Abstract

Nonlinear index of refraction of a series of organic solvents, measured by the nonlinear imaging (z-scan) technique, is compared with the same values derived from optical third-harmonic generation (THG). The systematic differences in the values obtained from the z-scan measurements and from THG are attributed to three factors: the value of the standard used in THG measurements, important rotational contribution in z-scan measurements, and the difference in dispersion for n2 derived from Kerr susceptibility and those derived from THG measurements. Using the recently proposed standard silica susceptibility value, one obtains a very good agreement for silica and significant differences for the solvents, particularly for CS2 and chlorobenzene. A correction based on a three-level model for centrosymmetric media is applied for dispersion.

© 2008 Optical Society of America

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  1. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
    [CrossRef]
  2. B. Buchalter and G. R. Meredith, “Third-order optical susceptibility of glasses determined by third harmonic generation,” Appl. Opt. 21, 3221-3224 (1982).
    [CrossRef] [PubMed]
  3. C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
    [CrossRef]
  4. U. Gubbler and C. Bosshard, “Optical third-harmonic generation of fused silica in gas atmosphere: Absolute value of the third-order nonlinear optical susceptibility χ(3),” Phys. Rev. B 61, 10702-10710 (2000).
    [CrossRef]
  5. A. Mito, K. Hagimoto, and C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Molecular Crystals and Liquid Crystals Science and Technology Section B: Nonlinear Optics, 13 (1-3), 3-18 (1995).
  6. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37, 546-550 (1998).
    [CrossRef]
  7. J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765-767 (1982).
    [CrossRef]
  8. N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
    [CrossRef]
  9. C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
    [CrossRef]
  10. F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352-2363 (1985).
    [CrossRef] [PubMed]
  11. G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation,” J. Chem. Phys. 78, 1533 (1983).
    [CrossRef]
  12. D. M. Burland, C. Walsh, F. Kajzar, and C. Sentein, “Comparison of hyperpolarizabilities obtained with different experimental methods and theoretical techniques,” J. Opt. Soc. Am. B 8, 2269-2281 (1991).
    [CrossRef]
  13. R. F. Shi and A. F. Garito, “Introduction: conventions and standards for nonlinear optical processes,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.G.Kuzyk and C.W.Dirk, eds. (Marcel Dekker, 1998).
  14. G. Boudebs and S. Cherukulappurath, “Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system,” Opt. Commun. 250, 416-420 (2005).
    [CrossRef]
  15. F. Kajzar and J. M. Nunzi, “Third order effects and applications,” in Functional Polymers and Polymeric Materials, T.Richardson, ed. (Wiley & Sons, 2000), pp. 327-363.
  16. G. A. Kenney-Wallace, S. Paone, and C. Kalpouzos, “Femtosecond laser spectroscopy and dynamics of solvation in liquids and electrolytes,” Faraday Discuss. Chem. Soc. 85, 185-198 (1988).
    [CrossRef]
  17. E. W. Van Stryland and M. Sheik-Bahae, “Z-scan,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, Inc., 1998), pp. 767-692.
  18. I. A. Heisler, R. R. B. Correia, and S. L. S. Cunha “Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures,” J. Chem. Phys. 125, 184503 (2006).
    [CrossRef] [PubMed]
  19. W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
    [CrossRef]
  20. R. Norwood, Four Wave Mixing, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 693-765.
  21. B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513-526 (1971).
    [CrossRef]
  22. S. Kershaw, Two-Photon Absorption, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 515-654.
  23. M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the resonant eletronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
    [CrossRef] [PubMed]
  24. C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27-36 (1992).
    [CrossRef]
  25. W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
    [CrossRef]
  26. J. Van Beek, F. Kajzar, and A. C. Albrecht, “Resonant third-harmonic generation in all-trans β-Carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region,” J. Chem. Phys. 95, 6400 (1991).
    [CrossRef]
  27. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystrene thin films: Multiple reflection effects and the onset of a two-photon resonance,” J. Chem. Phys. 161, 299-311 (1992).
  28. F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
    [CrossRef] [PubMed]
  29. R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical materials,” Opt. Mater. 1, 185-194 (1992).
    [CrossRef]
  30. M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183-1185 (2000).
    [CrossRef]
  31. K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurements of the nonlinear index of silica-core and dispersion shifted fibers,” Opt. Lett. 19, 257-259 (1994).
    [CrossRef] [PubMed]
  32. R. H. Stolen and S. H. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448-1453 (1978).
    [CrossRef]
  33. R. Miller., “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
    [CrossRef]
  34. M. I. Bell, “Frequency dependence of Miller's rule for nonlinear susceptibilities,” Phys. Rev. B 6, 516521 (1972).
    [CrossRef]
  35. F. Kajzar, “Impact of dimensionality, conjugation length, scaling laws and electronic structure on nonlinear optical properties of conjugated polymers,” Nonlinear Opt. 5, 329-338 (1993).

2006 (1)

I. A. Heisler, R. R. B. Correia, and S. L. S. Cunha “Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures,” J. Chem. Phys. 125, 184503 (2006).
[CrossRef] [PubMed]

2005 (1)

G. Boudebs and S. Cherukulappurath, “Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system,” Opt. Commun. 250, 416-420 (2005).
[CrossRef]

2000 (4)

F. Kajzar and J. M. Nunzi, “Third order effects and applications,” in Functional Polymers and Polymeric Materials, T.Richardson, ed. (Wiley & Sons, 2000), pp. 327-363.

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

U. Gubbler and C. Bosshard, “Optical third-harmonic generation of fused silica in gas atmosphere: Absolute value of the third-order nonlinear optical susceptibility χ(3),” Phys. Rev. B 61, 10702-10710 (2000).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183-1185 (2000).
[CrossRef]

1998 (5)

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37, 546-550 (1998).
[CrossRef]

R. F. Shi and A. F. Garito, “Introduction: conventions and standards for nonlinear optical processes,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.G.Kuzyk and C.W.Dirk, eds. (Marcel Dekker, 1998).

E. W. Van Stryland and M. Sheik-Bahae, “Z-scan,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, Inc., 1998), pp. 767-692.

R. Norwood, Four Wave Mixing, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 693-765.

S. Kershaw, Two-Photon Absorption, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 515-654.

1995 (1)

A. Mito, K. Hagimoto, and C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Molecular Crystals and Liquid Crystals Science and Technology Section B: Nonlinear Optics, 13 (1-3), 3-18 (1995).

1994 (2)

K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurements of the nonlinear index of silica-core and dispersion shifted fibers,” Opt. Lett. 19, 257-259 (1994).
[CrossRef] [PubMed]

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

1993 (2)

F. Kajzar, “Impact of dimensionality, conjugation length, scaling laws and electronic structure on nonlinear optical properties of conjugated polymers,” Nonlinear Opt. 5, 329-338 (1993).

N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
[CrossRef]

1992 (3)

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical materials,” Opt. Mater. 1, 185-194 (1992).
[CrossRef]

B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystrene thin films: Multiple reflection effects and the onset of a two-photon resonance,” J. Chem. Phys. 161, 299-311 (1992).

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27-36 (1992).
[CrossRef]

1991 (2)

J. Van Beek, F. Kajzar, and A. C. Albrecht, “Resonant third-harmonic generation in all-trans β-Carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region,” J. Chem. Phys. 95, 6400 (1991).
[CrossRef]

D. M. Burland, C. Walsh, F. Kajzar, and C. Sentein, “Comparison of hyperpolarizabilities obtained with different experimental methods and theoretical techniques,” J. Opt. Soc. Am. B 8, 2269-2281 (1991).
[CrossRef]

1990 (3)

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

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the resonant eletronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

1988 (1)

G. A. Kenney-Wallace, S. Paone, and C. Kalpouzos, “Femtosecond laser spectroscopy and dynamics of solvation in liquids and electrolytes,” Faraday Discuss. Chem. Soc. 85, 185-198 (1988).
[CrossRef]

1987 (2)

W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
[CrossRef]

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
[CrossRef]

1985 (1)

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352-2363 (1985).
[CrossRef] [PubMed]

1983 (1)

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation,” J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

1982 (2)

1978 (1)

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

1972 (1)

M. I. Bell, “Frequency dependence of Miller's rule for nonlinear susceptibilities,” Phys. Rev. B 6, 516521 (1972).
[CrossRef]

1971 (1)

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513-526 (1971).
[CrossRef]

1964 (1)

R. Miller., “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
[CrossRef]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical materials,” Opt. Mater. 1, 185-194 (1992).
[CrossRef]

Albrecht, A. C.

B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystrene thin films: Multiple reflection effects and the onset of a two-photon resonance,” J. Chem. Phys. 161, 299-311 (1992).

J. Van Beek, F. Kajzar, and A. C. Albrecht, “Resonant third-harmonic generation in all-trans β-Carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region,” J. Chem. Phys. 95, 6400 (1991).
[CrossRef]

Bell, M. I.

M. I. Bell, “Frequency dependence of Miller's rule for nonlinear susceptibilities,” Phys. Rev. B 6, 516521 (1972).
[CrossRef]

Bosshard, C.

U. Gubbler and C. Bosshard, “Optical third-harmonic generation of fused silica in gas atmosphere: Absolute value of the third-order nonlinear optical susceptibility χ(3),” Phys. Rev. B 61, 10702-10710 (2000).
[CrossRef]

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

Boudebs, G.

G. Boudebs and S. Cherukulappurath, “Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system,” Opt. Commun. 250, 416-420 (2005).
[CrossRef]

Buchalter, B.

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation,” J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

B. Buchalter and G. R. Meredith, “Third-order optical susceptibility of glasses determined by third harmonic generation,” Appl. Opt. 21, 3221-3224 (1982).
[CrossRef] [PubMed]

Burland, D. M.

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical materials,” Opt. Mater. 1, 185-194 (1992).
[CrossRef]

Cheng, L.-T.

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27-36 (1992).
[CrossRef]

Cherukulappurath, S.

G. Boudebs and S. Cherukulappurath, “Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system,” Opt. Commun. 250, 416-420 (2005).
[CrossRef]

Correia, R. R. B.

I. A. Heisler, R. R. B. Correia, and S. L. S. Cunha “Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures,” J. Chem. Phys. 125, 184503 (2006).
[CrossRef] [PubMed]

Cunha, S. L. S.

I. A. Heisler, R. R. B. Correia, and S. L. S. Cunha “Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures,” J. Chem. Phys. 125, 184503 (2006).
[CrossRef] [PubMed]

Danieli, R.

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

Dirk, C. W.

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27-36 (1992).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the resonant eletronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

Garito, A. F.

R. F. Shi and A. F. Garito, “Introduction: conventions and standards for nonlinear optical processes,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.G.Kuzyk and C.W.Dirk, eds. (Marcel Dekker, 1998).

Gubbler, U.

U. Gubbler and C. Bosshard, “Optical third-harmonic generation of fused silica in gas atmosphere: Absolute value of the third-order nonlinear optical susceptibility χ(3),” Phys. Rev. B 61, 10702-10710 (2000).
[CrossRef]

Gubler, U.

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

Hagan, D.

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

Hagimoto, K.

A. Mito, K. Hagimoto, and C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Molecular Crystals and Liquid Crystals Science and Technology Section B: Nonlinear Optics, 13 (1-3), 3-18 (1995).

Halbout, J. M.

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765-767 (1982).
[CrossRef]

Hanzlik, C.

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation,” J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

Heisler, I. A.

I. A. Heisler, R. R. B. Correia, and S. L. S. Cunha “Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures,” J. Chem. Phys. 125, 184503 (2006).
[CrossRef] [PubMed]

Hellwarth, R. W.

N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
[CrossRef]

Kaatz, P.

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

Kajzar, F.

F. Kajzar and J. M. Nunzi, “Third order effects and applications,” in Functional Polymers and Polymeric Materials, T.Richardson, ed. (Wiley & Sons, 2000), pp. 327-363.

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

F. Kajzar, “Impact of dimensionality, conjugation length, scaling laws and electronic structure on nonlinear optical properties of conjugated polymers,” Nonlinear Opt. 5, 329-338 (1993).

B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystrene thin films: Multiple reflection effects and the onset of a two-photon resonance,” J. Chem. Phys. 161, 299-311 (1992).

J. Van Beek, F. Kajzar, and A. C. Albrecht, “Resonant third-harmonic generation in all-trans β-Carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region,” J. Chem. Phys. 95, 6400 (1991).
[CrossRef]

D. M. Burland, C. Walsh, F. Kajzar, and C. Sentein, “Comparison of hyperpolarizabilities obtained with different experimental methods and theoretical techniques,” J. Opt. Soc. Am. B 8, 2269-2281 (1991).
[CrossRef]

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352-2363 (1985).
[CrossRef] [PubMed]

Kalpouzos, C.

G. A. Kenney-Wallace, S. Paone, and C. Kalpouzos, “Femtosecond laser spectroscopy and dynamics of solvation in liquids and electrolytes,” Faraday Discuss. Chem. Soc. 85, 185-198 (1988).
[CrossRef]

W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
[CrossRef]

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
[CrossRef]

Kenney, G. A.

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
[CrossRef]

Kenney-Wallace, G. A.

G. A. Kenney-Wallace, S. Paone, and C. Kalpouzos, “Femtosecond laser spectroscopy and dynamics of solvation in liquids and electrolytes,” Faraday Discuss. Chem. Soc. 85, 185-198 (1988).
[CrossRef]

W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
[CrossRef]

Kershaw, S.

S. Kershaw, Two-Photon Absorption, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 515-654.

Kim, K. S.

Knize, R. J.

N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
[CrossRef]

Kuzyk, M. G.

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183-1185 (2000).
[CrossRef]

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27-36 (1992).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the resonant eletronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

Leclerc, M.

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

Lin, S. H.

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

Lotshaw, W. T.

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
[CrossRef]

W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
[CrossRef]

Mazerant, W.

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

McMorrow, D.

W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
[CrossRef]

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
[CrossRef]

Meier, U.

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

Meredith, G. R.

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation,” J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

B. Buchalter and G. R. Meredith, “Third-order optical susceptibility of glasses determined by third harmonic generation,” Appl. Opt. 21, 3221-3224 (1982).
[CrossRef] [PubMed]

Messier, J.

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352-2363 (1985).
[CrossRef] [PubMed]

Milam, D.

Miller., R.

R. Miller., “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
[CrossRef]

Mito, A.

A. Mito, K. Hagimoto, and C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Molecular Crystals and Liquid Crystals Science and Technology Section B: Nonlinear Optics, 13 (1-3), 3-18 (1995).

Neher, D.

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

Norwood, R.

R. Norwood, Four Wave Mixing, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 693-765.

Nunzi, J. M.

F. Kajzar and J. M. Nunzi, “Third order effects and applications,” in Functional Polymers and Polymeric Materials, T.Richardson, ed. (Wiley & Sons, 2000), pp. 327-363.

Orr, B. J.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513-526 (1971).
[CrossRef]

Paone, S.

G. A. Kenney-Wallace, S. Paone, and C. Kalpouzos, “Femtosecond laser spectroscopy and dynamics of solvation in liquids and electrolytes,” Faraday Discuss. Chem. Soc. 85, 185-198 (1988).
[CrossRef]

Partanen, J. P.

N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
[CrossRef]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical materials,” Opt. Mater. 1, 185-194 (1992).
[CrossRef]

Quoi, K. W.

Reed, W. A.

Rossini, S.

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

Said, A. A.

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

Sentein, C.

Sheik-Bahae, M.

E. W. Van Stryland and M. Sheik-Bahae, “Z-scan,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, Inc., 1998), pp. 767-692.

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

Shi, R. F.

R. F. Shi and A. F. Garito, “Introduction: conventions and standards for nonlinear optical processes,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.G.Kuzyk and C.W.Dirk, eds. (Marcel Dekker, 1998).

Stegeman, G. I.

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

Stolen, R. H.

Stryland, E. W.

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

Takahashi, C.

A. Mito, K. Hagimoto, and C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Molecular Crystals and Liquid Crystals Science and Technology Section B: Nonlinear Optics, 13 (1-3), 3-18 (1995).

Taliani, C.

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

Tang, C. L.

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765-767 (1982).
[CrossRef]

Tang, N.

N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
[CrossRef]

Torruellas, W. E.

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

Van Beek, B.

B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystrene thin films: Multiple reflection effects and the onset of a two-photon resonance,” J. Chem. Phys. 161, 299-311 (1992).

Van Beek, J.

J. Van Beek, F. Kajzar, and A. C. Albrecht, “Resonant third-harmonic generation in all-trans β-Carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region,” J. Chem. Phys. 95, 6400 (1991).
[CrossRef]

Van Stryland, E. W.

E. W. Van Stryland and M. Sheik-Bahae, “Z-scan,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, Inc., 1998), pp. 767-692.

Walsh, C.

Ward, J. F.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513-526 (1971).
[CrossRef]

Wei, T. H.

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

Zamboni, R.

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

Zanoni, R.

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

R. Miller., “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
[CrossRef]

J. M. Halbout and C. L. Tang, “Femtosecond interferometry for nonlinear optics,” Appl. Phys. Lett. 40, 765-767 (1982).
[CrossRef]

Chem. Phys. Lett. (2)

W. T. Lotshaw, D. McMorrow, C. Kalpouzos, and G. A. Kenney-Wallace, “Femtosecond dynamics of the optical Kerr effect in liquid nitrobenzene and chlorobenzene,” Chem. Phys. Lett. 136, 323-328 (1987).
[CrossRef]

W. E. Torruellas, D. Neher, R. Zanoni, G. I. Stegeman, F. Kajzar, and M. Leclerc, “Dispersion measurement of the third order nonlinear susceptibility of polythiophene thin films,” Chem. Phys. Lett. 175, 11 (1990).
[CrossRef]

Faraday Discuss. Chem. Soc. (1)

G. A. Kenney-Wallace, S. Paone, and C. Kalpouzos, “Femtosecond laser spectroscopy and dynamics of solvation in liquids and electrolytes,” Faraday Discuss. Chem. Soc. 85, 185-198 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Int. J. Quantum Chem. (1)

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27-36 (1992).
[CrossRef]

J. Chem. Phys. (4)

J. Van Beek, F. Kajzar, and A. C. Albrecht, “Resonant third-harmonic generation in all-trans β-Carotene: The vibronic origins of the third-order nonlinear susceptibility in the visible region,” J. Chem. Phys. 95, 6400 (1991).
[CrossRef]

B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystrene thin films: Multiple reflection effects and the onset of a two-photon resonance,” J. Chem. Phys. 161, 299-311 (1992).

I. A. Heisler, R. R. B. Correia, and S. L. S. Cunha “Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures,” J. Chem. Phys. 125, 184503 (2006).
[CrossRef] [PubMed]

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation,” J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

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

J. Phys. Chem. (1)

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91, 2028-2030 (1987).
[CrossRef]

Mol. Phys. (1)

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513-526 (1971).
[CrossRef]

Nonlinear Opt. (1)

F. Kajzar, “Impact of dimensionality, conjugation length, scaling laws and electronic structure on nonlinear optical properties of conjugated polymers,” Nonlinear Opt. 5, 329-338 (1993).

Opt. Commun. (1)

G. Boudebs and S. Cherukulappurath, “Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system,” Opt. Commun. 250, 416-420 (2005).
[CrossRef]

Opt. Lett. (2)

Opt. Mater. (1)

R. Adair, L. L. Chase, and S. A. Payne, “Dispersion of the nonlinear refractive index of optical materials,” Opt. Mater. 1, 185-194 (1992).
[CrossRef]

Phys. Rev. A (3)

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352-2363 (1985).
[CrossRef] [PubMed]

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

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the resonant eletronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

Phys. Rev. B (4)

M. I. Bell, “Frequency dependence of Miller's rule for nonlinear susceptibilities,” Phys. Rev. B 6, 516521 (1972).
[CrossRef]

N. Tang, J. P. Partanen, R. W. Hellwarth, and R. J. Knize, “Third-order optical nonlinearity of C60, C70, and CS2 in benzene at 1.06 μm,” Phys. Rev. B 48, 8404-8408 (1993).
[CrossRef]

C. Bosshard, U. Gubler, P. Kaatz, W. Mazerant, and U. Meier, “Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities,” Phys. Rev. B 61, 10688-10701 (2000).
[CrossRef]

U. Gubbler and C. Bosshard, “Optical third-harmonic generation of fused silica in gas atmosphere: Absolute value of the third-order nonlinear optical susceptibility χ(3),” Phys. Rev. B 61, 10702-10710 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

F. Kajzar, C. Taliani, S. Rossini, R. Danieli, and R. Zamboni, “Dispersion of THG optical susceptibility in C60 thin films,” Phys. Rev. Lett. 73, 1617 (1994).
[CrossRef] [PubMed]

Other (6)

S. Kershaw, Two-Photon Absorption, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 515-654.

F. Kajzar and J. M. Nunzi, “Third order effects and applications,” in Functional Polymers and Polymeric Materials, T.Richardson, ed. (Wiley & Sons, 2000), pp. 327-363.

E. W. Van Stryland and M. Sheik-Bahae, “Z-scan,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, Inc., 1998), pp. 767-692.

R. F. Shi and A. F. Garito, “Introduction: conventions and standards for nonlinear optical processes,” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.G.Kuzyk and C.W.Dirk, eds. (Marcel Dekker, 1998).

R. Norwood, Four Wave Mixing, in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M.Kuzyk and C.Dirk, eds. (Marcel Dekker, 1998), pp. 693-765.

A. Mito, K. Hagimoto, and C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Molecular Crystals and Liquid Crystals Science and Technology Section B: Nonlinear Optics, 13 (1-3), 3-18 (1995).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup for z-scan (nonlinear imaging technique). The sample is translated through the focal point. The labels refer to lenses ( L 1 L 3 ) ; mirrors ( M 1 , M 2 ) ; beam splitters ( BS 1 , BS 2 ) ; neutral filters (tf).

Fig. 2
Fig. 2

Closed aperture z-scan normalized transmittance in the picosecond regime for 1 mm thick C S 2 (the incident peak intensity is 2.4 GW cm 2 ).

Fig. 3
Fig. 3

Energetic diagrams for (a) a THG generation and (b) OKE processes. Dashed lines show virtual states whereas solid lines show the excited states of unperturbed system.

Fig. 4
Fig. 4

Three-level-model calculation of χ THG ( 3 ) ( 3 ω ; ω , ω , ω ) susceptibilities dispersion for (a) one-photon level lying at 0.17 μ m and the two-photon level at 0.1 μ m (case of silica). (b) For benzene the one-photon level is taken at 0.27 μ m ; the two-photon level is at 0.15 μ m . The damping term in both cases is assumed to be 5000 cm 1 for both solvents.

Fig. 5
Fig. 5

Three-level-model calculation of real, imaginary parts and modulus of χ Kerr ( 3 ) ( ω ; ω , ω , ω ) susceptibilitity dispersion for (a) one-photon level lying at 0.18 μ m and the two-photon level at 0.11 μ m (case of silica). (b) For benzene the one-photon level is taken at 0.27 μ m while the two-photon level is at 0.15 μ m . The damping term in both cases is assumed to be 5000 cm 1 for both compounds.

Fig. 6
Fig. 6

Comparison of the dispersion of the modulus of χ THG ( 3 ) ( 3 ω ; ω , ω , ω ) and χ Kerr ( 3 ) ( ω ; ω , ω , ω ) susceptibilities for (a) silica and for (b) benzene calculated using the previous parameters. At 1064 nm χ OKE ( 3 ) ( 1064 ) χ THG ( 3 ) ( 1064 ) = 0.86 for silica and 0.54 for benzene.

Tables (3)

Tables Icon

Table 1 Comparison of THG and Kerr Susceptibilities

Tables Icon

Table 2 Dependence of the Ratio χ ( 3 ) OKE ( 1064 ) χ ( 3 ) THG ( 1064 ) on Damping Factor Γ

Tables Icon

Table 3 Dispersion of χ ( 3 ) Suceptibility and Nonlinear Index of Refraction between 355 nm and 1907 nm as Obtained from Miller’s Rule [23]. a

Equations (17)

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

E ( r , t ) = 1 2 [ E ( r ) e i ( k r ω t ) + c.c. ] ,
P ( r , t ) = 1 2 [ P ( r ) e i ( k r ω t ) + c.c. ] .
P I THG ( 3 ω ) = 1 4 χ I J K L ( 3 ) ( 3 ω ; ω , ω , ω ) E J E K E L ,
P I OKE ( ω ) = 3 4 χ I J K L ( 3 ) ( ω ; ω , ω , ω ) E J E K E L ,
n 2 = Δ n I ,
n 2 ( ω ) = 3 χ Kerr ( 3 ) ( ω ; ω , ω , ω ) 4 ε 0 c n 0 2 .
χ rot ( 3 ) = ( 0.92 ± 0.2 ) χ Kerr ( 3 ) C S 2 ,
χ rot ( 3 ) = ( 0.89 ± 0.11 ) χ Kerr ( 3 ) chlorobenzene .
χ ( 3 ) ( ω σ ; ω , ω , ω ) = N F 3 [ l m n μ g l μ l m μ m n μ n g ( 1 ( Ω lg ω σ ) ( Ω m g ω 1 ω 2 ) ( Ω n g ω 1 ) + 1 ( Ω lg * + ω 3 ) ( Ω m g ω 1 ω 2 ) ( Ω n g ω 1 ) + 1 ( Ω lg * + ω 1 ) ( Ω m g * + ω 1 + ω 2 ) ( Ω n g ω 3 ) + 1 ( Ω lg * + ω 1 ) ( Ω m g * + ω 1 + ω 2 ) ( Ω n g * + ω σ ) ) m n μ n g 2 μ m g 2 ( 1 ( Ω m g ω σ ) ( Ω m g ω 3 ) ( Ω n g ω 1 ) + 1 ( Ω m g ω 3 ) ( Ω n g * + ω 2 ) ( Ω n g ω 1 ) + 1 ( Ω m g * + ω σ ) ( Ω m g * + ω 3 ) ( Ω n g * + ω 1 ) + 1 ( Ω m g * + ω 3 ) ( Ω n g * + ω 1 ) ( Ω n g ω 2 ) ) ] ,
χ ( 3 ) ( 3 ω ; ω , ω , ω ) = N F μ n g 2 3 [ μ n m 2 μ n g 2 { 1 ( Ω n g 3 ω ) ( Ω n g 2 ω ) ( Ω n g ω ) + 1 ( Ω n g * + ω ) ( Ω n g 2 ω ) ( Ω n g ω ) + 1 ( Ω n g * + ω ) ( Ω n g + 2 ω ) ( Ω n g ω ) + 1 ( Ω n g * + ω ) ( Ω m g * + 2 ω ) ( Ω n g * + 3 ω ) } { 1 ( Ω m g 3 ω ) ( Ω m g ω ) ( Ω n g ω ) + 1 ( Ω m g ω ) ( Ω n g * + ω ) ( Ω n g ω ) + 1 ( Ω m g * + 3 ω ) ( Ω m g * + ω ) ( Ω n g + ω ) + 1 ( Ω m g * + ω ) ( Ω n g * + ω ) ( Ω n g ω ) } ] .
χ ( 3 ) ( ω ; ω , ω , ω ) = N F μ n g 4 3 3 [ μ n m 2 μ n g 2 { 1 ( Ω n g ω ) 2 ( Ω n g 2 ω ) + 1 ( Ω n g * + ω ) ( Ω n g 2 ω ) ( Ω n g ω ) + 1 ( Ω n g * + ω ) ( Ω m g * + 2 ω ) ( Ω n g + ω ) + 1 ( Ω m g * + ω ) ( Ω n g * + ω ) 2 + 1 Ω m g * ( Ω n g ω ) 2 + 1 Ω m g * ( Ω n g * + ω ) ( Ω n g ω ) + 1 Ω m g * ( Ω n g * + ω ) ( Ω n g + ω ) + 1 Ω m g * ( Ω n g * + ω ) 2 + 1 Ω m g * ( Ω n g ω ) 2 + 1 Ω m g * ( Ω n g * + ω ) ( Ω n g + ω ) + 1 Ω m g * ( Ω n g * + ω ) 2 + 1 Ω m g * ( Ω n g * 2 ω 2 ) } { 1 ( Ω m g + ω ) ( Ω n g ω ) 2 1 ( Ω m g + ω ) ( Ω n g * + ω ) ( Ω n g ω ) + 1 ( Ω m g * + ω ) ( Ω m g * ω ) ( Ω n g * + ω ) + 1 ( Ω m g * ω ) ( Ω n g * + ω ) ( Ω n g * ω ) + 1 ( Ω n g ω ) 2 ( Ω m g ω ) + 1 ( Ω m g ω ) ( Ω m g * ω ) ( Ω n g ω ) + 1 ( Ω m g ω ) ( Ω n g * ω 2 ) + 1 ( Ω m g ω ) ( Ω n g * + ω ) ( Ω n g + ω ) + 1 ( Ω m g * + ω ) 2 ( Ω n g * + ω ) + 1 ( Ω m g * + ω ) ( Ω n g * + ω ) ( Ω n g + ω ) + 1 ( Ω m g * + ω ) 2 ( Ω n g * ω ) + 1 ( Ω m g * + ω ) ( Ω n g * + ω ) ( Ω n g ω ) } ] ,
μ n m = { E 1 E [ μ n g 2 X 2 + μ n g 2 ] } 1 2 ,
E = ω n g ω m g .
d χ THG ( 3 ) d λ > d χ Kerr ( 3 ) d λ > 1 .
χ ( 3 ) ( 355 ) χ ( 3 ) ( 1907 ) [ χ ( 1 ) ( 355 ) χ ( 1 ) ( 1907 ) ] 4 ,
benzene : χ ( 3 ) Kerr χ ( 3 ) THG = 0.53 ,
silica : χ ( 3 ) Kerr χ ( 3 ) THG = 0.76 ,

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