Abstract

An oriented gas model for the second-order nonlinear optical response for optical second-harmonic generation in axially aligned nonlinear optical chromophores in chiral media is presented. Design criteria for the alignment of chromophores possessing Kleinman-disallowed traceless symmetric second-rank tensor hyperpolarizabilities β resulting in large nonlinear optical susceptibilities χ(2) are enumerated. These chromophores could be oriented in high-density, highly ordered structures due to the absence of dipolar interactions resulting in exceptionally large χ(2) values. The alignment of chromophores that have C2v or Dn (n>2) symmetry in two chiral nonpolar symmetry groups for the medium, D and D2, are considered. Criteria for response optimization and several physical examples are described. Additionally, certain nonpolar symmetry groups for the medium, of which the most easily realizable is probably D2, also admit Kleinman-allowed octupolar susceptibilities for which the optimum chromophore alignment is discussed.

© 2001 Optical Society of America

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References

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  1. J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev. 138, 1599–1606 (1965).
    [CrossRef]
  2. V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
    [CrossRef]
  3. 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 (2000).
    [CrossRef]
  4. 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]
  5. V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
    [CrossRef]
  6. V. Ostroverkhov, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
    [CrossRef]
  7. M. Joffre, D. Yaron, R. J. Silbey, and J. Zyss, “Second order nonlinearity in octupolar aromatic systems,” J. Chem. Phys. 97, 5607–5615 (1992).
    [CrossRef]
  8. T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigation of the hyperpolarizability in organic molecules from dipolar to octopolar systems,” J. Am. Chem. Soc. 116, 9320–9323 (1994).
    [CrossRef]
  9. S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
    [CrossRef]
  10. M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
    [CrossRef]

2001 (1)

V. Ostroverkhov, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
[CrossRef]

2000 (3)

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[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 (2000).
[CrossRef]

M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
[CrossRef]

1999 (1)

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

1998 (2)

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]

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

1994 (1)

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

1992 (1)

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

1965 (1)

J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev. 138, 1599–1606 (1965).
[CrossRef]

Blaster, D.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Boese, R.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Brasselet, S.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Cahill, P. A.

Carrell, H. L.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Cheng, H.

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

Chien, L. C.

Clays, K.

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

D’Sidocky, N.

Desiraju, G. R.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev. 138, 1599–1606 (1965).
[CrossRef]

Henderson, C. C.

Hubbard, S. F.

Hudson, C.

Joffre, M.

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

Katz, A. K.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Kauranen, M.

M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
[CrossRef]

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

Ma, L.

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

Musick, K.

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

Nangia, A.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Ostroverkhov, V.

V. Ostroverkhov, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
[CrossRef]

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[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 (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 (2000).
[CrossRef]

Persoons, A.

M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
[CrossRef]

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigation 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, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
[CrossRef]

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[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 (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]

Pu, L.

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

Reinhoudt, D.

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

Samyn, C.

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

Silbey, R. J.

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

Singer, K. D.

V. Ostroverkhov, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
[CrossRef]

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[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 (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]

Sukhomlinova, L.

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[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 (2000).
[CrossRef]

Thalladi, V. R.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Twieg, R. J.

V. Ostroverkhov, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
[CrossRef]

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[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 (2000).
[CrossRef]

Van Elshocht, S.

M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
[CrossRef]

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

Verbiest, T.

M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
[CrossRef]

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

T. Verbiest, K. Clays, C. Samyn, J. Wolff, D. Reinhoudt, and A. Persoons, “Investigation 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 (2000).
[CrossRef]

V. Ostroverkhov, R. G. Petschek, K. D. Singer, L. Sukhomlinova, R. J. Twieg, S.-X. Wang, and L. C. Chien, “Measurements of the hyperpolarizability tensor by means of hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 17, 1531–1542 (2000).
[CrossRef]

Weiss, H.-C.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

Wolff, J.

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

Yaron, D.

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

Zyss, J.

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

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

Chem. Phys. (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 (2000).
[CrossRef]

Chem. Phys. Lett. (2)

V. Ostroverkhov, R. G. Petschek, K. D. Singer, and R. J. Twieg, “Lambda-shaped chromophores for chiral nonlinear optical materials,” Chem. Phys. Lett. 340, 109–115 (2001).
[CrossRef]

S. Van Elshocht, T. Verbiest, M. Kauranen, L. Ma, H. Cheng, K. Musick, L. Pu, and A. Persoons, “Chiral 1, 1′-binaphthyl-based helical polymers as nonlinear optical materials,” Chem. Phys. Lett. 309, 315–320 (1999).
[CrossRef]

J. Am. Chem. Soc. (2)

V. R. Thalladi, S. Brasselet, H.-C. Weiss, D. Blaster, A. K. Katz, H. L. Carrell, R. Boese, J. Zyss, A. Nangia, and G. R. Desiraju, “Crystal engineering of some 2, 4, 6-triaryloxy-1, 3, 5-triazines: octupolar nonlinear materials,” J. Am. Chem. Soc. 120, 2563–2577 (1998).
[CrossRef]

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

J. Chem. Phys. (2)

M. Kauranen, S. Van Elshocht, T. Verbiest, and A. Persoons, “Tensor analysis of the second-order nonlinear optical susceptibility of chiral anisotropic thin films,” J. Chem. Phys. 112, 1497–1502 (2000).
[CrossRef]

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

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

Phys. Rev. (1)

J. A. Giordmaine, “Nonlinear optical properties of liquids,” Phys. Rev. 138, 1599–1606 (1965).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Euler angles for transformation between the molecular and bulk reference frames; (b) coordinate system for a Λ-shaped molecule.

Fig. 2
Fig. 2

Alignment examples for Λ-shaped molecules in a uniaxial macroscopic NLO system of D symmetry: (a) linearly stretched polymer chain and chromophores twisted by angle ψ; (b) a helical polymer—the twist of the polymers is defined by the helix pitch.

Fig. 3
Fig. 3

Alignment in biaxial D2 symmetry: (a) Λ-shaped molecules—twofold axes of the bulk are defined by the polymer stretch direction and the director of the nematic side-chain moieties; (b) nonpolar alignment of the one-dimensional chromophores utilizes the octupolar component of β.

Fig. 4
Fig. 4

Alignment of threefold propellerlike chromophores in a bulk of D symmetry.

Equations (24)

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

βijk=βijk(3s)+βijk(2m)+βijk(1s)+βijk(1m).
χIJKβijkIJK=βijk(3s)IJK+βijk(2m)IJK+βijk(1m)IJK+βijk(1s)IJKχIJK(3s)+χIJK(2m)+χIJK(1m)+χIJK(1s).
χ˜(2m)=χXYZ-1000-10002,
χ˜D(2m)=16(2χ˜ZZ-χ˜XX-χ˜YY)=16N2RZiRZj-RXiRXj-RYiRYjβ˜ij(2m).
β˜C2v(2m)=0Δβ/20Δβ/200000,Δβ=βzxx-βxxz.
χ˜(2m)(C2vD)
=16NΔβ2RZxRZy-RXxRXy-RYxRYy
=16NΔβ2(Zˆ·xˆ)(Zˆ·yˆ)-(Xˆ·xˆ)(Xˆ.yˆ)-(Yˆ·xˆ)(Yˆ·yˆ)=14NΔβsin2(θ)sin(2ψ).
χ˜s=χ˜XYZ(3s)=χ˜YZX(3s)==13(χXYZ+χYZX+χZXY),
χ˜(2m)=χYZX-χZXY000χZXY-χXYZ000χXYZ-χYZX.
χ˜(2m)=χ˜u-1000-10002+χ˜b-100010000,
χ˜u=χXYZ-χYZX2,χ˜b=2χZXY-χXYZ-χYZX2.
χ˜b=12NRYiRYj-RXiRXjβ˜ij(2m).
χ˜b=12NΔβRYxRYy-RXxRXy=12NΔβ(Yˆ·xˆ)(Yˆ·yˆ)-(Xˆ·xˆ)(Xˆ·yˆ)=116NΔβ4 cos(θ)cos(2ψ)sin(2ϕ)+[3+cos(2θ)]sin(2ψ)cos(2ϕ).
χ˜b(θ=0)=14NΔβsin[2(ψ+ϕ)],
χ˜b(θ=π)=14NΔβsin[2(ψ-ϕ)].
χ˜s=χ˜XYZ(3s)=RXiRYjRZkβ˜ijk(3s).
β˜zzz(3s)=15(2βzzz-2βxxz-βzxx),
β˜zxx(3s)=β˜xzx(3s)=β˜xxz(3s)=115(8βxxz+4βzxx-3βzzz),
β˜zyy(3s)=β˜yzy(3s)=β˜zyy(3s)=-115(3βzzz+2βxxz+βzxx),
χ˜s=N15βzzz(2RXzRYzRZz-RXzRYxRZx-RXxRYzRZx-RXxRYxRZz-RXzRYyRZy-RXyRYzRZy-RXyRYyRZz)+115(2βxxz+βzxx)(4RXzRYxRZx+4RXxRYzRZx+4RXxRYxRZz-RXzRYyRZy-RXyRYzRZy-RXyRYyRZz-3RXzRYzRZz),
χ˜s=N-12βzzz cos(θ)sin2(θ)sin(2ϕ)+148(2βxxz+βzxx)×[8 cos(2θ)cos(2ϕ)sin(2ψ)+3 cos(3θ)cos(2ψ)sin(2ϕ)+5 cos(θ)cos(2ψ)sin(2ϕ)+3 cos(θ)sin(2ϕ)-3 cos(3θ)sin(2ϕ)].
β˜D3(2m)=βxyz-1000-10002.
χ˜(D3D)=χXYZ=16N2RZiRZj-RXiRXj-RYiRYjβ˜ijD3=12Nβxyz2RZzRZz-RXzRXz-RYzRYz=14Nβxyz1+3 cos(2θ).

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