Abstract

We apply quadratic electroabsorption to thin-film solid solutions of squarylium dye molecules in poly(methyl methacrylate) polymer to study the electronic and reorientational mechanisms in the third-order nonlinear-optical susceptibility. To interpret the data, we have generalized quadratic electro-optic response theory to include both electronic and hindered-molecular-reorientation mechanisms. Such a theory predicts that the ratio of two independent third-order susceptibility tensor components, namely, χ3333(3)/χ1133(3), characterizes the relative contribution of each mechanism. We have designed and built an experiment that measures this ratio as a function of temperature and wavelength. Results show that at room temperature and near the first electronic transition wavelength the response is dominated by the electronic mechanism and that the reorientational contribution dominates when the sample is heated above its glass-transition temperature. Furthermore, far off resonance, the sign of the imaginary part of the third-order susceptibility is positive and is consistent with the two-level model. We also discuss the possible role of electrostriction in our analysis. Quadratic electroabsorption is thus shown to be a versatile tool for measuring the imaginary part of the third-order nonlinear-optical susceptibility, which yields information about the role of the interaction of the polymer host with the dopant molecule

© 1994 Optical Society of America

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  1. J. Meissier, F. Kajzar, P. Prasad, and D. Ulrich, eds., Nonlinear Optical Effects in Organic Polymers, Vol. 162 of NATO Advanced Science Institutes Series E: Applied Sciences (Kluwer, Dordrecht, The Netherlands, 1989).
    [CrossRef]
  2. See, for example, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., Materials for Nonlinear Optics: Chemical Perspectives, Vol. 455 of ACS Symposium Series (American Chemical Society, Washington, D.C., 1991).
    [CrossRef]
  3. K. D. Singer, J. E. Sohn, and S. J. Lalama, Appl. Phys. Lett. 49, 248 (1986).
    [CrossRef]
  4. H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
    [CrossRef]
  5. K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
    [CrossRef]
  6. M. G. Kuzyk, R. C. Moore, and L. A. King, J. Opt. Soc. Am. B 7, 64 (1990).
    [CrossRef]
  7. See, for example, D. McMorrow, W. T. Lotshaw, and G. A. Kenny-Wallace, IEEE J. Quantum Electron. 24, 443 (1988).
    [CrossRef]
  8. M. G. Kuzyk and C. W. Dirk, Appl. Phys. Lett. 54, 1628 (1989).
    [CrossRef]
  9. M. G. Kuzyk, C. W. Dirk, and J. E. Sohn, J. Opt. Soc. Am. B 5, 842 (1990).
    [CrossRef]
  10. S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).
  11. T. Kobayashi, H. Uchiki, and K. Minoshima, Synth. Met. 28, D699 (1989).
    [CrossRef]
  12. H. Uchiki and T. Kobayashi, J. Appl. Phys. 64, 2625 (1988).
    [CrossRef]
  13. T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
    [CrossRef]
  14. E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979); Mol. Cryst. Liq. Cryst. 52, 145 (1979).
    [CrossRef]
  15. S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
    [CrossRef]
  16. R. Meyrueix, J. P. Lecomte, and G. Tapolsky, Nonlinear Opt. 1, 201 (1991).
  17. N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Dover, New York, 1991).
  18. M. G. Kuzyk and C. Poga, in Molecular Nonlinear Optics: Materials, Physics and Devices, J. Zyss, ed. (Academic, San Diego, Calif., 1993).
  19. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies on Modern Optics (Cambridge U. Press, Cambridge, 1990).
    [CrossRef]
  20. G. T. Boyd, C. V. Francis, J. E. Trend, and D. A. Ender, J. Opt. Soc. Am. B 8, 887 (1991).
    [CrossRef]
  21. C. W. Dirk and M. G. Kuzyk, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 18 (1989).
    [CrossRef]
  22. Our definition of f is the reciprocal to the definition given in Ref. 23. We find the present definition more natural because the electronic response is constant.
  23. C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electro-absorption studies of molecular motion in dye-doped polymers,” in Nonlinear Optical Properties of Organic Materials V, Proc. Soc. Photo-Opt. Instrum. Eng.1775, 166 (1992).
    [CrossRef]
  24. B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).
    [CrossRef]
  25. Y. R. Shen, Principles of Nonlinear Optics (Wiley Interscience, New York, 1984).
  26. C. W. Dirk and M. G. Kuzyk, Phys. Rev. B 41, 1636 (1990).
    [CrossRef]
  27. D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
    [CrossRef]

1991 (2)

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, Nonlinear Opt. 1, 201 (1991).

G. T. Boyd, C. V. Francis, J. E. Trend, and D. A. Ender, J. Opt. Soc. Am. B 8, 887 (1991).
[CrossRef]

1990 (3)

C. W. Dirk and M. G. Kuzyk, Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk, R. C. Moore, and L. A. King, J. Opt. Soc. Am. B 7, 64 (1990).
[CrossRef]

M. G. Kuzyk, C. W. Dirk, and J. E. Sohn, J. Opt. Soc. Am. B 5, 842 (1990).
[CrossRef]

1989 (3)

M. G. Kuzyk and C. W. Dirk, Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

T. Kobayashi, H. Uchiki, and K. Minoshima, Synth. Met. 28, D699 (1989).
[CrossRef]

1988 (4)

H. Uchiki and T. Kobayashi, J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

See, for example, D. McMorrow, W. T. Lotshaw, and G. A. Kenny-Wallace, IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

1987 (1)

S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).

1986 (1)

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

1979 (1)

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979); Mol. Cryst. Liq. Cryst. 52, 145 (1979).
[CrossRef]

1971 (1)

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Boyd, G. T.

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies on Modern Optics (Cambridge U. Press, Cambridge, 1990).
[CrossRef]

Comizzoli, R. B.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies on Modern Optics (Cambridge U. Press, Cambridge, 1990).
[CrossRef]

Dentan, V.

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Dirk, C. W.

C. W. Dirk and M. G. Kuzyk, Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk, C. W. Dirk, and J. E. Sohn, J. Opt. Soc. Am. B 5, 842 (1990).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 18 (1989).
[CrossRef]

C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electro-absorption studies of molecular motion in dye-doped polymers,” in Nonlinear Optical Properties of Organic Materials V, Proc. Soc. Photo-Opt. Instrum. Eng.1775, 166 (1992).
[CrossRef]

Dumont, M.

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Ender, D. A.

Francis, C. V.

Fukaya, S.

T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
[CrossRef]

Hampsch, H. L.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
[CrossRef]

Havinga, E. E.

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979); Mol. Cryst. Liq. Cryst. 52, 145 (1979).
[CrossRef]

Holland, W. R.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Kaino, T.

S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).

Kajzar, F.

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Katz, H. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Kenny-Wallace, G. A.

See, for example, D. McMorrow, W. T. Lotshaw, and G. A. Kenny-Wallace, IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

King, L. A.

Kobayashi, T.

T. Kobayashi, H. Uchiki, and K. Minoshima, Synth. Met. 28, D699 (1989).
[CrossRef]

H. Uchiki and T. Kobayashi, J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
[CrossRef]

S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
[CrossRef]

Kubodera, K.

S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).

Kurihara, T.

S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).

Kuzyk, M. G.

M. G. Kuzyk, C. W. Dirk, and J. E. Sohn, J. Opt. Soc. Am. B 5, 842 (1990).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk, R. C. Moore, and L. A. King, J. Opt. Soc. Am. B 7, 64 (1990).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

M. G. Kuzyk and C. Poga, in Molecular Nonlinear Optics: Materials, Physics and Devices, J. Zyss, ed. (Academic, San Diego, Calif., 1993).

C. W. Dirk and M. G. Kuzyk, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 18 (1989).
[CrossRef]

C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electro-absorption studies of molecular motion in dye-doped polymers,” in Nonlinear Optical Properties of Organic Materials V, Proc. Soc. Photo-Opt. Instrum. Eng.1775, 166 (1992).
[CrossRef]

Lalama, S. J.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

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

Lecomte, J. P.

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, Nonlinear Opt. 1, 201 (1991).

Lévy, Y.

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Lotshaw, W. T.

See, for example, D. McMorrow, W. T. Lotshaw, and G. A. Kenny-Wallace, IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

Matsuda, H.

S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
[CrossRef]

Matsumoto, S.

S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).

McCrum, N. G.

N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Dover, New York, 1991).

McMorrow, D.

See, for example, D. McMorrow, W. T. Lotshaw, and G. A. Kenny-Wallace, IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

Meyrueix, R.

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, Nonlinear Opt. 1, 201 (1991).

Minoshima, K.

T. Kobayashi, H. Uchiki, and K. Minoshima, Synth. Met. 28, D699 (1989).
[CrossRef]

T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
[CrossRef]

Moore, R. C.

Morichére, D.

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Nakanishi, H.

S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
[CrossRef]

Nomura, S.

T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
[CrossRef]

Normura, S.

S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
[CrossRef]

Okada, S.

S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
[CrossRef]

Orr, B. J.

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Poga, C.

C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electro-absorption studies of molecular motion in dye-doped polymers,” in Nonlinear Optical Properties of Organic Materials V, Proc. Soc. Photo-Opt. Instrum. Eng.1775, 166 (1992).
[CrossRef]

M. G. Kuzyk and C. Poga, in Molecular Nonlinear Optics: Materials, Physics and Devices, J. Zyss, ed. (Academic, San Diego, Calif., 1993).

Read, B. E.

N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Dover, New York, 1991).

Robin, P.

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Schilling, M. L.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (Wiley Interscience, New York, 1984).

Singer, K. D.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

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

Sohn, J. E.

M. G. Kuzyk, C. W. Dirk, and J. E. Sohn, J. Opt. Soc. Am. B 5, 842 (1990).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

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

Tapolsky, G.

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, Nonlinear Opt. 1, 201 (1991).

Torkelson, J. M.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
[CrossRef]

Trend, J. E.

Uchiki, H.

T. Kobayashi, H. Uchiki, and K. Minoshima, Synth. Met. 28, D699 (1989).
[CrossRef]

H. Uchiki and T. Kobayashi, J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

Ueki, A.

T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
[CrossRef]

van Pelt, P.

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979); Mol. Cryst. Liq. Cryst. 52, 145 (1979).
[CrossRef]

Ward, J. F.

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Williams, G.

N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Dover, New York, 1991).

Wong, G. K.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
[CrossRef]

Yang, J.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
[CrossRef]

Appl. Phys. Lett. (4)

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

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, Appl. Phys. Lett. 53, 1800 (1988).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, Appl. Phys. Lett. 54, 1628 (1989).
[CrossRef]

S. Matsumoto, K. Kubodera, T. Kurihara, and T. Kaino, Appl. Phys. Lett. 54, 1630 (1987).

Ber. Bunsenges. Phys. Chem. (1)

E. E. Havinga and P. van Pelt, Ber. Bunsenges. Phys. Chem. 83, 816 (1979); Mol. Cryst. Liq. Cryst. 52, 145 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

See, for example, D. McMorrow, W. T. Lotshaw, and G. A. Kenny-Wallace, IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

J. Appl. Phys. (1)

H. Uchiki and T. Kobayashi, J. Appl. Phys. 64, 2625 (1988).
[CrossRef]

J. Opt. Soc. Am. B (3)

Macromolecules (1)

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Macromolecules 21, 526 (1988).
[CrossRef]

Mol. Phys. (1)

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).
[CrossRef]

Nonlinear Opt. (1)

R. Meyrueix, J. P. Lecomte, and G. Tapolsky, Nonlinear Opt. 1, 201 (1991).

Opt. Commun. (1)

D. Morichére, V. Dentan, F. Kajzar, P. Robin, Y. Lévy, and M. Dumont, Opt. Commun. 74, 69 (1989).
[CrossRef]

Phys. Rev. B (1)

C. W. Dirk and M. G. Kuzyk, Phys. Rev. B 41, 1636 (1990).
[CrossRef]

Synth. Met. (1)

T. Kobayashi, H. Uchiki, and K. Minoshima, Synth. Met. 28, D699 (1989).
[CrossRef]

Other (11)

T. Kobayashi, K. Minoshima, S. Nomura, S. Fukaya, and A. Ueki, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 182 (1990).
[CrossRef]

N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Dover, New York, 1991).

M. G. Kuzyk and C. Poga, in Molecular Nonlinear Optics: Materials, Physics and Devices, J. Zyss, ed. (Academic, San Diego, Calif., 1993).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies on Modern Optics (Cambridge U. Press, Cambridge, 1990).
[CrossRef]

J. Meissier, F. Kajzar, P. Prasad, and D. Ulrich, eds., Nonlinear Optical Effects in Organic Polymers, Vol. 162 of NATO Advanced Science Institutes Series E: Applied Sciences (Kluwer, Dordrecht, The Netherlands, 1989).
[CrossRef]

See, for example, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., Materials for Nonlinear Optics: Chemical Perspectives, Vol. 455 of ACS Symposium Series (American Chemical Society, Washington, D.C., 1991).
[CrossRef]

Y. R. Shen, Principles of Nonlinear Optics (Wiley Interscience, New York, 1984).

S. Normura, T. Kobayashi, H. Nakanishi, H. Matsuda, and S. Okada, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 272 (1991).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, in Nonlinear Optical Properties of Organic Materials II, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1147, 18 (1989).
[CrossRef]

Our definition of f is the reciprocal to the definition given in Ref. 23. We find the present definition more natural because the electronic response is constant.

C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electro-absorption studies of molecular motion in dye-doped polymers,” in Nonlinear Optical Properties of Organic Materials V, Proc. Soc. Photo-Opt. Instrum. Eng.1775, 166 (1992).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Sample’s geometry.

Fig. 2
Fig. 2

Quadratic electroabsorption experiment.

Fig. 3
Fig. 3

ISQ chromophore.

Fig. 4
Fig. 4

Linear absorption of an approximately 4-μm-thick film of ISQ (1% by weight) in PMMA.

Fig. 5
Fig. 5

a, Temperature dependence of the p-polarized electro-absorption response as a function of internal angle, b, Angular dependence of signal for s-polarized light.

Fig. 6
Fig. 6

Temperature dependence of the tensor ratio.

Fig. 7
Fig. 7

Temperature dependence of tensor ratio f1133. The solid and dotted curves are drawn separately for each run as a guide to the eye to show the difference in f1133 before and after annealing.

Fig. 8
Fig. 8

Temperature dependence of tensor ratio f3333. The solid and dotted curves are drawn separately for each run as a guide to the eye to show the difference in f3333 before and after annealing.

Fig. 9
Fig. 9

Temperature dependence of χ 1133 ( 3 ).

Fig. 10
Fig. 10

Dispersion of Im[α*(−ω; ω)α*(0; 0)] and b, Im[γ*(−ω; ω, 0, 0)] as calculated from the two-level model.

Equations (49)

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U ( θ , θ 0 ) = U E ( θ ) + U int ( θ , θ 0 ) .
μ * E cos θ ,
P i = N p i * i ,
p ˜ i * i = d Ω [ G ( θ , θ 0 ) p i * ω ] a i i ( Ω ) d Ω G ( θ , θ 0 ) ,
p i * i = d Ω 0 f ( θ 0 ) p ˜ i * i d Ω 0 f ( θ 0 ) .
p i * i = [ d Ω 0 d Ω [ G ( θ , θ 0 ) p i * ω a i i ( Ω ) d Ω G ( θ , θ 0 ) ] / d Ω 0 .
χ i j k l ( 3 ) ( ω ; ω 1 , ω 2 , ω 3 ) = 1 K 3 ( ω ; ω 1 , ω 2 , ω 3 ) D 3 ( E j ω 1 E k ω 2 E l ω 3 ) × 3 P i ( ω ) E j ω 1 E k ω 2 E l ω 3 | E = 0 .
K ( ω , ω 1 , ω 2 , ω 3 ) = 2 l + m + n p ,
χ i j k l ( 3 ) ( ω ; ω , 0 , 0 ) .
U int = 1 2 k θ ( θ θ 0 ) 2 ,
χ 1133 ( 3 ) ( ω ; ω , 0 , 0 ) = N 15 [ γ z z z z * ( ω ; ω , 0 , 0 ) 4 3 α z z * ( ω ; ω ) α z z * ( 0 ; 0 ) k θ ] ,
χ 3333 ( 3 ) ( ω ; ω , 0 , 0 ) = N 15 [ 3 γ z z z z * ( ω ; ω , 0 , 0 ) 8 3 α z z * ( ω ; ω ) α z z * ( 0 ; 0 ) k θ ] .
χ 1133 ( 3 ) ( ω ; ω , 0 , 0 ) = N 6 { 6 γ * ( ω ; ω , 0 , 0 ) × [ 1 15 11 3375 ( k θ k T ) ] + 2 α * ( ω ; ω ) α * ( 0 ; 0 ) k T × [ 2 45 + ( 92 10 , 125 ) ( k θ k T ) ] } ,
χ 3333 ( 3 ) ( ω ; ω , 0 , 0 ) = N 6 { 6 γ * ( ω ; ω , 0 , 0 ) × [ 1 5 76 1125 ( k θ k T ) ] + 2 α * ( ω ; ω ) α * ( 0 ; 0 ) k T × [ 4 45 ( 184 10 , 125 ) ( k θ k T ) ] } .
n i j = ( n 0 ) i j + ( n 0 ) i j 3 s i j k l 2 E k 0 E l 0 ,
n i = n 0 + n 0 3 2 s i E 0 2 ,
E 3 = 2 ( V rms / d ) cos ( Ω t ) .
E = t 1 t 2 exp ( 2 π l n I / λ ) 1 r 2 2 exp ( i δ ) E 0 .
I E * E = ( t 1 t 2 ) 2 exp ( 4 π l λ n I ) .
l = d cos θ int = d { 1 [ ( sin θ ) / n R ] } 1 / 2 ;
I 2 Ω = ( t 1 t 2 ) 2 I i exp [ 4 π d λ n 0 I ( 1 + sin 2 θ 2 n 0 R 2 ) ] × 2 π V rms λ d { 1 + sin 2 θ 2 n 0 R 2 [ 1 2 n 0 I n 0 R ( n 0 3 s ) R ( n 0 3 s ) I ] } , × ( n 0 3 s ) I ,
2 n 0 I n 0 R ( n 0 3 s ) R ( n 0 3 s ) I .
Re [ χ ( 1 ) ] = χ host ( 1 ) + N ћ μ 01 2 ( 2 ω 0 4 ω 0 2 + Γ 2 ) ,
Im [ χ ( 1 ) ] = N ћ μ 01 2 Γ ( 1 Γ 2 1 4 ω 0 2 + Γ 2 ) ,
= 1 + 4 π [ χ host ( 1 ) + χ dopant ( 1 ) ] .
n = n host + 2 π χ dopant n host ,
2 n 0 I n 0 R = 4 π Im [ χ dopant ( 1 ) ] / n host n host + ( 2 π Re [ χ dopant ( 1 ) ] / n host ) .
2 n 0 I n 0 R ( n 0 3 s ) R ( n 0 3 s ) I
I 0 = ( t 1 t 2 ) 2 I i exp [ 4 π d λ n 0 I ( 1 + sin 2 θ 2 n 0 R 2 ) ]
I 2 Ω = I 0 2 π V rms 2 λ d ( 1 + sin 2 θ 2 n 0 R 2 ) ( n 0 3 s ) I ,
( n 0 3 s ) I = λ d 4 π V rms 2 ( 1 + sin 2 θ 2 n 0 R 2 ) 1 I 2 Ω I sig .
( n 0 3 s ) I = λ d 4 π V rms 2 ( cos θ int ) I 2 Ω I sig .
P 1 ( 3 ) = χ 1133 ( 3 ) E 1 ω ( E 3 0 ) 2 = χ 1133 ( 3 ) E ω cos θ int ( E 3 0 ) 2 ,
P 3 ( 3 ) = χ 3333 ( 3 ) E 3 ω ( E 3 0 ) 2 = χ 3333 ( 3 ) E ω sin θ int ( E 3 0 ) 2 .
P p = P · p ˆ = ( P 1 ( 3 ) 1 ˆ + P 1 ( 3 ) 3 ˆ ) ( cos θ int 1 ˆ + sin θ int 3 ˆ ) = [ χ 1133 ( 3 ) cos 2 θ int + χ 3333 ( 3 ) sin 2 θ int ] E ω ( E 0 ) 2 .
χ p ( θ ) = χ 1133 ( 3 ) cos 2 θ int + χ 3333 ( 3 ) sin 2 θ int .
f i j k l = χ i j k l ( or ) / χ i j k l ( el ) ,
χ ( 3 ) = χ ( el ) + χ ( or ) .
f 1133 = 3 a a + 2 , f 3333 = 2 a 6 3 a + 6 .
χ 1133 ( 3 ) = χ 1133 ( el ) ( 1 + f 1133 ) ,
Im [ χ 1133 ( 3 ) ( ω ; ω , 0 , 0 ) ] = N 15 [ Im [ γ z z z z * ( ω ; ω , 0 , 0 ) ] 4 3 Im [ α z z * ( ω ; ω ) α z z * ( 0 ; 0 ) k θ ] .
α ( ω , ω ) = e 2 ћ g , n [ ( r i ) n g ( r j ) g n ω + ω n g + i Γ n g ( r j ) n g ( r i ) g n ω ω n g + i Γ n g ] × ρ g ( 0 ) ,
α ( ω ; ω ) = A ( 1 ω + ω 0 + i Γ 1 ω ω 0 + i Γ ) ,
α ( 0 ; 0 ) = A 2 ω 0 ω 0 2 + Γ 2 ,
A = e 2 h ( r i ) 1 g ( r j ) g 1 ρ g ( 0 ) .
α ( ω , ω ) α ( 0 ; 0 ) = 8 ω ω 0 2 Γ A 2 ( ω 0 2 + Γ 2 ) [ ( ω 0 + ω ) 2 + Γ 2 ] [ ( ω 0 ω ) 2 + Γ 2 ] ·
γ = K [ ( μ 01 ) 4 D 11 Δ μ 01 ( μ 01 ) 2 D 111 ] .
D 11 ( ω σ ; ω 1 , ω 2 , ω 3 ) = I ˆ 1 , 2 , 3 { [ ( ω 0 + i Γ ω σ ) ( ω 0 + i Γ ω 3 ) ( ω 0 + i Γ ω 1 ) ] 1 + [ ( ω 0 + i Γ ω 3 ) ( ω 0 + i Γ ω 2 ) ( ω 0 + i Γ ω 3 ) ] 1 + [ ( ω 0 i Γ ω σ ) ( ω 0 i Γ + ω 3 ) ( ω 0 i Γ + ω 1 ) ] 1 + [ ( ω 0 i Γ + ω 3 ) ( ω 0 + i Γ ω 2 ) ( ω 0 i Γ + ω 1 ) ] 1 } ,
D 11 = 96 Γ ω ω 0 [ 2 Γ 6 + Γ 4 ( ω 0 2 + 2 ω 2 ) + 2 Γ 2 ω 0 2 ( ω 2 2 ω 0 2 ) 3 ω 6 + 4 ω 0 4 ω 2 ω 0 2 ω 4 ] ( ω 0 2 + Γ 2 ) 2 [ ( ω 0 + ω ) 2 + Γ 2 ] 2 [ ( ω 0 ω ) 2 + Γ 2 ] 2 .

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