Abstract

Liquid crystals and polymer glasses can be formed into orientationally ordered materials by raising the temperature of the material to a temperature at which molecular motion is greatly enhanced, applying an external aligning field, and then cooling with the field applied. The resulting material exhibits second-order nonlinear-optical effects. In this paper, the relationship between the molecular hyperpolarizability and the macroscopic susceptibility is presented. The susceptibility is seen to depend on the microscopic order parameters commonly associated with liquid crystals and is discussed in the limits of one-dimensional molecules and poled polymer glasses. Agreement is found between the theory and second-harmonic-generation measurements of polymer glasses. Results of electro-optic measurements are compared with second-harmonic-generation measurements that suggest that the electro-optic effect is mostly electronic in origin.

© 1987 Optical Society of America

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References

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  1. A. F. Garito and K. D. Singer, Laser Focus 18(2), 59 (1982).
  2. J. Zyss, J. Molec. Electron. 1, 25 (1985).
  3. D. J. Williams, ed., Nonlinear Optical Properties of Organic and Polymeric Materials, ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).
    [Crossref]
  4. D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1987).
  5. J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
    [Crossref]
  6. K. Y. Wong and A. F. Garito, Phys. Rev. A 34, 5051 (1986).
    [Crossref] [PubMed]
  7. Y.-Z. Xie and Z.-C. Ou-Yang, Commun. Theor. Phys. 6, 1 (1986).
  8. I. C. Khoo and Y. R. Shen, Opt. Eng. 24, 579 (1985).
  9. N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
    [Crossref]
  10. S. D. Durbin and Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
    [Crossref]
  11. S. K. Saha and G. K. Wong, Appl. Phys. Lett. 34, 423 (1979).
    [Crossref]
  12. S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
    [Crossref]
  13. S. J. Gu, S. K. Saha, and G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
    [Crossref]
  14. Z.-C. Ou-Yang and Y.-Z. Xie, Phys. Rev. A 32, 1189 (1985).
    [Crossref]
  15. G. R. Meredith, J. G. Vandusen, and D. J. Williams, in Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).
  16. K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
    [Crossref]
  17. H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
    [Crossref]
  18. E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979).
    [Crossref]
  19. See, for example, J. F. Nye, Physical Properties of Crystals (Clarendon, London, 1957).
  20. C. W. Dirk (AT&T Bell Laboratories, Murray Hill, New Jersey 0794) and R. Twieg (personal communication).
  21. S. Kielich, IEEE J. Quantum Electron. QE-5, 562 (1969).
    [Crossref]
  22. S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, London, 1977).
  23. W. Maier and A. Saupe, Z. Naturforsch. 13a, 564 (1958); Z. Naturforsch. 14a, 882 (1959); Z. Naturforsch. 15a, 287 (1960).
  24. S. J. Lalama and A. F. Garito, Phys. Rev. A 20, 1179 (1979).
    [Crossref]
  25. K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981), and references therein.
    [Crossref]
  26. A. Saupe, in Liquid Crystals, G. H. Brown, G. J. Dienes, and M. M. Labes, eds. (Gordon and Breach, New York, 1966).
  27. See, for example, I. P. Kaminow, An Introduction to Electro-Optic Devices (Academic, New York, 1974).
  28. J. L. Oudar and D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
    [Crossref]
  29. D. A. Kleinman, Phys. Rev. 126, 1977 (1962).
    [Crossref]
  30. J. F. Ward and P. A. Franken, Phys. Rev. 133, A183 (1964).
    [Crossref]
  31. K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).
  32. C. C. Teng and A. F. Garito, Phys. Rev. B 28, 6766 (1983).
    [Crossref]
  33. C. W. Dirk, H. E. Katz, K. D. Singer, and J. E. Sohn, submitted to J. Chem. Phys.
  34. M. G. Kuzyk, J. E. Sohn, S. J. Lalama, and K. D. Singer, to be submitted to J. Opt. Soc. Am. B.
  35. M. Sigelle and R. Hierle, J. Appl. Phys. 52, 4199 (1981).
    [Crossref]
  36. G. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970), pp. 173–183.
  37. S. J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
    [Crossref]

1986 (4)

K. Y. Wong and A. F. Garito, Phys. Rev. A 34, 5051 (1986).
[Crossref] [PubMed]

Y.-Z. Xie and Z.-C. Ou-Yang, Commun. Theor. Phys. 6, 1 (1986).

K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

1985 (3)

Z.-C. Ou-Yang and Y.-Z. Xie, Phys. Rev. A 32, 1189 (1985).
[Crossref]

I. C. Khoo and Y. R. Shen, Opt. Eng. 24, 579 (1985).

J. Zyss, J. Molec. Electron. 1, 25 (1985).

1984 (1)

S. D. Durbin and Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
[Crossref]

1983 (1)

C. C. Teng and A. F. Garito, Phys. Rev. B 28, 6766 (1983).
[Crossref]

1982 (2)

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

A. F. Garito and K. D. Singer, Laser Focus 18(2), 59 (1982).

1981 (4)

S. J. Gu, S. K. Saha, and G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
[Crossref]

N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
[Crossref]

M. Sigelle and R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[Crossref]

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981), and references therein.
[Crossref]

1979 (3)

S. K. Saha and G. K. Wong, Appl. Phys. Lett. 34, 423 (1979).
[Crossref]

S. J. Lalama and A. F. Garito, Phys. Rev. A 20, 1179 (1979).
[Crossref]

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979).
[Crossref]

1977 (2)

S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
[Crossref]

J. L. Oudar and D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
[Crossref]

1969 (1)

S. Kielich, IEEE J. Quantum Electron. QE-5, 562 (1969).
[Crossref]

1965 (1)

S. J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
[Crossref]

1964 (1)

J. F. Ward and P. A. Franken, Phys. Rev. 133, A183 (1964).
[Crossref]

1962 (1)

D. A. Kleinman, Phys. Rev. 126, 1977 (1962).
[Crossref]

1958 (1)

W. Maier and A. Saupe, Z. Naturforsch. 13a, 564 (1958); Z. Naturforsch. 14a, 882 (1959); Z. Naturforsch. 15a, 287 (1960).

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970), pp. 173–183.

Baur, G.

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, London, 1977).

Chemla, D. S.

J. L. Oudar and D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
[Crossref]

Clark, N. A.

S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
[Crossref]

Cyvin, S. J.

S. J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
[Crossref]

Decius, J. C.

S. J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
[Crossref]

Dirk, C. W.

C. W. Dirk, H. E. Katz, K. D. Singer, and J. E. Sohn, submitted to J. Chem. Phys.

C. W. Dirk (AT&T Bell Laboratories, Murray Hill, New Jersey 0794) and R. Twieg (personal communication).

Durbin, S. D.

S. D. Durbin and Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
[Crossref]

Franken, P. A.

J. F. Ward and P. A. Franken, Phys. Rev. 133, A183 (1964).
[Crossref]

Garito, A. F.

K. Y. Wong and A. F. Garito, Phys. Rev. A 34, 5051 (1986).
[Crossref] [PubMed]

C. C. Teng and A. F. Garito, Phys. Rev. B 28, 6766 (1983).
[Crossref]

A. F. Garito and K. D. Singer, Laser Focus 18(2), 59 (1982).

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981), and references therein.
[Crossref]

S. J. Lalama and A. F. Garito, Phys. Rev. A 20, 1179 (1979).
[Crossref]

Gu, S. J.

S. J. Gu, S. K. Saha, and G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
[Crossref]

Havinga, E. E.

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979).
[Crossref]

Hierle, R.

M. Sigelle and R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[Crossref]

Jen, S.

S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
[Crossref]

Kaminow, I. P.

See, for example, I. P. Kaminow, An Introduction to Electro-Optic Devices (Academic, New York, 1974).

Katz, H. E.

C. W. Dirk, H. E. Katz, K. D. Singer, and J. E. Sohn, submitted to J. Chem. Phys.

Khoo, I. C.

I. C. Khoo and Y. R. Shen, Opt. Eng. 24, 579 (1985).

Kiefer, R.

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

Kielich, S.

S. Kielich, IEEE J. Quantum Electron. QE-5, 562 (1969).
[Crossref]

Kleinman, D. A.

D. A. Kleinman, Phys. Rev. 126, 1977 (1962).
[Crossref]

Kuzyk, M. G.

M. G. Kuzyk, J. E. Sohn, S. J. Lalama, and K. D. Singer, to be submitted to J. Opt. Soc. Am. B.

Lalama, S. J.

K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

S. J. Lalama and A. F. Garito, Phys. Rev. A 20, 1179 (1979).
[Crossref]

M. G. Kuzyk, J. E. Sohn, S. J. Lalama, and K. D. Singer, to be submitted to J. Opt. Soc. Am. B.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).

Maier, W.

W. Maier and A. Saupe, Z. Naturforsch. 13a, 564 (1958); Z. Naturforsch. 14a, 882 (1959); Z. Naturforsch. 15a, 287 (1960).

Meredith, G. R.

G. R. Meredith, J. G. Vandusen, and D. J. Williams, in Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).

Nye, J. F.

See, for example, J. F. Nye, Physical Properties of Crystals (Clarendon, London, 1957).

Oudar, J. L.

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

J. L. Oudar and D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
[Crossref]

Ou-Yang, Z.-C.

Y.-Z. Xie and Z.-C. Ou-Yang, Commun. Theor. Phys. 6, 1 (1986).

Z.-C. Ou-Yang and Y.-Z. Xie, Phys. Rev. A 32, 1189 (1985).
[Crossref]

Pershan, P. S.

S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
[Crossref]

Pilipetski, N. F.

N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
[Crossref]

Priestly, E. B.

S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
[Crossref]

Rauch, J. E.

S. J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
[Crossref]

Ringsdorf, H.

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

Saha, S. K.

S. J. Gu, S. K. Saha, and G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
[Crossref]

S. K. Saha and G. K. Wong, Appl. Phys. Lett. 34, 423 (1979).
[Crossref]

Saupe, A.

W. Maier and A. Saupe, Z. Naturforsch. 13a, 564 (1958); Z. Naturforsch. 14a, 882 (1959); Z. Naturforsch. 15a, 287 (1960).

A. Saupe, in Liquid Crystals, G. H. Brown, G. J. Dienes, and M. M. Labes, eds. (Gordon and Breach, New York, 1966).

Schmidt, H.-W.

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

Shen, Y. R.

I. C. Khoo and Y. R. Shen, Opt. Eng. 24, 579 (1985).

S. D. Durbin and Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
[Crossref]

Sigelle, M.

M. Sigelle and R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[Crossref]

Singer, K. D.

K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

A. F. Garito and K. D. Singer, Laser Focus 18(2), 59 (1982).

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981), and references therein.
[Crossref]

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).

M. G. Kuzyk, J. E. Sohn, S. J. Lalama, and K. D. Singer, to be submitted to J. Opt. Soc. Am. B.

C. W. Dirk, H. E. Katz, K. D. Singer, and J. E. Sohn, submitted to J. Chem. Phys.

Small, R. D.

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).

Sohn, J. E.

K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).

C. W. Dirk, H. E. Katz, K. D. Singer, and J. E. Sohn, submitted to J. Chem. Phys.

M. G. Kuzyk, J. E. Sohn, S. J. Lalama, and K. D. Singer, to be submitted to J. Opt. Soc. Am. B.

Sukhov, A. V.

N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
[Crossref]

Tabiryan, N. V.

N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
[Crossref]

Teng, C. C.

C. C. Teng and A. F. Garito, Phys. Rev. B 28, 6766 (1983).
[Crossref]

van Pelt, P.

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979).
[Crossref]

Vandusen, J. G.

G. R. Meredith, J. G. Vandusen, and D. J. Williams, in Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).

Ward, J. F.

J. F. Ward and P. A. Franken, Phys. Rev. 133, A183 (1964).
[Crossref]

Williams, D. J.

G. R. Meredith, J. G. Vandusen, and D. J. Williams, in Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).

Windscheid, F.

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

Wong, G. K.

S. J. Gu, S. K. Saha, and G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
[Crossref]

S. K. Saha and G. K. Wong, Appl. Phys. Lett. 34, 423 (1979).
[Crossref]

Wong, K. Y.

K. Y. Wong and A. F. Garito, Phys. Rev. A 34, 5051 (1986).
[Crossref] [PubMed]

Xie, Y.-Z.

Y.-Z. Xie and Z.-C. Ou-Yang, Commun. Theor. Phys. 6, 1 (1986).

Z.-C. Ou-Yang and Y.-Z. Xie, Phys. Rev. A 32, 1189 (1985).
[Crossref]

Zel’dovich, B. Ya.

N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
[Crossref]

Zyss, J.

J. Zyss, J. Molec. Electron. 1, 25 (1985).

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

Appl. Phys. Lett. (2)

S. K. Saha and G. K. Wong, Appl. Phys. Lett. 34, 423 (1979).
[Crossref]

K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
[Crossref]

Ber. Bunsenges. Phys. Chem. (1)

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979).
[Crossref]

Commun. Theor. Phys. (1)

Y.-Z. Xie and Z.-C. Ou-Yang, Commun. Theor. Phys. 6, 1 (1986).

IEEE J. Quantum Electron. (1)

S. Kielich, IEEE J. Quantum Electron. QE-5, 562 (1969).
[Crossref]

J. Appl. Phys. (1)

M. Sigelle and R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[Crossref]

J. Chem. Phys. (4)

S. J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
[Crossref]

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981), and references therein.
[Crossref]

J. L. Oudar and D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
[Crossref]

S. Jen, N. A. Clark, P. S. Pershan, and E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
[Crossref]

J. Molec. Electron. (1)

J. Zyss, J. Molec. Electron. 1, 25 (1985).

Laser Focus (1)

A. F. Garito and K. D. Singer, Laser Focus 18(2), 59 (1982).

Liq. Cryst. (GB) (1)

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, and F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[Crossref]

Molec. Cryst. Liq. Cryst. (1)

S. J. Gu, S. K. Saha, and G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
[Crossref]

Opt. Commun. (1)

N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, and B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
[Crossref]

Opt. Eng. (1)

I. C. Khoo and Y. R. Shen, Opt. Eng. 24, 579 (1985).

Phys. Rev. (2)

D. A. Kleinman, Phys. Rev. 126, 1977 (1962).
[Crossref]

J. F. Ward and P. A. Franken, Phys. Rev. 133, A183 (1964).
[Crossref]

Phys. Rev. A (5)

S. J. Lalama and A. F. Garito, Phys. Rev. A 20, 1179 (1979).
[Crossref]

S. D. Durbin and Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
[Crossref]

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

K. Y. Wong and A. F. Garito, Phys. Rev. A 34, 5051 (1986).
[Crossref] [PubMed]

Z.-C. Ou-Yang and Y.-Z. Xie, Phys. Rev. A 32, 1189 (1985).
[Crossref]

Phys. Rev. B (1)

C. C. Teng and A. F. Garito, Phys. Rev. B 28, 6766 (1983).
[Crossref]

Z. Naturforsch. (1)

W. Maier and A. Saupe, Z. Naturforsch. 13a, 564 (1958); Z. Naturforsch. 14a, 882 (1959); Z. Naturforsch. 15a, 287 (1960).

Other (12)

S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, London, 1977).

K. D. Singer, S. J. Lalama, J. E. Sohn, and R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).

C. W. Dirk, H. E. Katz, K. D. Singer, and J. E. Sohn, submitted to J. Chem. Phys.

M. G. Kuzyk, J. E. Sohn, S. J. Lalama, and K. D. Singer, to be submitted to J. Opt. Soc. Am. B.

A. Saupe, in Liquid Crystals, G. H. Brown, G. J. Dienes, and M. M. Labes, eds. (Gordon and Breach, New York, 1966).

See, for example, I. P. Kaminow, An Introduction to Electro-Optic Devices (Academic, New York, 1974).

G. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970), pp. 173–183.

G. R. Meredith, J. G. Vandusen, and D. J. Williams, in Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).

See, for example, J. F. Nye, Physical Properties of Crystals (Clarendon, London, 1957).

C. W. Dirk (AT&T Bell Laboratories, Murray Hill, New Jersey 0794) and R. Twieg (personal communication).

D. J. Williams, ed., Nonlinear Optical Properties of Organic and Polymeric Materials, ACS Symposium Series No. 233 (American Chemical Society, Washington, D.C., 1983).
[Crossref]

D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1987).

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Figures (5)

Fig. 1
Fig. 1

Disperse Red 1, an azo dye.

Fig. 2
Fig. 2

d33 versus poling field. Shaded area is calculated by using expressions (17)–(19). (Reference 16; used with permission.)

Fig. 3
Fig. 3

d33 versus number density. Shaded area is calculated by using expressions (17)–(19). (Reference 16; used with permission.)

Fig. 4
Fig. 4

Dispersion of d33/NEp using a two-level model.

Fig. 5
Fig. 5

Dispersion of r 33 e l / N E p, using a two-level model.

Tables (4)

Tables Icon

Table 1 Properties of Films Used in Second-Harmonic-Generation Measurements

Tables Icon

Table 2 Results of Second-Harmonic Generation at λ = 1.58 μma

Tables Icon

Table 3 Properties of Films Used in Electro-Optic Measurements

Tables Icon

Table 4 Results of Electro-Optic Measurements at λ = 0.633 μm

Equations (65)

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P i ( t ) = P i ( 0 ) ( t ) + χ i j ( 1 ) ( t ) E j ( t ) + χ i j k ( 2 ) ( t ) E j ( t ) E k ( t ) + χ i j k l ( 3 ) ( t ) E j ( t ) E k ( t ) E l ( t ) + ,
p I ( t ) = μ I 0 + α I J ( t ) E J ( t ) + β I J K ( t ) E J ( t ) E K ( t ) + γ I J K L ( t ) E J ( t ) E K ( t ) E L ( t ) + ,
χ i j k ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) = N f i ω 3 f j ω 1 f k ω 2 × I , J , K s = 1 n cos [ i , I ( s ) ] cos [ j , J ( s ) ] × cos [ k , K ( s ) ] β I J K ( s ) ,
P 1 ( 2 ) ( ω 3 ) = χ 131 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 3 ( ω 1 ) E 1 ( ω 2 ) + χ 113 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 1 ( ω 1 ) E 3 ( ω 2 ) , P 2 ( 2 ) ( ω 3 ) = χ 131 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 3 ( ω 1 ) E 2 ( ω 2 ) + χ 113 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 2 ( ω 1 ) E 3 ( ω 2 ) , P 3 ( 2 ) ( ω 3 ) = χ 311 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 1 ( ω 1 ) E 1 ( ω 2 ) + χ 311 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 2 ( ω 1 ) E 2 ( ω 2 ) + χ 333 ( 2 ) ( - ω 3 ; ω 1 , ω 2 ) E 3 ( ω 1 ) E 3 ( ω 2 ) .
χ i j k ( - ω 3 ; ω 1 , ω 2 ) = N β I J K * ( - ω 3 ; ω 1 , ω 2 ) i j k ,
χ i j k ( - ω 3 ; ω 1 , ω 2 ) = N β * I J K ( - ω 3 ; ω 1 , ω 2 ) a i I a i J a k K .
a i I a j J a k K = d Ω a i I a j J a k K G ( Ω , E p ) ,
G ( Ω , E p ) = exp [ - 1 k T ( U - m * · E p ) ] d Ω exp [ - 1 k T ( U - m * · E p ) ] ,
G ( θ , E p ) = l = 0 2 l + 1 2 A l P l ( cos θ ) ,
A l = - 1 1 d ( cos θ ) G ( θ , E p ) P l ( cos θ ) .
χ i j k = N E p k T [ u i j k ( 0 ) + u i j k ( 2 ) P 2 + u i j k ( 4 ) P 4 ] ,
χ 333 ~ N β z z z * m z * E p k T × ( 1 5 + 4 7 P 2 + 8 35 P 4 )
χ 311 = χ 113 = χ 131 ~ N β z z z * m z * E p k T × ( 1 15 + 1 21 P 2 - 8 70 P 4 ) .
β z z z * ( - ω 3 ; ω 1 , ω 2 ) m z * = f ω 3 f ω 1 f ω 2 f 0 β z z z ( - ω 3 ; ω 1 , ω 2 ) μ z .
f ω = n ω 2 + 2 3
f 0 = ( n 2 + 2 ) n 2 + 2 ,
χ 333 ~ N f ω 3 f ω 1 f ω 2 β z z z ( - ω 3 ; ω 1 , ω 2 ) L 3 ( p ) ,
L 3 ( p ) = p 5 - p 3 105 +
p = [ ( n 2 + 2 ) n 2 + 2 ] μ z E p k T .
G u ( Ω , E p ) = exp [ - 1 k T ( v U u v - m u * · E p ) ] d Ω exp [ - 1 k T ( v U u v - m u * · E p ) ] ,
χ i j k ( - ω 3 ; ω 1 , ω 2 ) = u N u ( β I J K * ) u a i I a j J a k K G u ( Ω , E p ) d Ω .
E j ( t ) = ½ [ e j ( ω 1 ) exp ( - i ω 1 t ) + e j ( ω 2 ) exp ( - i ω 2 t ) + c . c . ] ,
- ω 3 + ω 1 + ω 2 = 0
d i j k ( - 2 ω ; ω , ω ) = ½ χ i j k ( - 2 ω ; ω , ω ) .
P 1 ( 2 ) ( 2 ω ) = 2 d 15 ( - 2 ω ; ω , ω ) E 1 ( ω ) E 3 ( ω ) , P 2 ( 2 ) ( 2 ω ) = 2 d 15 ( - 2 ω ; ω , ω ) E 2 ( ω ) E 3 ( ω ) , P 3 ( 2 ) ( 2 ω ) = d 31 ( - 2 ω ; ω , ω ) [ E 1 2 ( ω ) + E 2 2 ( ω ) ] + d 33 ( - 2 ω ; ω , ω ) E 3 2 ( ω ) .
β I J K ( - 2 ω ; ω , ω ) = ½ β I J K ( - 2 ω ; ω , ω ) .
B i j ( E ) - B i j ( 0 ) = [ 1 ( E ) ] i j - [ 1 ( 0 ) ] i j r i j , k E k ,
Δ χ i j = Δ i j = - i i Δ B i j j j
P i ( t ) = 0 Δ χ i j E j ( t ) = - 0 i i j j r i j , k E j ( t ) E k ( t ) .
E j ( t ) = E j cos ( ω 1 t + ϕ 1 ) = ½ [ e j ( ω 1 ) exp ( - i ω 1 t ) + e j * ( - ω 1 ) exp ( i ω 1 t ) ]
E k ( t ) = E k cos ( ω 2 t + ϕ 2 ) = ½ [ e k ( ω 2 ) exp ( - i ω 2 t ) + e k * ( - ω 2 ) exp ( i ω 2 t ) ] ,
P i ( ω ) = - 0 i i ( ω ) j j ( ω ) r i j , k e j ω e k 0 .
P i ( t ) = 0 χ i j k E j ( t ) E k ( t ) ,
χ i j k ( - ω ; ω , 0 ) = - ½ i i ( ω ) j j ( ω ) r i j , k ( - ω ; ω , 0 ) ,
r i j , k ( - ω ; ω , 0 ) = - 2 n 2 χ i j k ( - ω ; ω , 0 ) .
r u k = r u k e l + r u k B + r u k R ,
β z z z ( - ω 3 ; ω 1 , ω 2 ) = e 3 z 01 2 ( z 11 - z 00 ) 2 × ω 0 2 ( 3 ω 0 2 + ω 1 ω 2 - ω 3 2 ) ( ω 0 2 - ω 1 2 ) ( ω 0 2 - ω 2 2 ) ( ω 0 2 - ω 3 2 ) ,
r i j , k e l ( - ω ; ω , 0 ) = - 4 d k i j n i 2 ( ω ) n j 2 ( ω ) × f i i ω f j j ω f k k 0 f k k 2 ω f i i 2 ω f j j ω × ( 3 ω 0 2 - ω 2 ) ( ω 0 2 - ω 2 ) ( ω 0 2 - 4 ω 2 ) 3 ω 0 2 ( ω 0 2 - ω 2 ) 2 ,
χ i j k ( - ω 3 ; ω 1 , ω 2 ) = N β I J K * ( - ω 3 ; ω 1 , ω 2 ) i j k ,
β I J K * i j k = d Ω a i I a i J a k K G ( Ω , E p ) β I J K * ,
d Ω = 0 2 π d ϕ 0 2 π d ψ - 1 1 d ( cos θ ) ,
a = ( + cos θ cos ϕ cos ψ - sin ϕ sin ψ + cos θ sin ϕ cos ψ + cos ϕ sin ψ - sin θ cos ψ - cos θ cos ϕ sin ψ - sin ϕ cos ψ - cos θ sin ϕ sin ψ + cos ϕ cos ψ + sin θ sin ψ + sin θ cos ϕ + sin θ sin ϕ + cos θ ) ,
G ( Ω , E p ) = exp [ - ( U - m * · E p ) / k T ] exp [ - ( U - m * · E p ) / k T ] d Ω ,
exp [ - ( U - m * · E p ) / k T ] ( 1 + m * + E p k T ) exp ( - U / k T ) .
- m * · E p = - a 3 l m * l E 3 .
G ( Ω , E p ) ( 1 + a 3 l m * l E 3 / k T ) exp ( - U / k T ) exp ( - U / k T ) d Ω .
P i = - 1 1 d ( cos θ ) P i ( cos θ ) e - U / k T - 1 1 d ( cos θ ) e - U / k T .
χ i j k = N E p k T [ u i j k ( 0 ) + u i j k ( 2 ) P 2 + u i j k ( 4 ) P 4 ] ,
γ 0 = ( β x x x * 0 0 0 β y y y * 0 0 0 β z z z * ) ,
γ 1 = ( 0 β x y y * β x z z * β y x x * 0 β y z z * β z x x * β z y y * 0 ) ,
γ 2 = ( 0 β y x y * β z x z * β x y x * 0 β z y z * β x z x * β y z y * 0 ) ,
γ 3 = ( 0 β y y x * β z z x * β x x y * 0 β z z y * β x x z * β y y z * 0 ) ,
m * = ( m x * m y * m z * m x * m y * m z * m x * m y * m z * ) ,
u 333 ( 0 ) = ¹ / ₁₅ [ m * ( 3 γ 0 + γ ) ] i i ,
u 333 ( 2 ) = ² / [ 3 ( m * γ 0 ) z z - ( m * γ 0 ) i i ] - ¹ / ₂₁ [ 2 ( m * γ ) i i - 3 ( m * γ + γ m * ) z z ] ,
u 333 ( 4 ) = ¹ / ₃₅ [ 5 ( m * γ 0 ) z z + 3 ( m * γ 0 ) i i - 5 ( m * γ + γ m * ) z z + ( m * γ ) i i ] ;
u 131 ( 0 ) = ¹ / ₁₅ [ ( m * γ 0 ) i i + 2 ( m * γ 2 ) i i ] ,
u 131 ( 2 ) = ¹ / ₄₂ [ 3 ( m * γ 0 ) z z - ( m * γ 0 ) i i - 5 ( m * γ 2 ) i i + 18 ( γ 2 m * ) z z - 3 ( m * γ 2 ) z z ] ,
u 131 ( 4 ) = - ¹ / ₇₀ [ 5 ( m * γ 0 ) z z + 3 ( m * γ 0 ) i i + ( m * γ 2 ) i i - 5 ( γ 2 m * + m * γ 2 ) z z ] ;
u 113 ( 0 ) = ¹ / ₁₅ [ ( m * γ 0 ) i i + 2 ( m * γ 3 ) i i ] ,
u 113 ( 2 ) = ¹ / ₄₂ [ 3 ( m * γ 0 ) z z - ( m * γ 0 ) i i - 5 ( m * γ 3 ) i i + 18 ( γ 3 m * ) z z - 3 ( m * γ 3 ) z z ] ,
u 113 ( 4 ) = - ¹ / ₇₀ [ 5 ( m * γ 0 ) z z + 3 ( m * γ 0 ) i i + ( m * γ 3 ) i i - 5 ( γ 3 m * + m * γ 3 ) z z ] ;
u 311 ( 0 ) = ¹ / ₁₅ [ ( m * γ 0 ) i i + 2 ( m * γ 1 ) i i ] ,
u 311 ( 2 ) = ¹ / ₄₂ [ 3 ( m * γ 0 ) z z - ( m * γ 0 ) i i - 5 ( m * γ 1 ) i i + 18 ( γ 1 m * ) z z - 3 ( m * γ 1 ) z z ] ,
u 311 ( 4 ) = - ¹ / ₇₀ [ 5 ( m * γ 0 ) z z + 3 ( m * γ 0 ) i i + ( m * γ 1 ) i i - 5 ( γ 1 m * + m * γ 1 ) z z ] .

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