Abstract

Studies of the nonlinear absorption and refraction of a variety of heavy-metal oxide and sulfide glasses are reported. The third-order nonlinearities were measured with ~100-fs pulses at wavelengths between 600 nm and 1.25 μm, allowing for what we believe is the first systematic study of the dispersion of the third-order nonlinearities of these glasses. The results confirm that the nonlinearities of heavy-metal oxide glasses are determined by heavy-metal content, as reported previously. The measured nonlinear refractive indices are predicted reasonably well by the semiempirical Boling–Glass–Owyoung formula and include several results that are among the largest nonresonant nonlinearities reported. The measured dispersion of the nonlinearities is consistent with simple theoretical expectations. Finally, most of the glasses obey Kleinman’s symmetry, from which we conclude that the origin of the femtosecond-time-scale nonlinearities is electronic.

© 1995 Optical Society of America

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  1. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. QE-23, 2089 (1987).
    [CrossRef]
  2. C. Radzewicz, G. W. Pearson, and J. S. Krasisnski, “Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti:sapphire self modelocked laser,” Opt. Commun. 102, 464 (1993).
    [CrossRef]
  3. E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719 (1989).
    [CrossRef]
  4. 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 (1989).
    [CrossRef]
  5. J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
    [CrossRef]
  6. E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
    [CrossRef]
  7. H. Nasu, Y. Ibara, and K. Kubodera, “Optical third-harmonic generation from some high-index glasses,” J. Non-Cryst. Solids 110, 229 (1989).
    [CrossRef]
  8. H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
    [CrossRef]
  9. I. Thomazeau, J. Etchepare, G. Grillon, and A. Migus, “Electronic nonlinear optical susceptibilities of silicate glasses,” Opt. Lett. 10, 223 (1985).
    [CrossRef] [PubMed]
  10. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140 (1989).
    [CrossRef] [PubMed]
  11. T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65, 1739 (1994); D. C. Hutchings and E. W. van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065 (1992); D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622 (1994).
    [CrossRef]
  12. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. van Stryland, “Sensitive measurement of optical nonlinearity using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  13. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
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  14. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
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  16. N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, “Resonant and non-resonant effects in photonic glasses,” J. Non-Cryst. Solids (to be published).
  17. The third order nonlinear susceptibility χ(3)(−ω; ω, ω, −ω) contains a term which is proportional to 1/(ω0− ω− ω+ ω)(ω0− ω− ω)(ω0− ω) off resonance, where ω0corresponds to the fundamental absorption frequency; see Ref. 14.
  18. F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
    [CrossRef]
  19. H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
    [CrossRef]
  20. 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 (1987).
    [CrossRef]
  21. D. M. Bishop, “Dispersion formulas for certain nonlinear optical processes,” Phys. Rev. Lett. 61, 322 (1988).
    [CrossRef] [PubMed]
  22. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337 (1989).
    [CrossRef]
  23. N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electrooptical properties of high refractive index glasses,” in Glasses for Optoelectronics, G. C. Righini, ed. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
    [CrossRef]
  24. B. J. Orr and J. F. Ward, “Perturbation theory of the nonlinear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
    [CrossRef]
  25. D. P. Shelton, “Hyperpolarizability dispersion measured for Kr and Xe,” J. Chem. Phys. 84, 404 (1986).
    [CrossRef]
  26. V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibility of Ar, N2, and O2measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
    [CrossRef] [PubMed]
  27. J. G. Bergman and G. K. Crane, “Structural aspects of nonlinear optics-oxide systems ABOx,” J. Solid State Chem. 12, 172 (1975).
    [CrossRef]
  28. M. E. Lines, “Bond-orbital theory of linear and nonlinear electronic response in ionic crystals. II. Nonlinear response,” Phys. Rev. B 41, 3383 (1990).
    [CrossRef]
  29. N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978); Eq. (2) is shown to be equivalent to a more familiar form of the BGO formula, which involves the Abbé number in this reference.
    [CrossRef]
  30. D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977 (1962).
    [CrossRef]
  31. I. J. Biggio and J. F. Ward, “Measurement of the hyper-polarizability ratio χyyyy(−2ω; 0, ω, ω)/χyyxx(−2ω; 0, ω, ω) for the inert gases,” Phys. Rev. A 9, 35 (1974).
    [CrossRef]
  32. V. Mizrahi and D. P. Shelton, “Deviations from Kleinman symmetry measured for several simple atoms and molecules,” Phys. Rev. A 31, 3145 (1985).
    [CrossRef] [PubMed]
  33. R. Hellwarth, J. Cherlow, and T-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964 (1975).
    [CrossRef]
  34. R. S. 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 (1988).
    [CrossRef] [PubMed]

1995 (1)

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
[CrossRef]

1994 (2)

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65, 1739 (1994); D. C. Hutchings and E. W. van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065 (1992); D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622 (1994).
[CrossRef]

1993 (3)

Y. Pang, V. Yanovsky, F. W. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
[CrossRef] [PubMed]

C. Radzewicz, G. W. Pearson, and J. S. Krasisnski, “Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti:sapphire self modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

1992 (1)

1990 (3)

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

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

M. E. Lines, “Bond-orbital theory of linear and nonlinear electronic response in ionic crystals. II. Nonlinear response,” Phys. Rev. B 41, 3383 (1990).
[CrossRef]

1989 (6)

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

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140 (1989).
[CrossRef] [PubMed]

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

H. Nasu, Y. Ibara, and K. Kubodera, “Optical third-harmonic generation from some high-index glasses,” J. Non-Cryst. Solids 110, 229 (1989).
[CrossRef]

E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719 (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 (1989).
[CrossRef]

1988 (2)

1987 (2)

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 (1987).
[CrossRef]

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

1986 (1)

D. P. Shelton, “Hyperpolarizability dispersion measured for Kr and Xe,” J. Chem. Phys. 84, 404 (1986).
[CrossRef]

1985 (3)

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibility of Ar, N2, and O2measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Shelton, “Deviations from Kleinman symmetry measured for several simple atoms and molecules,” Phys. Rev. A 31, 3145 (1985).
[CrossRef] [PubMed]

I. Thomazeau, J. Etchepare, G. Grillon, and A. Migus, “Electronic nonlinear optical susceptibilities of silicate glasses,” Opt. Lett. 10, 223 (1985).
[CrossRef] [PubMed]

1978 (1)

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978); Eq. (2) is shown to be equivalent to a more familiar form of the BGO formula, which involves the Abbé number in this reference.
[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 (1975).
[CrossRef]

J. G. Bergman and G. K. Crane, “Structural aspects of nonlinear optics-oxide systems ABOx,” J. Solid State Chem. 12, 172 (1975).
[CrossRef]

1974 (1)

I. J. Biggio and J. F. Ward, “Measurement of the hyper-polarizability ratio χyyyy(−2ω; 0, ω, ω)/χyyxx(−2ω; 0, ω, ω) for the inert gases,” Phys. Rev. A 9, 35 (1974).
[CrossRef]

1971 (1)

B. J. Orr and J. F. Ward, “Perturbation theory of the nonlinear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

1962 (1)

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

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337 (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 (1987).
[CrossRef]

Aitken, B. G.

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electrooptical properties of high refractive index glasses,” in Glasses for Optoelectronics, G. C. Righini, ed. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, “Resonant and non-resonant effects in photonic glasses,” J. Non-Cryst. Solids (to be published).

Andrejco, M. J.

Bergman, J. G.

J. G. Bergman and G. K. Crane, “Structural aspects of nonlinear optics-oxide systems ABOx,” J. Solid State Chem. 12, 172 (1975).
[CrossRef]

Biggio, I. J.

I. J. Biggio and J. F. Ward, “Measurement of the hyper-polarizability ratio χyyyy(−2ω; 0, ω, ω)/χyyxx(−2ω; 0, ω, ω) for the inert gases,” Phys. Rev. A 9, 35 (1974).
[CrossRef]

Bishop, D. M.

D. M. Bishop, “Dispersion formulas for certain nonlinear optical processes,” Phys. Rev. Lett. 61, 322 (1988).
[CrossRef] [PubMed]

Boling, N. L.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978); Eq. (2) is shown to be equivalent to a more familiar form of the BGO formula, which involves the Abbé number in this reference.
[CrossRef]

Borrelli, N. F.

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[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 (1989).
[CrossRef]

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electrooptical properties of high refractive index glasses,” in Glasses for Optoelectronics, G. C. Righini, ed. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, “Resonant and non-resonant effects in photonic glasses,” J. Non-Cryst. Solids (to be published).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337 (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 (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 (1975).
[CrossRef]

Crane, G. K.

J. G. Bergman and G. K. Crane, “Structural aspects of nonlinear optics-oxide systems ABOx,” J. Solid State Chem. 12, 172 (1975).
[CrossRef]

DeLong, K. W.

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 (1989).
[CrossRef]

Etchepare, J.

Friberg, R. S.

Friberg, S. R.

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

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

Fukunaga, T.

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

Glass, A. J.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978); Eq. (2) is shown to be equivalent to a more familiar form of the BGO formula, which involves the Abbé number in this reference.
[CrossRef]

Grillon, G.

Hagan, D. J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

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

Hall, D. W.

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 (1989).
[CrossRef]

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electrooptical properties of high refractive index glasses,” in Glasses for Optoelectronics, G. C. Righini, ed. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[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 (1975).
[CrossRef]

Ibara, Y.

H. Nasu, Y. Ibara, and K. Kubodera, “Optical third-harmonic generation from some high-index glasses,” J. Non-Cryst. Solids 110, 229 (1989).
[CrossRef]

Jackel, J. L.

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

Jin, J.

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

Kamiya, K.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
[CrossRef]

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

Kippelen, B.

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

Kleinman, D. A.

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

Kobayashi, M.

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

Kosinski, S. G.

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

Krasisnski, J. S.

C. Radzewicz, G. W. Pearson, and J. S. Krasisnski, “Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti:sapphire self modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Krauss, T. D.

T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65, 1739 (1994); D. C. Hutchings and E. W. van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065 (1992); D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622 (1994).
[CrossRef]

Krol, D. M.

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

Kubodera, K.

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

H. Nasu, Y. Ibara, and K. Kubodera, “Optical third-harmonic generation from some high-index glasses,” J. Non-Cryst. Solids 110, 229 (1989).
[CrossRef]

Lee, S. G.

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

Lines, M. E.

M. E. Lines, “Bond-orbital theory of linear and nonlinear electronic response in ionic crystals. II. Nonlinear response,” Phys. Rev. B 41, 3383 (1990).
[CrossRef]

Matsuoka, J.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
[CrossRef]

Migus, A.

Minkov, B. I.

Misawa, M.

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

Miyaji, F.

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

Mizrahi, V.

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140 (1989).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Shelton, “Deviations from Kleinman symmetry measured for several simple atoms and molecules,” Phys. Rev. A 31, 3145 (1985).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibility of Ar, N2, and O2measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

Nakamura, M.

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

Nasu, H.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
[CrossRef]

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

H. Nasu, Y. Ibara, and K. Kubodera, “Optical third-harmonic generation from some high-index glasses,” J. Non-Cryst. Solids 110, 229 (1989).
[CrossRef]

Newhouse, M. A.

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 (1989).
[CrossRef]

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, “Resonant and non-resonant effects in photonic glasses,” J. Non-Cryst. Solids (to be published).

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electrooptical properties of high refractive index glasses,” in Glasses for Optoelectronics, G. C. Righini, ed. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

Oliver, M. K.

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

Orr, B. J.

B. J. Orr and J. F. Ward, “Perturbation theory of the nonlinear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Owyoung, A.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978); Eq. (2) is shown to be equivalent to a more familiar form of the BGO formula, which involves the Abbé number in this reference.
[CrossRef]

Pang, Y.

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337 (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 (1987).
[CrossRef]

Pearson, G. W.

C. Radzewicz, G. W. Pearson, and J. S. Krasisnski, “Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti:sapphire self modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Peyghambarian, N.

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

Powers, J. D.

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

Radzewicz, C.

C. Radzewicz, G. W. Pearson, and J. S. Krasisnski, “Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti:sapphire self modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Said, A. A.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

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

Saifi, M. A.

Sakka, S.

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

Sfez, B. G.

Sheik-Bahae, M.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

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

Shelton, D. P.

D. P. Shelton, “Hyperpolarizability dispersion measured for Kr and Xe,” J. Chem. Phys. 84, 404 (1986).
[CrossRef]

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibility of Ar, N2, and O2measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Shelton, “Deviations from Kleinman symmetry measured for several simple atoms and molecules,” Phys. Rev. A 31, 3145 (1985).
[CrossRef] [PubMed]

Silberberg, Y.

Smith, P. W.

R. S. 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 (1988).
[CrossRef] [PubMed]

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

Stegeman, G. I.

Sugimoto, O.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
[CrossRef]

Thomazeau, I.

van Stryland, E. W.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

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

Vogel, E. M.

E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719 (1989).
[CrossRef]

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

Wang, J.

Ward, J. F.

I. J. Biggio and J. F. Ward, “Measurement of the hyper-polarizability ratio χyyyy(−2ω; 0, ω, ω)/χyyxx(−2ω; 0, ω, ω) for the inert gases,” Phys. Rev. A 9, 35 (1974).
[CrossRef]

B. J. Orr and J. F. Ward, “Perturbation theory of the nonlinear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Wei, T.

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

Wei, T. H.

Weidman, D. L.

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 (1989).
[CrossRef]

Weiner, A. M.

Wise, F. W.

T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65, 1739 (1994); D. C. Hutchings and E. W. van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065 (1992); D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622 (1994).
[CrossRef]

Y. Pang, V. Yanovsky, F. W. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
[CrossRef] [PubMed]

Yang, T-T.

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

Yanovsky, V.

Yoko, T.

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

Young, J.

Yumoto, J.

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

Appl. Phys. Lett. (3)

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 (1989).
[CrossRef]

J. Yumoto, S. G. Lee, B. Kippelen, N. Peyghambarian, B. G. Aitken, and N. F. Borrelli, “Enhancement of optical nonlinearity of heavy-metal oxide glasses by replacing lead and bismuth with thallium,” Appl. Phys. Lett. 63, 2630 (1993).
[CrossRef]

T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65, 1739 (1994); D. C. Hutchings and E. W. van Stryland, “Nondegenerate two-photon absorption in zinc blende semiconductors,” J. Opt. Soc. Am. B 9, 2065 (1992); D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622 (1994).
[CrossRef]

IEEE J. Quantum Electron. (3)

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

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

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601 (1978); Eq. (2) is shown to be equivalent to a more familiar form of the BGO formula, which involves the Abbé number in this reference.
[CrossRef]

J. Am. Ceram. Soc. (2)

E. M. Vogel, “Glasses as nonlinear photonic materials,” J. Am. Ceram. Soc. 72, 719 (1989).
[CrossRef]

H. Nasu, K. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73, 1794 (1990).
[CrossRef]

J. Chem. Phys. (1)

D. P. Shelton, “Hyperpolarizability dispersion measured for Kr and Xe,” J. Chem. Phys. 84, 404 (1986).
[CrossRef]

J. Non-Cryst. Solids (4)

E. M. Vogel, S. G. Kosinski, D. M. Krol, J. L. Jackel, S. R. Friberg, M. K. Oliver, and J. D. Powers, “Structural and optical study of silicate glasses for nonlinear optical devices,” J. Non-Cryst. Solids 107, 244 (1989).
[CrossRef]

H. Nasu, Y. Ibara, and K. Kubodera, “Optical third-harmonic generation from some high-index glasses,” J. Non-Cryst. Solids 110, 229 (1989).
[CrossRef]

F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, and M. Misawa, “Neutron and x-ray diffraction studies of PbO–Ga2O3and Bi2O3–Ga2O3glasses,” J. Non-Cryst. Solids 175, 211 (1994).
[CrossRef]

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321 (1995).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Solid State Chem. (1)

J. G. Bergman and G. K. Crane, “Structural aspects of nonlinear optics-oxide systems ABOx,” J. Solid State Chem. 12, 172 (1975).
[CrossRef]

Mol. Phys. (1)

B. J. Orr and J. F. Ward, “Perturbation theory of the nonlinear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Opt. Commun. (1)

C. Radzewicz, G. W. Pearson, and J. S. Krasisnski, “Use of ZnS as an additional highly nonlinear intracavity self-focusing element in a Ti:sapphire self modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (1)

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

Phys. Rev. A (2)

I. J. Biggio and J. F. Ward, “Measurement of the hyper-polarizability ratio χyyyy(−2ω; 0, ω, ω)/χyyxx(−2ω; 0, ω, ω) for the inert gases,” Phys. Rev. A 9, 35 (1974).
[CrossRef]

V. Mizrahi and D. P. Shelton, “Deviations from Kleinman symmetry measured for several simple atoms and molecules,” Phys. Rev. A 31, 3145 (1985).
[CrossRef] [PubMed]

Phys. Rev. B (3)

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

M. E. Lines, “Bond-orbital theory of linear and nonlinear electronic response in ionic crystals. II. Nonlinear response,” Phys. Rev. B 41, 3383 (1990).
[CrossRef]

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

Phys. Rev. Lett. (2)

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibility of Ar, N2, and O2measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

D. M. Bishop, “Dispersion formulas for certain nonlinear optical processes,” Phys. Rev. Lett. 61, 322 (1988).
[CrossRef] [PubMed]

Other (4)

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

N. F. Borrelli, B. G. Aitken, M. A. Newhouse, and D. W. Hall, “Electrooptical properties of high refractive index glasses,” in Glasses for Optoelectronics, G. C. Righini, ed. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).
[CrossRef]

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, “Resonant and non-resonant effects in photonic glasses,” J. Non-Cryst. Solids (to be published).

The third order nonlinear susceptibility χ(3)(−ω; ω, ω, −ω) contains a term which is proportional to 1/(ω0− ω− ω+ ω)(ω0− ω− ω)(ω0− ω) off resonance, where ω0corresponds to the fundamental absorption frequency; see Ref. 14.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup: AP’s, apertures; BS, beam splitter; L’s, lenses; M, mirror; PD’s, photodiodes.

Fig. 2
Fig. 2

(a) Open-aperture (S = 1) scan of the LaGa sulfide glass VA measured at 770 nm. The sample is 2 mm thick, and this scan was recorded with 100-fs pulses at a peak intensity I = 7.6 GW/cm2. The open-aperture data (dotted curve) were fitted with the theoretical curve (solid curve) where β = 0.31 cm/GW. (b) Closed-aperture scan (S = 0.5) of the PbBi oxide glass PbBi1 at 770 nm. The scan was taken with 100-fs pulses at a peak intensity I = 3.5 GW/cm2. The data were fitted with β = 0.71 cm/GW and χ 1111 ( 3 ) = 1.6 × 10 - 12 esu. The vertical axes represent fractional transmittance changes normalized with respect to the transmittance in the absence of the sample.

Fig. 3
Fig. 3

Real part of the third-order susceptibility, Re χ 1111 ( 3 ) ( - ω ; ω , ω , - ω ), and the two-photon absorption coefficient β of the LaGa sulfide glass VA plotted versus wavelength.

Fig. 4
Fig. 4

Nonresonant third-order nonlinearity χ1111(−ω; ω, ω, −ω) of the metal oxide glasses versus metal ion concentration.

Fig. 5
Fig. 5

Comparison of χ 1111 ( 3 ) ( - ω ; ω , ω , - ω ) of the samples measured at 990 nm and 1.25 μm with χ 1111 ( 3 ) calculated according to the Boling–Glass–Owyoung semiempirical formula.

Tables (4)

Tables Icon

Table 1 Chemical Compositions and Linear Indices of the Glasses at the Na d Line

Tables Icon

Table 2 Real Part of the Third-Order Susceptibility, Re χ 1111 ( 3 ) ( - ω ; ω , ω , - ω ), measured at 600, 770, and 990 nm and 1.06 and 1.25 μma

Tables Icon

Table 3 Linear Absorption Edges and TPA Coefficients at 600, 770, and 990 nma

Tables Icon

Table 4 Measured Values of χ 1111 ( 3 ) ( - ω ; ω , ω , - ω ) / 2 χ 1122 ( 3 ) ( - ω ; ω , ω , - ω ) at 1.25 μm

Equations (3)

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

χ 1111 ( 3 ) ( ω σ = ω 1 + ω 2 + ω 3 ) = L 4 24 ( 1 + C ω L 2 ω 0 2 ) i N i γ i .
χ 1111 ( 3 ) = ( g s ) ( n 0 2 + 2 ) 2 ( n 0 2 - 1 ) 2 576 π 2 ω 0 ( N s ) ,
χ 1111 ( 3 ) ( - ω ; ω , ω , - ω ) / 2 χ 1122 ( 3 ) ( - ω ; ω , ω , - ω )

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