Abstract

We present nonlinear refraction results for liquids methanol and acetic acid obtained with the Z-scan technique and 28 femtosecond (fs) 800 nm laser pulses. In contrast to the positive lensing effect obtained previously with picosecond and nanosecond laser pulses, a negative lensing effect is observed. The associated mechanism features the third-order polarization arising from the nonlinear response of the molecular skeletal motion that is driven into resonance through its electrostatic coupling to the valence electron cloud distorted by the fs laser field.

© 2007 Optical Society of America

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  1. E. Jakeman, “Photon correlation,” p90ff, and H. Z. Cummins, “Light beating spectroscopy,” p232ff, in “Photon correlation and light Beating spectroscopy”, edited by H. Z. Cummins and E. R. Pike, (Plenum Press, New York, 1974).
  2. G. D. Goodno, G. Dadusc, and R. J. D. Miller, “Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics,” J. Opt. Soc. Am. B 15, 1791–1794 (1998).
    [CrossRef]
  3. J. K. Wahlstrand, R. Merlin, X. Li, S. T. Cundiff, and O. E. Martinez, “Impulsive stimulated Raman scattering: comparison between phase-sensitive and spectrally filtered techniques,” Opt. Lett. 30, 926–928 (2005).
    [CrossRef] [PubMed]
  4. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
    [CrossRef]
  5. A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E.W. Van Stryland, “Determination of bound and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
    [CrossRef]
  6. R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
    [CrossRef]
  7. T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
    [CrossRef]
  8. M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133–136 (1999).
    [CrossRef]
  9. A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13, 7976–7981 (2005).
    [CrossRef] [PubMed]
  10. K. S. Bindra and A. K. Kar, “Role of femtosecond pulses in distinguishing third- and fifth-order nonlinearity for semiconductor-doped glasses,” Appl. Phys. Lett. 79, 3761–3763 (2001).
    [CrossRef]
  11. T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
    [CrossRef]
  12. K. H. Lee, W. R. Cho, J. H. Park, J. S. Kim, S. H. Park, and U. Kim, “Measurement of free-carrier nonlinearities in ZnSe based on the Z-scan technique with a nanosecond laser,” Opt. Lett. 19, 1116–1118 (1994).
    [PubMed]
  13. H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
    [CrossRef]
  14. M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
    [CrossRef]
  15. B. M. Ladanyi and Y. Q. Liang, “Interaction-induced contributions to polarizability anisotropy relaxation in polar liquids,” J. Chem. Phys. 103, 6325–6332 (1995).
    [CrossRef]
  16. S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).
  17. See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
    [CrossRef]
  18. M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
    [CrossRef]
  19. Converted from n2 = 5.7×10-12 (esu) as given by R.W. Hellwarth, “Effect of molecular redistribution on the nonlinear refractive index of liquids,” Phy. Rev. 152, 156–165 (1966).
    [CrossRef]
  20. See, for example, Robert W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), Table 4.1.1.
  21. T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
    [CrossRef]
  22. One of our recent results on ps Z-scan, to be published in a forthcoming paper.
  23. Y. X. Yan, E. B. Gamble, and K. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
    [CrossRef]
  24. See, for example, P. N. Butcher, Nonlinear Optical Phenomena, p21, Chap. 4, Bulletin 200, Engineering Experiment Station, Ohio State University, Columbus, Ohio, 43210, USA (1965) and P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, Cambridge, 1990), §5.3.2.
  25. See, for example, R. W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), §9.3. ; also C. Flytzanis, Theory of Nonlinear Optical Susceptibilities, §II.D, in Quantum Electronics: A Treatise, Vol 1, Nonlinear Optics, Part A, 2, (Academic Press, Inc., New York, 1975).
  26. J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
    [CrossRef]
  27. R. W. Boyd, Nonlinear optics , (Academic Press, San Diego, 1992), §4.4 & §9.5.
  28. See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
    [CrossRef]
  29. T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
    [CrossRef]
  30. See, for example, F. T. Ulaby, Fundamentals of Applied Electromagnetics, media edition, (Prentice Hall, Upper Saddle River, New Jersey, 2004), Chap. 8.

2006 (1)

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

2005 (2)

2004 (1)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

2001 (1)

K. S. Bindra and A. K. Kar, “Role of femtosecond pulses in distinguishing third- and fifth-order nonlinearity for semiconductor-doped glasses,” Appl. Phys. Lett. 79, 3761–3763 (2001).
[CrossRef]

2000 (1)

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

1999 (3)

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133–136 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

1998 (1)

1997 (1)

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

1996 (1)

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

1995 (2)

B. M. Ladanyi and Y. Q. Liang, “Interaction-induced contributions to polarizability anisotropy relaxation in polar liquids,” J. Chem. Phys. 103, 6325–6332 (1995).
[CrossRef]

See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
[CrossRef]

1994 (1)

1992 (2)

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E.W. Van Stryland, “Determination of bound and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

1991 (1)

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

1985 (1)

Y. X. Yan, E. B. Gamble, and K. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

1971 (1)

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

1966 (1)

Converted from n2 = 5.7×10-12 (esu) as given by R.W. Hellwarth, “Effect of molecular redistribution on the nonlinear refractive index of liquids,” Phy. Rev. 152, 156–165 (1966).
[CrossRef]

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Berstein, E.

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

Bindra, K. S.

K. S. Bindra and A. K. Kar, “Role of femtosecond pulses in distinguishing third- and fifth-order nonlinearity for semiconductor-doped glasses,” Appl. Phys. Lett. 79, 3761–3763 (2001).
[CrossRef]

Bloembergen, N.

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

Boyd, R. W.

See, for example, R. W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), §9.3. ; also C. Flytzanis, Theory of Nonlinear Optical Susceptibilities, §II.D, in Quantum Electronics: A Treatise, Vol 1, Nonlinear Optics, Part A, 2, (Academic Press, Inc., New York, 1975).

R. W. Boyd, Nonlinear optics , (Academic Press, San Diego, 1992), §4.4 & §9.5.

Boyd, Robert W.

See, for example, Robert W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), Table 4.1.1.

Butcher, P. N.

See, for example, P. N. Butcher, Nonlinear Optical Phenomena, p21, Chap. 4, Bulletin 200, Engineering Experiment Station, Ohio State University, Columbus, Ohio, 43210, USA (1965) and P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, Cambridge, 1990), §5.3.2.

See, for example, P. N. Butcher, Nonlinear Optical Phenomena, p21, Chap. 4, Bulletin 200, Engineering Experiment Station, Ohio State University, Columbus, Ohio, 43210, USA (1965) and P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, Cambridge, 1990), §5.3.2.

Chang, S.

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Chen, C. W.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

Chen, M. J.

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

Chia, C.

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Chiang, H. P.

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

Cho, M.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

Cho, W. R.

Cotter, D.

See, for example, P. N. Butcher, Nonlinear Optical Phenomena, p21, Chap. 4, Bulletin 200, Engineering Experiment Station, Ohio State University, Columbus, Ohio, 43210, USA (1965) and P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, Cambridge, 1990), §5.3.2.

Coulter, D. R.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

Cummins, H. Z.

E. Jakeman, “Photon correlation,” p90ff, and H. Z. Cummins, “Light beating spectroscopy,” p232ff, in “Photon correlation and light Beating spectroscopy”, edited by H. Z. Cummins and E. R. Pike, (Plenum Press, New York, 1974).

Cundiff, S. T.

Dadusc, G.

Demirdoven, N.

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

Falconieri, M.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133–136 (1999).
[CrossRef]

Fecko, C. J.

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

Fleming, G. R.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

Flytzanis, C.

See, for example, R. W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), §9.3. ; also C. Flytzanis, Theory of Nonlinear Optical Susceptibilities, §II.D, in Quantum Electronics: A Treatise, Vol 1, Nonlinear Optics, Part A, 2, (Academic Press, Inc., New York, 1975).

Gamble, E. B.

Y. X. Yan, E. B. Gamble, and K. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Ganeev, R. A.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Gnoli, A.

Golonzka, O.

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

Goodno, G. D.

Haba, O.

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

Hagan, D. J.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E.W. Van Stryland, “Determination of bound and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

Hellwarth, R.W.

Converted from n2 = 5.7×10-12 (esu) as given by R.W. Hellwarth, “Effect of molecular redistribution on the nonlinear refractive index of liquids,” Phy. Rev. 152, 156–165 (1966).
[CrossRef]

Hsu, C. C.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Huang, T.-H.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
[CrossRef]

Inoue, J.

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

Ishizawa, N.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Jakeman, E.

E. Jakeman, “Photon correlation,” p90ff, and H. Z. Cummins, “Light beating spectroscopy,” p232ff, in “Photon correlation and light Beating spectroscopy”, edited by H. Z. Cummins and E. R. Pike, (Plenum Press, New York, 1974).

Ji, W.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Kar, A. K.

K. S. Bindra and A. K. Kar, “Role of femtosecond pulses in distinguishing third- and fifth-order nonlinearity for semiconductor-doped glasses,” Appl. Phys. Lett. 79, 3761–3763 (2001).
[CrossRef]

Kawaguchi, H.

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

Kawazoe, T.

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

Khalil, M.

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

Kim, J. S.

Kim, U.

Kuo, C. T.

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Kuroda, H.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Ladanyi, B. M.

B. M. Ladanyi and Y. Q. Liang, “Interaction-induced contributions to polarizability anisotropy relaxation in polar liquids,” J. Chem. Phys. 103, 6325–6332 (1995).
[CrossRef]

Lax, M.

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

Lee, K. H.

Li, H.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Li, X.

Liang, Y. Q.

B. M. Ladanyi and Y. Q. Liang, “Interaction-induced contributions to polarizability anisotropy relaxation in polar liquids,” J. Chem. Phys. 103, 6325–6332 (1995).
[CrossRef]

Lin, H. D.

See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
[CrossRef]

Lin, J. Y.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

Lin, S. H.

See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
[CrossRef]

Lin, Y. D.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

Liu, R. T.

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Maradudin, A. A.

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

Martinez, O. E.

Merlin, R.

Miller, R. J. D.

Nelson, D. F.

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

Nelson, K.

Y. X. Yan, E. B. Gamble, and K. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Park, J. H.

Park, S. H.

Perry, J. W.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

Razzari, L.

Righini, M.

Rosenthal, S. J.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

Ryasnyansky, A. I.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[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 and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

Sakakibara, S.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Salvetti, G.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133–136 (1999).
[CrossRef]

Scherer, N. F.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

Schmidt, M. E.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

Sence, M.

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

Sence, M. J.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

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 and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

Soileau, M. J.

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

Suzuki, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Tang, J.-L.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

Tokmakoff, A.

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

Treatise, A

See, for example, R. W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), §9.3. ; also C. Flytzanis, Theory of Nonlinear Optical Susceptibilities, §II.D, in Quantum Electronics: A Treatise, Vol 1, Nonlinear Optics, Part A, 2, (Academic Press, Inc., New York, 1975).

Tsai, C. P.

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Tse, W. S.

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Turu, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

Ueda, M.

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

Ulaby, F. T.

See, for example, F. T. Ulaby, Fundamentals of Applied Electromagnetics, media edition, (Prentice Hall, Upper Saddle River, New Jersey, 2004), Chap. 8.

Van Stryland, E. W.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

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 and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

Wahlstrand, J. K.

Wang, J.

Wei, T. H.

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E.W. Van Stryland, “Determination of bound and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405–414 (1992).
[CrossRef]

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

Xie, X.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

Yan, Y. X.

Y. X. Yan, E. B. Gamble, and K. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Yen, S. M.

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

Young, J.

Zhang, X.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Zhou, F.

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

Appl. Phys. B (4)

H. Li, F. Zhou, X. Zhang, and W. Ji, “Picosecond Z-scan study of bound electronic Kerr effect in LiNbO3 crystal associated with two-photon absorption,” Appl. Phys. B 64, 659–662 (1997).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992), and T. H. Wei, Ph.D. dissertation, University of North Texas, Denton, TX, USA (1992).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78, 433–438 (2004).
[CrossRef]

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133–136 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

K. S. Bindra and A. K. Kar, “Role of femtosecond pulses in distinguishing third- and fifth-order nonlinearity for semiconductor-doped glasses,” Appl. Phys. Lett. 79, 3761–3763 (2001).
[CrossRef]

See, for example, T. H. Wei, T.-H. Huang, H. D. Lin, and S. H. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2268 (1995).
[CrossRef]

Chem. Phys. Lett. (1)

M. Khalil, O. Golonzka, N. Demirdoven, C. J. Fecko, and A. Tokmakoff, “Polarization-selective femtosecond Raman spectroscopy of isotropic and anisotropic vibrational dynamics in liquids,” Chem. Phys. Lett. 321, 231–237 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26760 (1990).
[CrossRef]

IEEE Journal of Selected Topics in Quantum Electronics (1)

T.-H. Huang, C. C. Hsu, T. H. Wei, S. Chang, S. M. Yen, C. P. Tsai, R. T. Liu, C. T. Kuo, W. S. Tse, and C. Chia, “The transient optical Kerr effect of simple liquids studied with an ultrafast laser with variable pulse width,” IEEE Journal of Selected Topics in Quantum Electronics 2, 756–768 (1996).
[CrossRef]

J. Chem. Phys. (2)

B. M. Ladanyi and Y. Q. Liang, “Interaction-induced contributions to polarizability anisotropy relaxation in polar liquids,” J. Chem. Phys. 103, 6325–6332 (1995).
[CrossRef]

Y. X. Yan, E. B. Gamble, and K. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

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

Mol. Cryst. Liq. Cryst. (1)

M. J. Soileau, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, M. Sence, and E.W. Van Stryland, “Nonlinear optical characterization of organic materials,” Mol. Cryst. Liq. Cryst. 207, 97 (1991).
[CrossRef]

Molecular Physics (1)

T.-H. Huang, C. C. Hsu, T. H. Wei, M. J. Chen, S. Chang, W. S. Tse, H. P. Chiang, and C. T. Kuo, “The ultrafast dynamics of liquid CBrCl3 studied with optical Kerr effect and Raman scattering,” Molecular Physics 96, 389–396 (1999).
[CrossRef]

Opt. Commun. (2)

J.-L. Tang, C. W. Chen, J. Y. Lin, Y. D. Lin, C. C. Hsu, T. H. Wei, and T.-H. Huang, “Ultrafast motion of liquids C2H4Cl2 and C2H4Br2 studied with a femtosecond laser,” Opt. Commun. 266, 669–675 (2006).
[CrossRef]

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phy. Rev. (1)

Converted from n2 = 5.7×10-12 (esu) as given by R.W. Hellwarth, “Effect of molecular redistribution on the nonlinear refractive index of liquids,” Phy. Rev. 152, 156–165 (1966).
[CrossRef]

Phys. Rev. B (1)

See, for example, 1) M. Lax and D. F. Nelson, “Linear and nonlinear electrodynamics in elastic anisotropic dielectrics theory of acoustically induced optical harmonic generation,” Phys. Rev. B 4, 3694–3731, 1971; 2) A. A. Maradudin and E. Berstein, Proc. Int. Conf. Semi cond. Moscow p. 1009, 1968; and 3) N. Bloembergen, Nonlinear Optics, (W. A. Benjamin, Inc., New York, 1965), §4.3 and §4.4.
[CrossRef]

Other (8)

See, for example, Robert W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), Table 4.1.1.

S. J. Rosenthal, N. F. Scherer, M. Cho, X. Xie, M. E. Schmidt, and G. R. Fleming, in Ultrafast Phenomena, edited by J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer, Berlin), Vol. 8, p. 616 (1993).

R. W. Boyd, Nonlinear optics , (Academic Press, San Diego, 1992), §4.4 & §9.5.

See, for example, F. T. Ulaby, Fundamentals of Applied Electromagnetics, media edition, (Prentice Hall, Upper Saddle River, New Jersey, 2004), Chap. 8.

E. Jakeman, “Photon correlation,” p90ff, and H. Z. Cummins, “Light beating spectroscopy,” p232ff, in “Photon correlation and light Beating spectroscopy”, edited by H. Z. Cummins and E. R. Pike, (Plenum Press, New York, 1974).

See, for example, P. N. Butcher, Nonlinear Optical Phenomena, p21, Chap. 4, Bulletin 200, Engineering Experiment Station, Ohio State University, Columbus, Ohio, 43210, USA (1965) and P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge University Press, Cambridge, 1990), §5.3.2.

See, for example, R. W. Boyd, Nonlinear Optics, (Academic Press, New York, 1992), §9.3. ; also C. Flytzanis, Theory of Nonlinear Optical Susceptibilities, §II.D, in Quantum Electronics: A Treatise, Vol 1, Nonlinear Optics, Part A, 2, (Academic Press, Inc., New York, 1975).

One of our recent results on ps Z-scan, to be published in a forthcoming paper.

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Figures (6)

Fig. 1.
Fig. 1.

The optical layout of a Z-scan experiment. BS stands for beam splitter; S, sample; D1 and D2, photo-detectors; AC, autocorrelator; the knife-edges before D2, removable iris (1.4 mm in radius) and 40 cm from z=0.

Fig. 2.
Fig. 2.

Close-aperture Z-scan curves for liquids methanol (top frame) and acetic acid (bottom frame). Middle frame: a typical open-aperture Z-scan curve of liquids methanol and acetic acid recorded with a 28 fs 800 nm laser. Solid lines are simulated.

Fig. 3.
Fig. 3.

This schematics illustrates negative lensing caused by the insertion of the sample (shaded) in a tightly focused Gaussian laser beam (solid curves). D2 represents the photo-detector. With sample insertion the incident Gaussian beam profile is distorted to the one shown with the broken curves.

Fig. 4.
Fig. 4.

The change of the valley amplitude, relative to that of the peak amplitude, with the fs laser power.

Fig. 5.
Fig. 5.

This schematic shows the focusing, in free space, of the enormous light rays contained in a fs laser beam to a beam waist of about 26 microns.

Fig. 6.
Fig. 6.

Resonance structure of the effective susceptibility. Adapted from Boyd, Fig. 9.3.3.

Equations (34)

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n = n 1 + n 2 I r t ,
r t dz ' kn = k [ n 1 + n 2 I r t ] ,
ħ Ω = ħ ω 1 ħ ω 2 ,
E ( r , t ) = E 0,1 e i ( r k 1 ω 1 t ) + E 0,2 e i ( r k 2 ω 2 t ) + c . c .
R r t = R ( Ω ) e i ( r k Ω Ω t ) + c . c . ,
R ̈ + γ R ̇ + Ω 0 2 R = F ( t ) M .
F r t = dW dR = 1 2 ( α R ) o E 2 r t
= ( α R ) o ( E 0,1 E 0,2 * e i ( r k Ω Ω t ) + c . c . ) ,
R ( Ω ) = ( α R ) o E 0,1 E 0,2 * M 1 Ω o 2 Ω 2 i γΩ .
α ( t ) = α o + ( α R ) o R ( t ) + ,
P r t = N μ ind r t ,
μ ind r t = { α o + ( α R ) o R r t } E r t .
P ( 3 ) r t = N ( α R ) o R r t E r t ,
P ( 3 ) r t = N ( α R ) o [ R ( Ω ) e i ( r k Ω Ω t ) + c . c . ] [ E 0,1 e i ( r k 1 ω 1 t ) + E 0,2 e i ( r k 2 ω 2 t ) + c . c . ] .
P ( 3 ) r t = N ( α R ) o [ R ( Ω ) e i ( r k Ω Ω t ) + R * ( Ω ) e i ( r k Ω Ω t ) ] E 0,1 e i ( r k 1 ω 1 t )
= N ( α R ) o [ R ( Ω ) e i r ( k Ω + k 1 ) E 0,1 e i ( Ω + ω 1 ) t + R * ( Ω ) E 0,1 e i r k 2 e i ω 2 t ] .
P ( 3 ) r t = [ N ( α R ) o R * ( Ω ) E 0,1 e i r k 2 ] e i ω 2 t .
P r t = P r ω e iωt .
P ( 3 ) r ω 2 = N ( α R ) o R * ( Ω ) E 0,1 e i r k 2 .
P ( 3 ) r ω 2 = N M ( α R ) o 2 E 0,1 2 E 0,2 1 Ω o 2 Ω 2 + i γΩ e i r k 2
= N M ( α R ) o 2 1 Ω o 2 Ω 2 + i γΩ I ω 1 E 0,2 e i r k 2
= χ eff ( ω 2 ) I ω 1 E 0,2 e i r k 2
χ eff ( ω 2 ) χ ABCD ( 3 ) ( ω 2 = ω 1 + ω 2 ω 1 )
= N M ( α R ) o 2 1 Ω o 2 ( ω 1 ω 2 ) 2 + ( ω 1 ω 2 )
Ω o ω 1 ω 2
χ eff ( ω 2 ) N M ( α R ) o 2 1 [ Ω o ( ω 1 ω 2 ) ] 2 Ω o + Ω o
N 2 M Ω o ( α R ) o 2 1 [ ω 2 ( ω 1 Ω o ) ] + 2 ,
n 2 = r = 1 + χ
= 1 + 1 o E ( P ( 0 ) + P ( 1 ) + P ( 2 ) + P ( 3 ) + ) .
n 2 ( ω ) = 1 o E { χ ( 1 ) + χ eff ( ω ) I ω 1 } E 0 e izk
= 1 + { a 1 ω o 2 ω 2 + i γ ω + bI ω 1 1 [ ω ( ω 1 Ω o ) ] + i γ 2 } ,
n ( ω ) 1 + 1 2 a 1 ω o 2 ω 2 + i γ ω + 1 2 bI ω 1 1 [ ω ( ω 1 Ω o ) ] + i γ 2 .
n r ( ω ) 1 + 1 2 a ω o ω ( ω o ω ) 2 + ( γ 2 ) 2 + 1 2 bI ω 1 ω ( ω 1 Ω o ) [ ω ( ω 1 Ω o ) ] 2 + ( γ 2 ) 2 .
n r ( ω ) 1 + 1 2 a ω o ω ( ω o ω ) 2 + ( γ 2 ) 2 1 2 bI ω 1 ( ω 1 Ω o ) ω [ ω ( ω 1 Ω o ) ] 2 + ( γ 2 ) 2 .

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