Abstract

The optical Kerr effect was measured with 130-fs laser pulses for a variety of metal-doped silicate glasses, including pairs of glasses with comparable refractive index and Abbe number but different dopant cations. The nonlinear response appeared to be instantaneous within the resolution of the experiment, matching the measured autocorrelation function of the incident laser pulses, and therefore potentially useful in ultrafast photonic switching applications. We explain the absence of any detectable slow nuclear components through a detailed time-domain analysis of the contributions to an optical Kerr effect measurement made with ultrashort pulses. This analysis describes nonresonant vibrational contributions that are temporally indistinguishable from electronic contributions. The measured third-order susceptibilities of the Ti-, Nb-, and La-doped glasses were significantly overestimated by semiempirical models based on linear material parameters, such as the model developed by Lines [J. Appl. Phys.69, 6876 (1991)] and the equation given by Boling–Glass–Owyoung [IEEE J. Quantum Electron. QE-14, 601 (1978)].

© 2000 Optical Society of America

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  1. W. Koechner, Solid State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988), Secs. 4.3 and 11.3, and references therein.
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    [CrossRef]
  3. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. QE-23, 2089–2094 (1987).
    [CrossRef]
  4. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
    [CrossRef]
  5. M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
    [CrossRef]
  6. N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
    [CrossRef]
  7. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
    [CrossRef]
  8. I. Thomazeau, J. Etchepare, G. Grillon, and A. Migus, “Electronic nonlinear optical susceptibilities of silicate glasses,” Opt. Lett. 10, 223–225 (1985).
    [CrossRef] [PubMed]
  9. E. M. Vogel, D. M. Krol, J. L. Jackel, and J. S. Aitchison, “Structure and nonlinear optical properties of glasses for photonic switching,” Mat. Res. Soc. Symp. Proc. 152, 83–87 (1989).
    [CrossRef]
  10. R. Hellwarth, J. Cherlow, and T.-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
    [CrossRef]
  11. K. A. Nelson, “Time resolved spectroscopy,” in Encyclopedia of Physics, Science, and Technology (Academic, New York, 1989), p. 607.
  12. R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
    [CrossRef]
  13. D. Heiman, R. W. Hellwarth, and D. S. Hamilton, “Raman scattering and nonlinear refractive index measurements of optical glasses,” J. Non-Cryst. Solids 34, 63–79 (1979).
    [CrossRef]
  14. D. Heiman, D. S. Hamilton, and R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
    [CrossRef]
  15. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904–906 (1988).
    [CrossRef] [PubMed]
  16. N. Sugimoto, H. Kanabara, S. Fujiwara, K. Tanaka, and K. Hirao, “Ultrafast response of third-order optical nonlinearity in glasses containing Bi2O3,” Opt. Lett. 21, 1637–1639 (1996).
    [CrossRef] [PubMed]
  17. I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy metal doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
    [CrossRef]
  18. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  19. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
    [CrossRef]
  20. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977–1979 (1962).
    [CrossRef]
  21. I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
    [CrossRef]
  22. D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
    [CrossRef]
  23. M. D. Levenson and J. J. Song, “Coherent Raman spectroscopy,” in Coherent Nonlinear Optics, M. S. Feld and V. S. Letokov, eds. (Springer-Verlag, Berlin, 1980), pp. 293–373.
  24. A. Owyoung, “The origins of the nonlinear refractive indices of liquids and glasses,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1972), pp. 25, 32, 49, 63.
  25. D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
    [CrossRef]
  26. W. L. Smith, “Nonlinear refractive index,” in Handbook of Laser Science and Technology, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1986), Vol. III, Pt. 1, pp. 259–264.
  27. K. Sala, G. A. Kenney-Wallace, and G. E. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. QE-16, 990–996 (1980).
    [CrossRef]
  28. E. P. Ippen and C. V. Shank, “Picosecond response of a high repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 26, 92–93 (1975).
    [CrossRef]
  29. J.-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713–718 (1983).
    [CrossRef]
  30. Y.-X. Yan and K. A. Nelson, “Impulsive stimulated light scattering. II. Comparison to frequency domain light-scattering spectroscopy,” J. Chem. Phys. 87, 6257–6265 (1987).
    [CrossRef]
  31. D. McMorrow and W. T. Lotshaw, “The frequency response of condensed-phase media to femtosecond optical pulses: spectral filter effects,” Chem. Phys. Lett. 174, 85–94 (1990).
    [CrossRef]
  32. D. McMorrow, “Separation of nuclear and electronic contributions to femtosecond four-wave mixing data,” Opt. Commun. 86, 236–244 (1991).
    [CrossRef]
  33. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1165 (1989).
    [CrossRef]
  34. The Raman data available from Ref. 13 did not extend below 30 cm−1, so we had to extrapolate the scattered intensities below 30 cm−1. As per Ref. 13, we excluded the very-low-frequency excess light scattering peak from our integrations and assumed that the intensity goes to zero at zero frequency. The numerical values of the ratio A(0)/B(0) calculated from our fit were quite sensitive to the choice of extrapolation function, ranging from ~0.50 to ~0.72 for SF6 glass. These values can be compared with the value 0.73 of this ratio reported in Ref. 13. However, the effect on the resulting Kerr signals was negligible (less than a few percent).
  35. G. L. Eesley, “Coherent Raman spectroscopy,” J. Quant. Spectrosc. Radiat. Transfer 22, 507–576 (1979).
    [CrossRef]
  36. N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1977), pp. 41–43.
  37. N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electric-field-induced birefringence properties of high-refractive-index glasses exhibiting large Kerr nonlinearities,” J. Appl. Phys. 70, 2774–2779 (1991).
    [CrossRef]
  38. R. T. Williams and E. J. Frieble, “Radiation damage in optically transmitting crystals and glasses,” in Handbook of Laser Science and Technology, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1986), Vol. III, Part 1, pp. 388–398.

1996 (2)

N. Sugimoto, H. Kanabara, S. Fujiwara, K. Tanaka, and K. Hirao, “Ultrafast response of third-order optical nonlinearity in glasses containing Bi2O3,” Opt. Lett. 21, 1637–1639 (1996).
[CrossRef] [PubMed]

I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
[CrossRef]

1995 (1)

1991 (3)

M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

D. McMorrow, “Separation of nuclear and electronic contributions to femtosecond four-wave mixing data,” Opt. Commun. 86, 236–244 (1991).
[CrossRef]

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electric-field-induced birefringence properties of high-refractive-index glasses exhibiting large Kerr nonlinearities,” J. Appl. Phys. 70, 2774–2779 (1991).
[CrossRef]

1990 (2)

D. McMorrow and W. T. Lotshaw, “The frequency response of condensed-phase media to femtosecond optical pulses: spectral filter effects,” Chem. Phys. Lett. 174, 85–94 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1989 (4)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

E. M. Vogel, D. M. Krol, J. L. Jackel, and J. S. Aitchison, “Structure and nonlinear optical properties of glasses for photonic switching,” Mat. Res. Soc. Symp. Proc. 152, 83–87 (1989).
[CrossRef]

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1165 (1989).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

1988 (3)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904–906 (1988).
[CrossRef] [PubMed]

1987 (3)

S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. QE-23, 2089–2094 (1987).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
[CrossRef]

Y.-X. Yan and K. A. Nelson, “Impulsive stimulated light scattering. II. Comparison to frequency domain light-scattering spectroscopy,” J. Chem. Phys. 87, 6257–6265 (1987).
[CrossRef]

1985 (1)

1983 (1)

J.-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713–718 (1983).
[CrossRef]

1980 (1)

K. Sala, G. A. Kenney-Wallace, and G. E. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. QE-16, 990–996 (1980).
[CrossRef]

1979 (3)

G. L. Eesley, “Coherent Raman spectroscopy,” J. Quant. Spectrosc. Radiat. Transfer 22, 507–576 (1979).
[CrossRef]

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, “Raman scattering and nonlinear refractive index measurements of optical glasses,” J. Non-Cryst. Solids 34, 63–79 (1979).
[CrossRef]

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

1978 (1)

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

1977 (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[CrossRef]

1975 (2)

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

E. P. Ippen and C. V. Shank, “Picosecond response of a high repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 26, 92–93 (1975).
[CrossRef]

1962 (1)

A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977–1979 (1962).
[CrossRef]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
[CrossRef]

Aitchison, J. S.

E. M. Vogel, D. M. Krol, J. L. Jackel, and J. S. Aitchison, “Structure and nonlinear optical properties of glasses for photonic switching,” Mat. Res. Soc. Symp. Proc. 152, 83–87 (1989).
[CrossRef]

Aitken, B. G.

I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
[CrossRef]

I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy metal doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
[CrossRef]

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electric-field-induced birefringence properties of high-refractive-index glasses exhibiting large Kerr nonlinearities,” J. Appl. Phys. 70, 2774–2779 (1991).
[CrossRef]

Boling, N. L.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

Borrelli, N. F.

I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
[CrossRef]

I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy metal doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
[CrossRef]

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electric-field-induced birefringence properties of high-refractive-index glasses exhibiting large Kerr nonlinearities,” J. Appl. Phys. 70, 2774–2779 (1991).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
[CrossRef]

Cherlow, J.

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

Dumbaugh, W. H.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Eesley, G. L.

G. L. Eesley, “Coherent Raman spectroscopy,” J. Quant. Spectrosc. Radiat. Transfer 22, 507–576 (1979).
[CrossRef]

Etchepare, J.

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Friberg, S. R.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904–906 (1988).
[CrossRef] [PubMed]

S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. QE-23, 2089–2094 (1987).
[CrossRef]

Fujiwara, S.

Glass, A. J.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

Gordon, J. P.

Grillon, G.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Hall, D. W.

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electric-field-induced birefringence properties of high-refractive-index glasses exhibiting large Kerr nonlinearities,” J. Appl. Phys. 70, 2774–2779 (1991).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Hall, G. E.

K. Sala, G. A. Kenney-Wallace, and G. E. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. QE-16, 990–996 (1980).
[CrossRef]

Hamilton, D. S.

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, “Raman scattering and nonlinear refractive index measurements of optical glasses,” J. Non-Cryst. Solids 34, 63–79 (1979).
[CrossRef]

Haus, H. A.

Heiman, D.

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, “Raman scattering and nonlinear refractive index measurements of optical glasses,” J. Non-Cryst. Solids 34, 63–79 (1979).
[CrossRef]

Hellwarth, R.

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

Hellwarth, R. W.

D. Heiman, R. W. Hellwarth, and D. S. Hamilton, “Raman scattering and nonlinear refractive index measurements of optical glasses,” J. Non-Cryst. Solids 34, 63–79 (1979).
[CrossRef]

D. Heiman, D. S. Hamilton, and R. W. Hellwarth, “Brillouin scattering measurements on optical glasses,” Phys. Rev. B 19, 6583–6592 (1979).
[CrossRef]

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[CrossRef]

Hirao, K.

Ippen, E. P.

E. P. Ippen and C. V. Shank, “Picosecond response of a high repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 26, 92–93 (1975).
[CrossRef]

Jackel, J. L.

E. M. Vogel, D. M. Krol, J. L. Jackel, and J. S. Aitchison, “Structure and nonlinear optical properties of glasses for photonic switching,” Mat. Res. Soc. Symp. Proc. 152, 83–87 (1989).
[CrossRef]

Kanabara, H.

Kang, I.

I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
[CrossRef]

I. Kang, T. D. Krauss, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Femtosecond measurement of enhanced optical nonlinearities of sulfide glasses and heavy metal doped oxide glasses,” J. Opt. Soc. Am. B 12, 2053–2059 (1995).
[CrossRef]

Kenney-Wallace, G. A.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

K. Sala, G. A. Kenney-Wallace, and G. E. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. QE-16, 990–996 (1980).
[CrossRef]

Kleinman, A.

A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977–1979 (1962).
[CrossRef]

Krauss, T.

I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
[CrossRef]

Krauss, T. D.

Krol, D. M.

E. M. Vogel, D. M. Krol, J. L. Jackel, and J. S. Aitchison, “Structure and nonlinear optical properties of glasses for photonic switching,” Mat. Res. Soc. Symp. Proc. 152, 83–87 (1989).
[CrossRef]

Lines, M. E.

M. E. Lines, “Oxide glasses for fast photonic switching: a comparative study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

Lotshaw, W. T.

D. McMorrow and W. T. Lotshaw, “The frequency response of condensed-phase media to femtosecond optical pulses: spectral filter effects,” Chem. Phys. Lett. 174, 85–94 (1990).
[CrossRef]

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

McMorrow, D.

D. McMorrow, “Separation of nuclear and electronic contributions to femtosecond four-wave mixing data,” Opt. Commun. 86, 236–244 (1991).
[CrossRef]

D. McMorrow and W. T. Lotshaw, “The frequency response of condensed-phase media to femtosecond optical pulses: spectral filter effects,” Chem. Phys. Lett. 174, 85–94 (1990).
[CrossRef]

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[CrossRef]

Migus, A.

Nelson, K. A.

Y.-X. Yan and K. A. Nelson, “Impulsive stimulated light scattering. II. Comparison to frequency domain light-scattering spectroscopy,” J. Chem. Phys. 87, 6257–6265 (1987).
[CrossRef]

Newhouse, M. A.

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electric-field-induced birefringence properties of high-refractive-index glasses exhibiting large Kerr nonlinearities,” J. Appl. Phys. 70, 2774–2779 (1991).
[CrossRef]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[CrossRef]

Oudar, J.-L.

J.-L. Oudar, “Coherent phenomena involved in the time-resolved optical Kerr effect,” IEEE J. Quantum Electron. QE-19, 713–718 (1983).
[CrossRef]

Owyoung, A.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4, 875–881 (1987).
[CrossRef]

Said, A. A.

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K. Sala, G. A. Kenney-Wallace, and G. E. Hall, “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quantum Electron. QE-16, 990–996 (1980).
[CrossRef]

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
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Sfez, B. G.

Shank, C. V.

E. P. Ippen and C. V. Shank, “Picosecond response of a high repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 26, 92–93 (1975).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

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Smith, P. W.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. W. Smith, “Femtosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904–906 (1988).
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S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. QE-23, 2089–2094 (1987).
[CrossRef]

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I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988).
[CrossRef]

Stolen, R. H.

Sugimoto, N.

Tanaka, K.

Thomazeau, I.

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van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

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E. M. Vogel, D. M. Krol, J. L. Jackel, and J. S. Aitchison, “Structure and nonlinear optical properties of glasses for photonic switching,” Mat. Res. Soc. Symp. Proc. 152, 83–87 (1989).
[CrossRef]

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M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
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I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken, and N. F. Borrelli, “Time domain observation of nuclear contributions to the optical nonlinearities of glasses,” Phys. Rev. B 54, 12641–12644 (1996).
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[CrossRef]

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E. M. Vogel, “Glasses as non-linear photonic materials,” J. Am. Ceram. Soc. 72, 719–724 (1989); N. F. Borrelli and D. W. Hall, “Nonlinear optical properties of glasses” in Optical Properties of Glass, D. R. Uhlmann and N. J. Kreidl, eds. (American Ceramic Society, Westerville, Ohio, 1991), pp. 87–124.
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W. L. Smith, “Nonlinear refractive index,” in Handbook of Laser Science and Technology, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1986), Vol. III, Pt. 1, pp. 259–264.

N. Bloembergen, Nonlinear Optics (Benjamin, Reading, Mass., 1977), pp. 41–43.

The Raman data available from Ref. 13 did not extend below 30 cm−1, so we had to extrapolate the scattered intensities below 30 cm−1. As per Ref. 13, we excluded the very-low-frequency excess light scattering peak from our integrations and assumed that the intensity goes to zero at zero frequency. The numerical values of the ratio A(0)/B(0) calculated from our fit were quite sensitive to the choice of extrapolation function, ranging from ~0.50 to ~0.72 for SF6 glass. These values can be compared with the value 0.73 of this ratio reported in Ref. 13. However, the effect on the resulting Kerr signals was negligible (less than a few percent).

R. T. Williams and E. J. Frieble, “Radiation damage in optically transmitting crystals and glasses,” in Handbook of Laser Science and Technology, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1986), Vol. III, Part 1, pp. 388–398.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of time-resolved OKE experiment. Pump and probe pulses are derived from the same laser pulse by use of a 95%/5% beam splitter. Time delay is achieved with a retroflector mounted on a computer-controlled translation stage. Beam polarization and intensity are controlled with a combination of Glan prism polarizers and quartz half-wave retardation plates. Beams are focused with a 100-mm focal-length lens and are crossed at an angle of 7°. A quarter-wave retardation plate generates the local oscillator signal for optical heterodyning.

Fig. 2
Fig. 2

Logarithmic (Ln) plot of typical experimental OKE signal and sech2 fitted curve for SF58 glass, after subtraction of a sloped linear baseline.

Fig. 3
Fig. 3

Polarized (solid curve) and depolarized (dotted curve) Raman spectra of SF6 glass, excited at 458 nm, with background fluorescence subtracted (based on Ref. 13).

Fig. 4
Fig. 4

Nuclear response functions a(t) (bottom) and b(t) (top) of SF6 glass, calculated from the Raman spectra shown in Fig. 3, from relations (6) and (7).

Fig. 5
Fig. 5

Calculated OHD Kerr signals shown as a function of delay time, τ, assuming sech2 pump and probe pulses of width (a) 130 fs and (b) 13 fs. Short-dashed curve, nuclear contribution; medium-dashed curve, electronic contribution; long-dashed curve, coherent coupling contribution; solid curve, sum of all the contributions.

Fig. 6
Fig. 6

Experimentally determined values of n2 versus values predicted by the BGO equation for the 14 glasses studied.

Tables (1)

Tables Icon

Table 1 Nonlinear Refractive Indices of Metal-Doped Silicate Glassesa,b

Equations (11)

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T(τ)=-+Iprobe(t-τ){1+sin[ϕ(t)]}dt,
Pi(3)(t)=Fj(t)-+ds[σijklδ(t-s)+dijkl(t-s)]×Fk(s)Fl(s),
dijkl(t)=a(t)δijδkl+12b(t)(δilδjk+δikδjl),
Fi(t)=Re[Ei(t)exp(-iω1t)+ei(t)exp(-iω2t)].
Py(3)(t)=2σ3e(t)|E(t)|2+e(t)-+b(t-s)|E(s)|2ds+E(t)×-+[a(t-s)+12b(t-s)]e(s)E(s)ds.
B(ω)1(ν-ω)3d2σdΩdω[1-exp(-ω/kT)],
A(ω)1(ν-ω)312d2σdΩdω-d2σdΩdω×[1-exp(-ω/kT)],
b(t)=2π0dωB(ω)sin ωt(t>0).
Shetero(τ)=-Py(3)(t)e(t)dt.
n2=k(nd-1)(nd2+2)2/{νd[1.52+(nd2+2)(nd+1)νd/6nd]1/2},
n2=4.0×10-14(n02+2)3(n02-1)d2n0Es2

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