Abstract

For analyzing the propagation of ultrashort optical pulses, Raman gain is conveniently described as a response function in the time domain. In this paper we develop the Raman response function for silica-core fibers and use it to study the effect of Raman gain in regimes of normal and anomalous dispersion.

© 1989 Optical Society of America

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  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  2. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
    [CrossRef]
  3. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
    [CrossRef] [PubMed]
  4. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
    [CrossRef] [PubMed]
  5. R. W. Hellwarth, A. Owyoung, and N. George, “Origin of the nonlinear refractive index of CCl4,” Phys. Rev. A 4, 2342–2347 (1971).
    [CrossRef]
  6. R. W. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
    [CrossRef]
  7. Y. Kodama, “Optical solitons in monomode optical fibers,” J. Stat. Phys. 39, 567–614 (1985).
    [CrossRef]
  8. N. Tzor and J. I. Gersten, “Nonlinear wave propagation in a transparent medium,” in Optical Properties of Highly Transparent Solids, S. Mitra and B. Bendow, eds. (Plenum, New York, 1976), pp. 373–379; A. D. Boardman and G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
    [CrossRef]
  9. Y. R. Shen and N. Bloembergen, “Theory of stimulated Raman and Brillouin scattering,” Phys. Rev. 137A, 1787–1805 (1965).
    [CrossRef]
  10. P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137A, 801–817 (1965).
    [CrossRef]
  11. A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier-induced phase noise in angle-modulated optical-fiber systems,” IEEE J. Lightwave Technol. LT-2, 6–10 (1984).
    [CrossRef]
  12. W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964).
    [CrossRef]
  13. D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry,” J. Appl. Phys. 47, 2497–2501 (1976).
    [CrossRef]
  14. R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
    [CrossRef]
  15. R. H. Stolen, C. Lee, and R. K. Jain, “Development of the stimulated Raman spectrum in single-mode fibers,” J. Opt. Soc. Am. B 1, 652–657 (1984); R. H. Stolen and M. A. Bosch, “Low-frequency and low-temperature Raman scattering in silica fibers,” Phys. Rev. Lett. 48, 805–808 (1982).
    [CrossRef]
  16. R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–281 (1973).
    [CrossRef]
  17. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation and picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  18. W. J. Tomlinson, H. A. Haus, and R. H. Stolen, “Curious features of nonlinear pulse propagation in single-mode optical fibers,” J. Opt. Soc. Am. A 2(13), P33 (1985).
  19. A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:YAG laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
    [CrossRef]
  20. J. P. Heritage, Bellcore, Red Bank, New Jersey 07701 (personal communication).
  21. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
    [CrossRef] [PubMed]
  22. W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
    [CrossRef]
  23. W. Zhao and E. Bourkoff, “Femtosecond pulse propagation in optical fibers: higher order effects,” IEEE J. Quantum Electron. QE-24, 365–372 (1988); E. A. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. M. Prokhorov, “Optical fiber-grating pulse compression,” Opt. Quantum Electron. 20, 343–355 (1988).
    [CrossRef]
  24. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986); E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. R. Stelnakh, and A. A. Formichev, “Stimulated-Raman conversion of multi-soliton pulses in quartz optical fibers,” Pisma Zh. Eksp. Teor. Fiz 41, 242 (1985) [JETP Lett. 41, 294–297 (1985)].
    [CrossRef] [PubMed]
  25. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [CrossRef] [PubMed]
  26. T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
    [CrossRef]
  27. M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
    [CrossRef]
  28. S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
    [CrossRef]
  29. K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. 13, 392–394 (1988).
    [CrossRef] [PubMed]
  30. V. A. Vysloukh and T. A. Matveena, “Influence of inertia of nonlinear response on compression of femtosecond pulses,” Sov. J. Quantum Electron. 17, 498–500 (1987).
    [CrossRef]
  31. D. Schadt and B. Jaskorzynska, “Frequency chirp and spectra due to self-phase modulation and stimulated Raman scattering influenced by pulse walk-off in optical fibers,” J. Opt. Soc. Am. B 4, 856–862 (1987).
    [CrossRef]
  32. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].
  33. R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
    [CrossRef]

1988 (2)

W. Zhao and E. Bourkoff, “Femtosecond pulse propagation in optical fibers: higher order effects,” IEEE J. Quantum Electron. QE-24, 365–372 (1988); E. A. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. M. Prokhorov, “Optical fiber-grating pulse compression,” Opt. Quantum Electron. 20, 343–355 (1988).
[CrossRef]

K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. 13, 392–394 (1988).
[CrossRef] [PubMed]

1987 (2)

V. A. Vysloukh and T. A. Matveena, “Influence of inertia of nonlinear response on compression of femtosecond pulses,” Sov. J. Quantum Electron. 17, 498–500 (1987).
[CrossRef]

D. Schadt and B. Jaskorzynska, “Frequency chirp and spectra due to self-phase modulation and stimulated Raman scattering influenced by pulse walk-off in optical fibers,” J. Opt. Soc. Am. B 4, 856–862 (1987).
[CrossRef]

1986 (4)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986); E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. R. Stelnakh, and A. A. Formichev, “Stimulated-Raman conversion of multi-soliton pulses in quartz optical fibers,” Pisma Zh. Eksp. Teor. Fiz 41, 242 (1985) [JETP Lett. 41, 294–297 (1985)].
[CrossRef] [PubMed]

J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
[CrossRef] [PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

1985 (5)

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

Y. Kodama, “Optical solitons in monomode optical fibers,” J. Stat. Phys. 39, 567–614 (1985).
[CrossRef]

W. J. Tomlinson, H. A. Haus, and R. H. Stolen, “Curious features of nonlinear pulse propagation in single-mode optical fibers,” J. Opt. Soc. Am. A 2(13), P33 (1985).

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

1984 (4)

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:YAG laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

R. H. Stolen, C. Lee, and R. K. Jain, “Development of the stimulated Raman spectrum in single-mode fibers,” J. Opt. Soc. Am. B 1, 652–657 (1984); R. H. Stolen and M. A. Bosch, “Low-frequency and low-temperature Raman scattering in silica fibers,” Phys. Rev. Lett. 48, 805–808 (1982).
[CrossRef]

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier-induced phase noise in angle-modulated optical-fiber systems,” IEEE J. Lightwave Technol. LT-2, 6–10 (1984).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation and picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

1978 (1)

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

1976 (1)

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

1975 (1)

R. W. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

1973 (2)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–281 (1973).
[CrossRef]

1972 (1)

1971 (1)

R. W. Hellwarth, A. Owyoung, and N. George, “Origin of the nonlinear refractive index of CCl4,” Phys. Rev. A 4, 2342–2347 (1971).
[CrossRef]

1970 (1)

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

1969 (1)

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

1968 (1)

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[CrossRef]

1965 (2)

Y. R. Shen and N. Bloembergen, “Theory of stimulated Raman and Brillouin scattering,” Phys. Rev. 137A, 1787–1805 (1965).
[CrossRef]

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137A, 801–817 (1965).
[CrossRef]

1964 (1)

W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964).
[CrossRef]

Bekki, N.

Bloembergen, N.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Y. R. Shen and N. Bloembergen, “Theory of stimulated Raman and Brillouin scattering,” Phys. Rev. 137A, 1787–1805 (1965).
[CrossRef]

Bourkoff, E.

W. Zhao and E. Bourkoff, “Femtosecond pulse propagation in optical fibers: higher order effects,” IEEE J. Quantum Electron. QE-24, 365–372 (1988); E. A. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. M. Prokhorov, “Optical fiber-grating pulse compression,” Opt. Quantum Electron. 20, 343–355 (1988).
[CrossRef]

Bret, G.

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[CrossRef]

Carman, R. L.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Cherlow, J.

R. W. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

Chraplyvy, A. R.

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier-induced phase noise in angle-modulated optical-fiber systems,” IEEE J. Lightwave Technol. LT-2, 6–10 (1984).
[CrossRef]

de Silvestri, S.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

Denariez, M.

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[CrossRef]

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

Downer, M. C.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

Fork, R. L.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

Fujimoto, J. G.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

Gamble, E. B.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

George, N.

R. W. Hellwarth, A. Owyoung, and N. George, “Origin of the nonlinear refractive index of CCl4,” Phys. Rev. A 4, 2342–2347 (1971).
[CrossRef]

Gersten, J. I.

N. Tzor and J. I. Gersten, “Nonlinear wave propagation in a transparent medium,” in Optical Properties of Highly Transparent Solids, S. Mitra and B. Bendow, eds. (Plenum, New York, 1976), pp. 373–379; A. D. Boardman and G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
[CrossRef]

Gordon, J. P.

J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation and picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Gustafson, T. K.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. 13, 392–394 (1988).
[CrossRef] [PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Haus, H. A.

W. J. Tomlinson, H. A. Haus, and R. H. Stolen, “Curious features of nonlinear pulse propagation in single-mode optical fibers,” J. Opt. Soc. Am. A 2(13), P33 (1985).

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

Hellwarth, R. W.

R. W. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

R. W. Hellwarth, A. Owyoung, and N. George, “Origin of the nonlinear refractive index of CCl4,” Phys. Rev. A 4, 2342–2347 (1971).
[CrossRef]

Henry, P. S.

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier-induced phase noise in angle-modulated optical-fiber systems,” IEEE J. Lightwave Technol. LT-2, 6–10 (1984).
[CrossRef]

Heritage, J. P.

J. P. Heritage, Bellcore, Red Bank, New Jersey 07701 (personal communication).

Ippen, E. P.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–281 (1973).
[CrossRef]

Jain, R. K.

Jaskorzynska, B.

Johnson, A. M.

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:YAG laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

Jones, W. J.

W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964).
[CrossRef]

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

Kelley, P. L.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

Knox, W. H.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

Kodama, Y.

Y. Kodama, “Optical solitons in monomode optical fibers,” J. Stat. Phys. 39, 567–614 (1985).
[CrossRef]

Lee, C.

Lifsitz, J. R.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

Lin, C.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Maker, P. D.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137A, 801–817 (1965).
[CrossRef]

Mamyshev, P. V.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

Marcuse, D.

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier-induced phase noise in angle-modulated optical-fiber systems,” IEEE J. Lightwave Technol. LT-2, 6–10 (1984).
[CrossRef]

Matveena, T. A.

V. A. Vysloukh and T. A. Matveena, “Influence of inertia of nonlinear response on compression of femtosecond pulses,” Sov. J. Quantum Electron. 17, 498–500 (1987).
[CrossRef]

Milam, D.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

Nelson, K. A.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

Owyoung, A.

R. W. Hellwarth, A. Owyoung, and N. George, “Origin of the nonlinear refractive index of CCl4,” Phys. Rev. A 4, 2342–2347 (1971).
[CrossRef]

Prokorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

Schadt, D.

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

Shank, C. V.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Raman and Brillouin scattering,” Phys. Rev. 137A, 1787–1805 (1965).
[CrossRef]

Shimizu, F.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Simpson, W. M.

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:YAG laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

Smith, R. G.

Stoicheff, B. P.

W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964).
[CrossRef]

Stolen, R. H.

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. J. Tomlinson, H. A. Haus, and R. H. Stolen, “Curious features of nonlinear pulse propagation in single-mode optical fibers,” J. Opt. Soc. Am. A 2(13), P33 (1985).

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:YAG laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

R. H. Stolen, C. Lee, and R. K. Jain, “Development of the stimulated Raman spectrum in single-mode fibers,” J. Opt. Soc. Am. B 1, 652–657 (1984); R. H. Stolen and M. A. Bosch, “Low-frequency and low-temperature Raman scattering in silica fibers,” Phys. Rev. Lett. 48, 805–808 (1982).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation and picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–281 (1973).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and N. Bekki, “Fission of optical solitons induced by stimulated Raman effect,” Opt. Lett. 13, 392–394 (1988).
[CrossRef] [PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Taran, J. P.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137A, 801–817 (1965).
[CrossRef]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

Tomlinson, W. J.

Tzor, N.

N. Tzor and J. I. Gersten, “Nonlinear wave propagation in a transparent medium,” in Optical Properties of Highly Transparent Solids, S. Mitra and B. Bendow, eds. (Plenum, New York, 1976), pp. 373–379; A. D. Boardman and G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
[CrossRef]

Vysloukh, V. A.

V. A. Vysloukh and T. A. Matveena, “Influence of inertia of nonlinear response on compression of femtosecond pulses,” Sov. J. Quantum Electron. 17, 498–500 (1987).
[CrossRef]

Wang, C. S.

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Weber, M. J.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Williams, L. R.

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

Yang, T.

R. W. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

Zhao, W.

W. Zhao and E. Bourkoff, “Femtosecond pulse propagation in optical fibers: higher order effects,” IEEE J. Quantum Electron. QE-24, 365–372 (1988); E. A. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. M. Prokhorov, “Optical fiber-grating pulse compression,” Opt. Quantum Electron. 20, 343–355 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, and C. V. Shank, “Optical pulse compression to 8 fsec at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:YAG laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–281 (1973).
[CrossRef]

Chem. Phys. Lett. (1)

S. de Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson, “Femtosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated Raman scattering in α-perylene crystal from 20 to 300 K,” Chem. Phys. Lett. 116, 146–152 (1985).
[CrossRef]

IEEE J. Lightwave Technol. (1)

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier-induced phase noise in angle-modulated optical-fiber systems,” IEEE J. Lightwave Technol. LT-2, 6–10 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Zhao and E. Bourkoff, “Femtosecond pulse propagation in optical fibers: higher order effects,” IEEE J. Quantum Electron. QE-24, 365–372 (1988); E. A. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. M. Prokhorov, “Optical fiber-grating pulse compression,” Opt. Quantum Electron. 20, 343–355 (1988).
[CrossRef]

J. Appl. Phys. (1)

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

J. Opt. Soc. Am. A (1)

W. J. Tomlinson, H. A. Haus, and R. H. Stolen, “Curious features of nonlinear pulse propagation in single-mode optical fibers,” J. Opt. Soc. Am. A 2(13), P33 (1985).

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

J. Stat. Phys. (1)

Y. Kodama, “Optical solitons in monomode optical fibers,” J. Stat. Phys. 39, 567–614 (1985).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (4)

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969).
[CrossRef]

M. Denariez and G. Bret, “Investigation of Rayleigh wings and Brillouin-stimulated scattering in liquids,” Phys. Rev. 171, 160–171 (1968).
[CrossRef]

Y. R. Shen and N. Bloembergen, “Theory of stimulated Raman and Brillouin scattering,” Phys. Rev. 137A, 1787–1805 (1965).
[CrossRef]

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137A, 801–817 (1965).
[CrossRef]

Phys. Rev. A (3)

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

R. W. Hellwarth, A. Owyoung, and N. George, “Origin of the nonlinear refractive index of CCl4,” Phys. Rev. A 4, 2342–2347 (1971).
[CrossRef]

R. L. Carman, F. Shimizu, C. S. Wang, and N. Bloembergen, “Theory of Stokes pulse shapes in transient Raman scattering,” Phys. Rev. A 2, 60–72 (1970).
[CrossRef]

Phys. Rev. B (1)

R. W. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

Phys. Rev. Lett. (3)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation and picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

W. J. Jones and B. P. Stoicheff, “Inverse Raman spectra: induced absorption at optical frequencies,” Phys. Rev. Lett. 13, 657–659 (1964).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. A. Vysloukh and T. A. Matveena, “Influence of inertia of nonlinear response on compression of femtosecond pulses,” Sov. J. Quantum Electron. 17, 498–500 (1987).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokorov, and V. N. Serkin, “Formation of ultrashort pulses by the spectral filtration technique on stimulated combination scattering in fiber light guides,” Zh. Eksp. Teor. Fiz. 89, 781 (1986) [Sov. Phys. JETP 62, 448–455 (1985)].

Other (2)

J. P. Heritage, Bellcore, Red Bank, New Jersey 07701 (personal communication).

N. Tzor and J. I. Gersten, “Nonlinear wave propagation in a transparent medium,” in Optical Properties of Highly Transparent Solids, S. Mitra and B. Bendow, eds. (Plenum, New York, 1976), pp. 373–379; A. D. Boardman and G. S. Cooper, “Power-dependent polarization of optical pulses,” J. Opt. Soc. Am. B 5, 403–418 (1988).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Imaginary and (b) real third-order susceptibilities for an exponential response function with a response time τ = 76 fsec (dashed curves) and for fused silica (solid curves). The imaginary part of N2(Ω) is proportional to Raman gain and is arbitrarily normalized to unity at the peak gain. The real part of N2(Ω) is obtained with a Kramers–Kronig transform of N2″(Ω) and is plotted in the same arbitrary units as N2″(Ω).

Fig. 2
Fig. 2

The Raman time response function for silica-core fibers.

Fig. 3
Fig. 3

The effect on the response function of spectral features of the Raman-gain curve: (a) gain and response for a silica-core fiber, (b) gain and response with sharp spectral features removed, (c) contribution of the 604-cm−1 Raman line, (d) contribution of Raman bands beyond 750 cm−1, (e) Lorentzian fit to half-gain points of the silica gain curve.

Fig. 4
Fig. 4

Calculated output pulse showing stimulated Raman-like instability for positive GVD. This calculation is for a normalized input pulse amplitude A = 173, a fiber length z/z0 = 0.004, and an exponential Raman response function with a response time τ/t0 = 0.02. The intensity variable is |V/A|2.

Fig. 5
Fig. 5

Pulse shape leaving the fiber in a calculation modeling an 8-fsec compression experiment with positive GVD,22 for an input pulse with a FWHM of 40 fsec (t0 = 22.7 fsec), normalized input pulse amplitude A = 7, and fiber length z/z0 = 0.5. The intensity variable is |V/A|2: (a) with Raman response function of Fig. 2, (b) without response function.

Fig. 6
Fig. 6

Spectra of the pulses in Figs. 5(a) and 5(b). On this normalized frequency scale unity corresponds to 234 cm−1.

Fig. 7
Fig. 7

Pulse shapes for negative GVD for various fiber lengths for an input pulse with a FWHM of 40 fsec (t0 = 22.7 fsec) and an amplitude A = 1: (a) input pulse (z/z0 = 0.0), (b) pulse after z/z0 = 3.0, (c) pulse after z/z0 = 6.0 (27.2 cm).

Fig. 8
Fig. 8

Average frequency shift along the fiber for the input pulse of Fig. 7.

Equations (15)

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i ( u z + k 1 u t ) = k 2 2 2 u t 2 + κ u 2 u ,
N 2 u ( t ) 2 N 2 u ( t ) 2 + N 2 R τ - t d t u ( t ) 2 exp [ - ( t - t ) τ ] .
u ( t ) = u 1 cos ( w p t - k p z ) + u 2 cos ( ω s t - k s z ) .
N 2 ( Ω ) = N 2 + N 2 R / ( 1 + Ω 2 τ 2 ) , N 2 ( Ω ) = N 2 R Ω τ / ( 1 + Ω 2 τ 2 ) ,
g = ( 2 ω p / c ) N 2 ( Ω ) .
N 2 u ( t ) 2 N 2 u ( t ) 2 + N 2 R - t d t u ( t ) 2 f ( t - t ) ,
N 2 ( Ω ) = N 2 R 0 f ( t - t ) exp [ i Ω ( t - t ) ] d ( t - t ) .
N 2 R f ( t - t ) = 1 2 π - N 2 ( Ω ) exp [ - i Ω ( t - t ) ] d Ω .
N 2 R f ( s ) = 2 π 0 d Ω N 2 ( Ω ) cos ( Ω s ) = 2 π 0 d Ω N 2 ( Ω ) sin ( Ω s ) ,
g = ( a Ω + b Ω 3 ) cm / W ,
V ( z / z 0 ) = i π 4 [ ± 2 V ( t / t 0 ) 2 - 2 V 2 V ] ,
z 0 = π 2 c 2 t 0 2 / D ( λ 0 ) λ 0 ,
I 0 = 10 - 7 n c λ 0 / ( 16 π n 2 z 0 ) W / cm 2 .
u ( t ) d s f ( s ) u ( t - s ) 2 u ( t ) u ( t ) 2 × - f ( s ) d s - u ( t ) t u ( t ) 2 - s f ( s ) d s .
N 2 ( Ω ) = N 2 R 0 f ( s ) sin ( Ω s ) d s = N 2 ( 0 ) + Ω N 2 ( 0 ) Ω + ,

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