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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  1. A. F. Garito, 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, J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1987).
  5. J. Zyss, J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
    [CrossRef]
  6. K. Y. Wong, A. F. Garito, Phys. Rev. A 34, 5051 (1986).
    [CrossRef] [PubMed]
  7. Y.-Z. Xie, Z.-C. Ou-Yang, Commun. Theor. Phys. 6, 1 (1986).
  8. I. C. Khoo, Y. R. Shen, Opt. Eng. 24, 579 (1985).
  9. N. F. Pilipetski, A. V. Sukhov, N. V. Tabiryan, B. Ya. Zel’dovich, Opt. Commun. 37, 280 (1981).
    [CrossRef]
  10. S. D. Durbin, Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
    [CrossRef]
  11. S. K. Saha, G. K. Wong, Appl. Phys. Lett. 34, 423 (1979).
    [CrossRef]
  12. S. Jen, N. A. Clark, P. S. Pershan, E. B. Priestly, J. Chem. Phys. 66, 4635 (1977).
    [CrossRef]
  13. S. J. Gu, S. K. Saha, G. K. Wong, Molec. Cryst. Liq. Cryst. 69, 287 (1981).
    [CrossRef]
  14. Z.-C. Ou-Yang, Y.-Z. Xie, Phys. Rev. A 32, 1189 (1985).
    [CrossRef]
  15. G. R. Meredith, J. G. Vandusen, 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, S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
    [CrossRef]
  17. H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
    [CrossRef]
  18. E. E. Havinga, 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, A. Saupe, Z. Naturforsch. 13a, 564 (1958); Z. Naturforsch. 14a, 882 (1959); Z. Naturforsch. 15a, 287 (1960).
  24. S. J. Lalama, A. F. Garito, Phys. Rev. A 20, 1179 (1979).
    [CrossRef]
  25. K. D. Singer, 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, 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, D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
    [CrossRef]
  29. D. A. Kleinman, Phys. Rev. 126, 1977 (1962).
    [CrossRef]
  30. J. F. Ward, P. A. Franken, Phys. Rev. 133, A183 (1964).
    [CrossRef]
  31. K. D. Singer, S. J. Lalama, J. E. Sohn, R. D. Small, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla, J. Zyss, eds. (Academic, New York, 1987).
  32. C. C. Teng, A. F. Garito, Phys. Rev. B 28, 6766 (1983).
    [CrossRef]
  33. C. W. Dirk, H. E. Katz, K. D. Singer, J. E. Sohn, submitted to J. Chem. Phys.
  34. M. G. Kuzyk, J. E. Sohn, S. J. Lalama, K. D. Singer, to be submitted to J. Opt. Soc. Am. B.
  35. M. Sigelle, 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, J. C. Decius, J. Chem. Phys. 43, 4083 (1965).
    [CrossRef]

1986

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

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

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

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

1985

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

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

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

1984

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

1983

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

1982

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

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

1981

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

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

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

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

1979

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

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

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

1977

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

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

1969

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

1965

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

1964

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

1962

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

1958

W. Maier, 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, 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, D. S. Chemla, J. Chem. Phys. 66, 2664 (1977).
[CrossRef]

Clark, N. A.

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

Cyvin, S. J.

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

Decius, J. C.

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

Dirk, C. W.

C. W. Dirk, H. E. Katz, K. D. Singer, 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, Y. R. Shen, Phys. Rev. A 30, 1419 (1984).
[CrossRef]

Franken, P. A.

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

Garito, A. F.

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

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

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

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

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

Gu, S. J.

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

Havinga, E. E.

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

Hierle, R.

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

Jen, S.

S. Jen, N. A. Clark, P. S. Pershan, 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, J. E. Sohn, submitted to J. Chem. Phys.

Khoo, I. C.

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

Kiefer, R.

H. Ringsdorf, H.-W. Schmidt, G. Baur, R. Kiefer, 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, K. D. Singer, to be submitted to J. Opt. Soc. Am. B.

Lalama, S. J.

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

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

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

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

Maier, W.

W. Maier, 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, 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, J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[CrossRef]

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

Ou-Yang, Z.-C.

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

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

Pershan, P. S.

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

Pilipetski, N. F.

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

Priestly, E. B.

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

Rauch, J. E.

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

Ringsdorf, H.

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

Saha, S. K.

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

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

Saupe, A.

W. Maier, 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, M. M. Labes, eds. (Gordon and Breach, New York, 1966).

Schmidt, H.-W.

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

Shen, Y. R.

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

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

Sigelle, M.

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

Singer, K. D.

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

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

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

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

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

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

Small, R. D.

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

Sohn, J. E.

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

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

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

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

Sukhov, A. V.

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

Tabiryan, N. V.

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

Teng, C. C.

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

van Pelt, P.

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

Vandusen, J. G.

G. R. Meredith, J. G. Vandusen, 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, P. A. Franken, Phys. Rev. 133, A183 (1964).
[CrossRef]

Williams, D. J.

G. R. Meredith, J. G. Vandusen, 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, F. Windscheid, Liq. Cryst. (GB) 1, 319 (1986).
[CrossRef]

Wong, G. K.

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

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

Wong, K. Y.

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

Xie, Y.-Z.

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

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

Zel’dovich, B. Ya.

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

Zyss, J.

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

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

Appl. Phys. Lett.

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

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

Ber. Bunsenges. Phys. Chem.

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

Commun. Theor. Phys.

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

IEEE J. Quantum Electron.

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

J. Appl. Phys.

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

J. Chem. Phys.

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

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

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

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

J. Molec. Electron.

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

Laser Focus

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

Liq. Cryst. (GB)

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

Molec. Cryst. Liq. Cryst.

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

Opt. Commun.

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

Opt. Eng.

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

Phys. Rev.

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

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

Phys. Rev. A

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

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

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

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

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

Phys. Rev. B

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

Z. Naturforsch.

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

Other

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

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

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

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

A. Saupe, in Liquid Crystals, G. H. Brown, G. J. Dienes, 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, 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, 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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