½ A A 2 + A P 1 2 + A P 2 2 + A S 2 ) A A × i ρ χ ( 3 ) A P 1 A P 2 A S * exp ( i Δ β z ) + ρ [ - χ ( 3 ) ( Δ ω ) A P 1 2 - χ ( 3 ) ( Δ ω ) A P 2 2 - χ ( 3 ) ( 2 Δ ω ) A S 2 ] A A .
χ ( 3 ) = 3 χ ( 3 ) = / n 0 n 2 .
χ , ( 3 ) = g R , ( Δ ω ) ζ 0 c 2 n 0 2 3 ω 0 .
P i = A eff n 0 2 Z A i 2 ,
G = 1 2 G SRS + 1 2 2 { Γ + [ Γ 2 + ( 2 Δ β G SRS ) 2 ] 1 / 2 } 1 / 2 ,
G SRS = ρ χ ( 3 ) A P 2 2 + ρ χ ( 3 ) A P 1 2 ,
Γ = G SRS 2 + 4 [ ρ χ ( 3 ) A P 1 A P 2 ] 2 - Δ β 2 ,
Δ β = Δ β + ½ ρ χ ( 3 ) ( A P 1 2 + A P 2 2 ) .
A P 1 ( z + Δ z ) = A P 1 ( z ) + ρ χ ( 3 ) A A ( z ) A S ( z ) A P 2 ( z ) × sin [ ϕ r ( z ) ] Δ z ,
Φ P 1 ( z + Δ z ) = Φ P 1 ( z ) + ρ χ ( 3 ) A S ( z ) A A ( z ) A P 2 ( z ) A P 1 ( z ) × cos [ ϕ r ( z ) ] Δ z ,
A S ( z + Δ z ) = A S ( z ) - ρ χ ( 3 ) A P 1 ( z ) A P 2 ( z ) A A ( z ) × sin [ ϕ r ( z ) ] Δ z ,
Φ S ( z + Δ z ) = Φ S ( z ) + ρ χ ( 3 ) A P 1 ( z ) A P 2 ( z ) A A ( z ) A S ( z ) × cos [ ϕ r ( z ) ] Δ z .
ϕ r ( z + Δ z ) = Φ P 1 ( z + Δ z ) - Φ P 1 ( z ) + Φ P 2 ( z + Δ z ) - Φ P 2 ( z ) - Φ S ( z + Δ z ) + Φ S ( z ) - Φ A ( z + Δ z ) + Φ A ( z ) + ϕ r ( z ) + Δ β 0 Δ z .
Δ β 0 = ½ ρ χ ( 3 ) ( A P 1 , max 2 + A P 2 , max 2 ) .
I sp ( z , t ) = 0.32 W cm 2 Δ z [ g R ( Δ ω ) I P 2 ( t ) + g R ( Δ ω ) I P 1 ( t ) ] ,

Metrics