Abstract

We describe improvements to a previously reported hyper-Rayleigh scattering technique [J. Opt. Soc. Am. B 15, 289 (1998) ], for measuring all rotational invariants of the first hyperpolarizability tensor. The full hyper-Rayleigh scattering tensor is expressed in terms of its rotationally invariant components leading to a figures of merit corresponding to each of the rotationally invariant tensors. With elliptically polarized incident light, the polarization state and the intensity of the harmonic light are measured at a scattering angle of 45°. A new analytical fitting method is applied to the signal for two polarization measurements to yield the invariants. We have measured several chiral and nonchiral chromophores to determine the hyperpolarizability tensor with which to analyze the measurement accuracy, to reveal structure property relationships, and to assess the applicability of the chromophores as nonlinear optical materials. Results for a series of chiral chromophores and for Crystal Violet are presented.

© 2000 Optical Society of America

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  1. J. Zyss, ed., Molecular Nonlinear Optics (Academic, Orlando, Fla., 1994).
  2. G. Lindsay and K. Singer, eds., Polymers for Second-Order Nonlinear Optics, Vol. 601 of ACS Symposium Series (American Chemical Society, Washington, D.C., 1995).
    [CrossRef]
  3. D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977–1979 (1962).
    [CrossRef]
  4. K. D. Singer, S. F. Hubbard, A. Schober, L. M. Hayden, and K. Johnson, “Second harmonic generation” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M. G. Kuzyk and C. W. Dirk, eds. (Marcel Dekker, New York, 1998), pp. 311–513.
  5. J. Zyss and I. Ledoux, “Nonlinear optics in multipolar media: theory and experiment,” Chem. Rev. 94, 77–105 (1994).
    [CrossRef]
  6. S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15, 257–288 (1998).
    [CrossRef]
  7. M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
    [CrossRef]
  8. T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
    [CrossRef]
  9. S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D’Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill, “Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules,” J. Opt. Soc. Am. B 15, 289–301 (1998).
    [CrossRef]
  10. M. Kozierowski, “Electric-dipole differential hyper-Rayleigh and hyper-Raman scattering of elliptically polarized light,” Phys. Rev. A 31, 509–510 (1985); G. Wagniere, “Theoretical investigation of Kleinman symmetry in molecules,” Appl. Phys. B 41, 169–172 (1986).
    [CrossRef] [PubMed]
  11. R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
    [CrossRef]
  12. V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
    [CrossRef]
  13. I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
    [CrossRef]
  14. P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
    [CrossRef]
  15. T. W. Chui and K. Y. Wong, “Study of hyper-Rayleigh scattering and two-photon absorption induced fluorescence from Crystal Violet,” J. Chem. Phys. 109, 1391–1396 (1998).
    [CrossRef]
  16. S. J. Lalama and A. F. Garito, “Origin of the nonlinear second-order optical susceptibilities of organic systems,” Phys. Rev. A 20, 1179–1194 (1979).
    [CrossRef]
  17. G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
    [CrossRef] [PubMed]
  18. X-ray crystal structures were determined by C. Barnes of the University of Missouri–Columbia, Columbia, Missouri.
  19. J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).
  20. S. Stadler, R. Dietrich, G. Bourhill, and Ch. Bräuchle, “Long-wavelength first hyperpolarizability measurements by hyper-Rayleigh scattering,” Opt. Lett. 21, 251–253 (1996).
    [CrossRef] [PubMed]
  21. H. B. Lueck, J. L. McHale, and W. D. Edwards, “Symmetry-breaking solvent effects on the electronic structure and spectra of a series of triphenylmethane dyes,” J. Am. Chem. Soc. 114, 2342–2348 (1992).
    [CrossRef]
  22. Y. Maruyama, M. Ishikawa, and H. Satozono, “Femtosecond isomerization of Crystal Violet in alcohols,” J. Am. Chem. Soc. 118, 6257–6263 (1996).
    [CrossRef]

2000 (1)

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

1998 (3)

1996 (4)

S. Stadler, R. Dietrich, G. Bourhill, and Ch. Bräuchle, “Long-wavelength first hyperpolarizability measurements by hyper-Rayleigh scattering,” Opt. Lett. 21, 251–253 (1996).
[CrossRef] [PubMed]

Y. Maruyama, M. Ishikawa, and H. Satozono, “Femtosecond isomerization of Crystal Violet in alcohols,” J. Am. Chem. Soc. 118, 6257–6263 (1996).
[CrossRef]

I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
[CrossRef]

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

1994 (2)

J. Zyss and I. Ledoux, “Nonlinear optics in multipolar media: theory and experiment,” Chem. Rev. 94, 77–105 (1994).
[CrossRef]

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

1993 (2)

G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
[CrossRef] [PubMed]

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).

1992 (3)

H. B. Lueck, J. L. McHale, and W. D. Edwards, “Symmetry-breaking solvent effects on the electronic structure and spectra of a series of triphenylmethane dyes,” J. Am. Chem. Soc. 114, 2342–2348 (1992).
[CrossRef]

M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
[CrossRef]

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

1979 (1)

S. J. Lalama and A. F. Garito, “Origin of the nonlinear second-order optical susceptibilities of organic systems,” Phys. Rev. A 20, 1179–1194 (1979).
[CrossRef]

1962 (1)

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

Bölger, B.

G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
[CrossRef] [PubMed]

Bourhill, G.

Brasselet, S.

Bräuchle, Ch.

Cahill, P. A.

Chien, L. C.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D’Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill, “Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules,” J. Opt. Soc. Am. B 15, 289–301 (1998).
[CrossRef]

Chui, T. W.

T. W. Chui and K. Y. Wong, “Study of hyper-Rayleigh scattering and two-photon absorption induced fluorescence from Crystal Violet,” J. Chem. Phys. 109, 1391–1396 (1998).
[CrossRef]

Clays, K.

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

D’Sidocky, N.

Denning, R. G.

I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
[CrossRef]

Detzer, N.

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

Dhenaut, C.

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).

Dietrich, R.

Edwards, W. D.

H. B. Lueck, J. L. McHale, and W. D. Edwards, “Symmetry-breaking solvent effects on the electronic structure and spectra of a series of triphenylmethane dyes,” J. Am. Chem. Soc. 114, 2342–2348 (1992).
[CrossRef]

Garito, A. F.

S. J. Lalama and A. F. Garito, “Origin of the nonlinear second-order optical susceptibilities of organic systems,” Phys. Rev. A 20, 1179–1194 (1979).
[CrossRef]

Glania, C.

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

Heesink, G. J. T.

G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
[CrossRef] [PubMed]

Henderson, C. C.

Hubbard, S. F.

Hudson, C.

Ishikawa, M.

Y. Maruyama, M. Ishikawa, and H. Satozono, “Femtosecond isomerization of Crystal Violet in alcohols,” J. Am. Chem. Soc. 118, 6257–6263 (1996).
[CrossRef]

Joffre, M.

M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
[CrossRef]

Kaatz, P.

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

Kleinman, D. A.

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

Krämer, P.

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

Laidlaw, W. M.

I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
[CrossRef]

Lalama, S. J.

S. J. Lalama and A. F. Garito, “Origin of the nonlinear second-order optical susceptibilities of organic systems,” Phys. Rev. A 20, 1179–1194 (1979).
[CrossRef]

Lebus, S.

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

Ledoux, I.

J. Zyss and I. Ledoux, “Nonlinear optics in multipolar media: theory and experiment,” Chem. Rev. 94, 77–105 (1994).
[CrossRef]

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).

Lueck, H. B.

H. B. Lueck, J. L. McHale, and W. D. Edwards, “Symmetry-breaking solvent effects on the electronic structure and spectra of a series of triphenylmethane dyes,” J. Am. Chem. Soc. 114, 2342–2348 (1992).
[CrossRef]

Maruyama, Y.

Y. Maruyama, M. Ishikawa, and H. Satozono, “Femtosecond isomerization of Crystal Violet in alcohols,” J. Am. Chem. Soc. 118, 6257–6263 (1996).
[CrossRef]

McHale, J. L.

H. B. Lueck, J. L. McHale, and W. D. Edwards, “Symmetry-breaking solvent effects on the electronic structure and spectra of a series of triphenylmethane dyes,” J. Am. Chem. Soc. 114, 2342–2348 (1992).
[CrossRef]

Morrison, I. D.

I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
[CrossRef]

Ostroverkhov, V.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

Ostroverkhova, O.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

Persoons, A.

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

Petschek, R. G.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D’Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill, “Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules,” J. Opt. Soc. Am. B 15, 289–301 (1998).
[CrossRef]

Reinhoudt, D.

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

Ruiter, A. G. T.

G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
[CrossRef] [PubMed]

Samyn, C.

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

Satozono, H.

Y. Maruyama, M. Ishikawa, and H. Satozono, “Femtosecond isomerization of Crystal Violet in alcohols,” J. Am. Chem. Soc. 118, 6257–6263 (1996).
[CrossRef]

Shelton, D. P.

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

Silbey, R.

M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
[CrossRef]

Singer, K. D.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D’Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill, “Measurements of Kleinman-disallowed hyperpolarizability in conjugated chiral molecules,” J. Opt. Soc. Am. B 15, 289–301 (1998).
[CrossRef]

Stadler, S.

Stammers, M. A.

I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
[CrossRef]

Sukhomlinova, L.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

Twieg, R. J.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

Van, T. C.

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).

van Hulst, N. F.

G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
[CrossRef] [PubMed]

Verbiest, T.

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

Wang, S.-X.

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

Wolff, J.

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

Wong, K. Y.

T. W. Chui and K. Y. Wong, “Study of hyper-Rayleigh scattering and two-photon absorption induced fluorescence from Crystal Violet,” J. Chem. Phys. 109, 1391–1396 (1998).
[CrossRef]

Wortmann, R.

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

Yaron, D.

M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
[CrossRef]

Zyss, J.

S. Brasselet and J. Zyss, “Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media,” J. Opt. Soc. Am. B 15, 257–288 (1998).
[CrossRef]

J. Zyss and I. Ledoux, “Nonlinear optics in multipolar media: theory and experiment,” Chem. Rev. 94, 77–105 (1994).
[CrossRef]

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).

M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
[CrossRef]

Chem. Phys. (2)

R. Wortmann, P. Krämer, C. Glania, S. Lebus, and N. Detzer, “Deviations from Kleinman symmetry of the second-order polarizability tensor in molecules with low-lying perpendicular electronic bands,” Chem. Phys. 173, 99–108 (1992).
[CrossRef]

V. Ostroverkhov, O. Ostroverkhova, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media,” Chem. Phys. 257, 263–274 (2000).
[CrossRef]

Chem. Rev. (1)

J. Zyss and I. Ledoux, “Nonlinear optics in multipolar media: theory and experiment,” Chem. Rev. 94, 77–105 (1994).
[CrossRef]

J. Am. Chem. Soc. (3)

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigations of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
[CrossRef]

H. B. Lueck, J. L. McHale, and W. D. Edwards, “Symmetry-breaking solvent effects on the electronic structure and spectra of a series of triphenylmethane dyes,” J. Am. Chem. Soc. 114, 2342–2348 (1992).
[CrossRef]

Y. Maruyama, M. Ishikawa, and H. Satozono, “Femtosecond isomerization of Crystal Violet in alcohols,” J. Am. Chem. Soc. 118, 6257–6263 (1996).
[CrossRef]

J. Chem. Phys. (4)

M. Joffre, D. Yaron, R. Silbey, and J. Zyss, “Second-order optical nonlinearity in octopolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
[CrossRef]

J. Zyss, T. C. Van, C. Dhenaut, and I. Ledoux, “Harmonic Rayleigh scattering from nonlinear octupolar molecular media: the case of Crystal Violet,” J. Chem. Phys. 177, 281–296 (1993).

P. Kaatz and D. P. Shelton, “Polarized hyper-Rayleigh light scattering measurements of nonlinear optical chromophores,” J. Chem. Phys. 105, 3918–3929 (1996).
[CrossRef]

T. W. Chui and K. Y. Wong, “Study of hyper-Rayleigh scattering and two-photon absorption induced fluorescence from Crystal Violet,” J. Chem. Phys. 109, 1391–1396 (1998).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. (1)

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

Phys. Rev. A (1)

S. J. Lalama and A. F. Garito, “Origin of the nonlinear second-order optical susceptibilities of organic systems,” Phys. Rev. A 20, 1179–1194 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

G. J. T. Heesink, A. G. T. Ruiter, N. F. van Hulst, and B. Bölger, “Determination of hyperpolarizability tensor components by hyper-Rayleigh scattering,” Phys. Rev. Lett. 71, 999–1002 (1993).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

I. D. Morrison, R. G. Denning, W. M. Laidlaw, and M. A. Stammers, “Measurement of first hyperpolarizabilities by hyper-Rayleigh scattering,” Rev. Sci. Instrum. 67, 1445–1453 (1996).
[CrossRef]

Other (5)

X-ray crystal structures were determined by C. Barnes of the University of Missouri–Columbia, Columbia, Missouri.

K. D. Singer, S. F. Hubbard, A. Schober, L. M. Hayden, and K. Johnson, “Second harmonic generation” in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, M. G. Kuzyk and C. W. Dirk, eds. (Marcel Dekker, New York, 1998), pp. 311–513.

J. Zyss, ed., Molecular Nonlinear Optics (Academic, Orlando, Fla., 1994).

G. Lindsay and K. Singer, eds., Polymers for Second-Order Nonlinear Optics, Vol. 601 of ACS Symposium Series (American Chemical Society, Washington, D.C., 1995).
[CrossRef]

M. Kozierowski, “Electric-dipole differential hyper-Rayleigh and hyper-Raman scattering of elliptically polarized light,” Phys. Rev. A 31, 509–510 (1985); G. Wagniere, “Theoretical investigation of Kleinman symmetry in molecules,” Appl. Phys. B 41, 169–172 (1986).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

HRS experiment with arbitrary ellipticity of incoming and outgoing polarizations.

Fig. 2
Fig. 2

Experimental setup for 45° hyper-Rayleigh scattering experiment: P, input polarizer; BS, beam splitter; L’s, lenses; BC, Berek compensator; ASL, aspherical lens; λ/4, quarter-wave plate; A, output polarizer, PMT’s photomultiplier tubes; F’s, filters.

Fig. 3
Fig. 3

Spectral content of the light scattered from a solution of Crystal Violet in acetone (grating, 300 grooves/mm; inset, 1200 grooves/mm).

Fig. 4
Fig. 4

Molecular structures of the studied molecules (with first-excited-state absorption maximum wavelengths). 1–8 are compound numbers; CV is Crystal Violet.

Fig. 5
Fig. 5

Polar plots of typical data points with fitted curves for (a) pNA, (b) Q-BNH, and (c) Crystal Violet.

Tables (4)

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Table 1 Irreducible Tensors Δ Used in the Decomposition (with Normalization Coefficients) a

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Table 2 Rotation Invariants with Respect to Kleinman-Allowed Vector Part

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Table 3 Figures of Merit of the Four Irreducible Components of β Tensor (esu)

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Table 4 Rotational Invariants of CV in Three Solvents

Equations (59)

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IILω3=GNBIJKLMN2 (ω3; ω1, ω2)EJω1EKω2(EMω1)*(ENω2)*,
BILK,LMN2βIJKβLMN*=L Δ(L)IJK,LMNβ2(L).
Ps= [1+(12)+(13)+(23)+(123)+(132)],
Pm= [2+2(23)-(12)-(13)-(123)-(132)],
Pm= [2-2(23)+(12)+(13)-(123)-(132)].
ijklmn=13 Δ(L)ijk,lmnΔ(L)ijk,lmn=δLL.
I2ω(e^i, e^o)(Iω)2L β2(L)Δ(L)IJK,LMN×(e^o*)I(e^i)J(e^i)K(e^o)L(e^i*)M(e^i*)N,
Iω=|Eω|2,Eω=e^i Eω.
I2ω(Ωi, Ωo)=GN(Iω)2L βL2ΔL(Ωi, Ωo),
Δ1ss=c1ss¹/ [AA*+4BB*+4 Re(BA*C)],
Δ1mm=c1mm/ [AA*+BB*-2 Re(BA*C)],
Δ1sm+=c1sm+/ [AA*-2BB*+Re(BA*C)],
Δ1sm-=c1sm-(4i/3)[Im(BA*C)],
Δ2mm=c2mm/ [AA*+BB*-2 Re(BA*C)]+c2mm (1-CC*),
Δ3ss=c3ss (1+2CC*)+c3ss¹/ [AA*+4BB*+4 Re(BA*C)],
e^i=cos(γi-αi)(xˆ sin γi+yˆ cos γi)+i sin(γi-αi)(yˆ sin γi-xˆ cos γi),
e^o=cos(γo-αo)×[(xˆ cos θ+zˆ sin θ)sin γo+yˆ cos γo]+i sin(γo-αo)×[ yˆ sin γo-(xˆ cos θ+zˆ sin θ)cos γo].
e^i=exp(iψ)2 [xˆ(i-cos 2γ)+yˆ sin 2γ],
e^o=azˆ+b[cos κ(xˆ cos ϕ+yˆ sin ϕ)+i sin κ(-xˆ sin ϕ+yˆ cos ϕ)].
AA*=½ (1+cos 4γ),
BB*=(b2/4)(2+cos 2κ cos 2ϕ+cos 4γ cos 2κ cos 2ϕ-sin 4γ cos 2κ sin 2ϕ-2 sin 2γ sin 2κ),
CC*=(b2/4)(2+cos 2κ cos 2ϕ+cos 4γ cos 2κ cos 2ϕ-sin 4γ cos 2κ sin 2ϕ+2 sin 2γ sin 2κ),
BA*C=(b2/4){1+cos 2κ cos 2ϕ+cos 4γ×(1+cos 2κ cos 2ϕ)-sin 4γ cos 2κ sin 2ϕ-(i/2)×[(cos 2γ-cos 6γ)cos 2κ cos 2ϕ+(sin 2γ+sin 6γ)cos 2κ sin 2ϕ]}.
 I2ω(γ; β, κ, ϕ)=GN(Iω)2
×n=0,2,4,6[an(β2, κ, ϕ)×cos nγ+bn(β2, κ, ϕ)sin nγ].
{a, b}n(βL2)=LA(κ, ϕ)n,LβL2 ,n=17
χ2=n(qn-An,LβL2)2.
χ2=ML,LβL2βL2-2ULβL2+const.,
ML,L=An,LAn,L,UL=qnAn,L.
(βL2) χ2=2ML,LβL2-2UL=0  βL2=(M-1)L,LUL.
βi2βj2c=Mi,m-1UmMj,l-1Ulc=qkqkcMi,m-1Ak,mMj,l-1Ak,l.
qkqkc=Δq2δkkβi2βj2c=Mi,m-1Mm,lMj,l-1.
β1ss2(1D)=35 βzzz2,β3ss2(1D)=257 βzzz2.
β3ss2β1ss2=2210.436.
LIJKLMNΔ(L)IJK,LMNΔ(L)IJK,LMNβ2(L)
=L δLLβ2(L)=β2(L),
Δ(L)IJK,LMNβIJKβLMN*=Δ(L)IJK,LMNβIJKβLMN*=Δ(L)IJK,LMNβIJKβLMN*.
β2(L)=Δ(L)IJK,LMNβIJKβLMN*.
β1ss2=11539i|βiii|2+ij[4|βiij|2+|βijj|2+Re(6βiiiβijj*+12βiijβjjj*+4βiijβjii*)]+ijkRe(4βiijβjkk*+βijjβikk*+4βiijβkkj*),
β1mm2=133ij[|βiij|2+|βijj|2-2 Re(βiijβjii*)]+ijkRe(βiijβkkj*+βijjβikk*-2βiijβjkk*),
β1sm+2=-13215ij[2|βiij|2-|βijj|2+Re(3βiijβjjj*-3βiiiβijj*-βiijβjii*)]+ijkRe(2βiijβkkj*-βiijβikk*-βiijβjkk*),
β1sm-2=-i 215ijIm(βiiiβijj*+βiijβjjj*+βiijβjii*)+ijkIm(βiijβjkk*),
β2mm2=135ij[|βiij|2+|βijj|2+2 Re(βiijβjii*)]+ijk[2|βijk|2+Re(2βiijβjkk*-βijjβikk*-βiijβkkj*-2βijkβjki*)],
β3ss2=11576i|βiii|2+ij[16|βiij|2+4|βijj|2+Re(16βiijβjii*-6βiiiβijj*-12βiijβjjj*)]+ijk[5|βijk|2+Re(10βijkβjki*-4βiijβjkk*-βijjβikk*-4βiijβkkj*)].
β1ss2(C2v)=1153 |3βzzz+2(βxxz+βyyz)+βzxx+βzyy|2,
β1mm2(C2v)=133 |βxxz+βyyz-βzxx-βzyy|2,
β2mm2(C2v)=135 |βxxz-βyyz-βzxx+βzyy|2,
β3ss2(C2v)=2157 {3|βzzz|2+8(|βxxz|2+|βyyz|2)+2(|βzxx|2+|βzyy|2)+Re[8(βxxzβzxx*+βyyzβzyy*)-6(βxxzβzzz*+βyyzβzzz*)-3(βzzzβzxx*+βzzzβzyy*)-2(βxxzβzyy*+βyyzβzxx*)-4βxxzβyyz*-βzxxβzyy*]}.
β1ss2(C3)=1153 |3βzzz+2βxxz+2βzxx|2,
β1mm2(C3)=433 |βxxz-βzxx|2,
β2mm2(C3)=45 |βxyz|2,
β1ss2(C3)=2157 [30(|βxxx|2+|βyyy|2)+3|βzzz|2+12|βxxz|2+Re(12βxxzβzxx*-12βxxzβzzz*-6βzzzβzxx*)].
β1ss2(D3)=β1mm2(D3)=0,
β2mm2(D3)=45 |βxyz|2,
β3ss2(D3)=47 |βxxx|2,
e^i=e^i*=yˆ,e^o=e^o*=yˆ,zˆ,
I=19 c1ssβ1ss2+49 c1mmβ1mm2+49 c1sm+β1sm+2+49 c2mm+23 c2mmβ2mm2+13 c3ss+19 c3ssβ3ss2
=1153 β1ss2+133 β1mm2+13215 β1sm+2+135 β2mm2+4157 β3ss2,
I=c1ssβ1ss2+(c3ss+c3ss)β3ss2=35 β1ss2+257 β3ss2.

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