Abstract

We present experimental data that show that the greatly improved performance of a new class of photorefractive polymers [see Donckers et al., Opt. Lett. 18, 1044 ( 1993)] is too large to be explained by the simple electro-optic photorefractive effect alone. In these materials a photoconducting polymer host is doped with a small concentration of a sensitizer and a large concentration of a nonlinear optical chromophore that has orientational mobility at ambient temperatures. We present a theoretical model for a new orientational enhancement mechanism in which both the birefringence of the sample and the electro-optic coefficient are periodically modulated by the space-charge field itself. The predictions of this model for the size of the enhancement (which is greater than an order of magnitude in diffraction efficiency), the polarization anisotropy between p-polarized and s-polarized readout, and the presence of index modulation at twice the grating wave vector are in good agreement with the measured properties. This orientational enhancement mechanism should be important in any system in which the nonlinear optical chromophores have sufficient orientational mobility and dipole moment so as to be oriented by the space-charge field itself.

© 1994 Optical Society of America

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  1. M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
    [Crossref]
  2. S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
    [Crossref]
  3. S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).
  4. S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
    [Crossref] [PubMed]
  5. W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
    [Crossref]
  6. C. A. Walsh and W. E. Moerner, J. Opt. Soc. Am. B 9, 1642 (1992); J. Opt. Soc. Am. B 10, 753 (1993).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  9. Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992).
    [Crossref]
  10. Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
    [Crossref]
  11. K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
    [Crossref]
  12. A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
    [Crossref]
  13. D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, and A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
    [Crossref]
  14. J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
    [Crossref]
  15. A. Agranat and Y. Yacoby, J. Opt. Soc. Am. B 5, 1792 (1988).
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  16. A. Agranat, V. Layva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
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  17. See P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications[Springer-Verlag, Berlin, 1988 (Vol. I); 1989 (Vol. II)].
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  19. E. Ochoa, F. Vachss, and L. Hesselink, J. Opt. Soc. Am. A 3, 181 (1986).
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  20. N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
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  21. G. C. Valley and M. B. Klein, Opt. Eng. 22, 704 (1983).
    [Crossref]
  22. J. Feinberg, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 417.
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  23. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
    [Crossref]
  24. A. Twarowski, J. Appl. Phys. 65, 2833 (1989).
    [Crossref]
  25. J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
    [Crossref]
  26. M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, J. Opt. Soc. Am. B 7, 842 (1990).
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  27. J. W. Wu, J. Opt. Soc. Am. B 8, 142 (1991).
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  28. D. J. Williams, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), Chap. II-7.
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    [Crossref]
  30. B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976), p. 144.
  31. M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
    [Crossref]
  32. H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
    [Crossref]
  33. 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]

1993 (1)

1992 (8)

C. A. Walsh and W. E. Moerner, J. Opt. Soc. Am. B 9, 1642 (1992); J. Opt. Soc. Am. B 10, 753 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

S. M. Silence, C. A. Walsh, J. C. Scott, and W. E. Moerner, Appl. Phys. Lett. 61, 2967 (1992); W. E. Moerner, C. A. Walsh, S. M. Silence, R. J. Twieg, T. J. Matray, J. C. Scott, V. Y. Lee, R. D. Miller, F. Hache, D. M. Burland, and G. C. Bjorklund, Proc. Mat. Res. Soc. 277, 121 (1992).
[Crossref]

Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992).
[Crossref]

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[Crossref]

K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
[Crossref]

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[Crossref]

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

1991 (3)

1990 (4)

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, and A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
[Crossref]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, J. Opt. Soc. Am. B 7, 842 (1990).
[Crossref]

1989 (3)

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
[Crossref]

A. Twarowski, J. Appl. Phys. 65, 2833 (1989).
[Crossref]

A. Agranat, V. Layva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
[Crossref] [PubMed]

1988 (3)

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

A. Agranat and Y. Yacoby, J. Opt. Soc. Am. B 5, 1792 (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]

1986 (1)

1983 (1)

G. C. Valley and M. B. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

1979 (1)

N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
[Crossref]

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[Crossref]

Agranat, A.

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976), p. 144.

Bjorklund, G. C.

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

Boyd, G. T.

Buettner, A. V.

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[Crossref]

Burland, D. M.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[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]

Cui, Y.

Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992).
[Crossref]

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[Crossref]

Dirk, C. W.

Donckers, M.

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

Donckers, M. C. J. M.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

Doran, G. E.

Ducharme, S.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
[Crossref] [PubMed]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

Ebert, M.

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

Ender, D. A.

Feinberg, J.

J. Feinberg, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 417.
[Crossref]

Francis, C. V.

Garmire, E. M.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

Glass, A. M.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

D. D. Nolte, D. H. Olson, G. E. Doran, W. H. Knox, and A. M. Glass, J. Opt. Soc. Am. B 7, 2217 (1990).
[Crossref]

Hache, F.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

Hall, H. K.

K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
[Crossref]

Hampsch, H. L.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
[Crossref]

Hesselink, L.

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]

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]

Klein, M. B.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

G. C. Valley and M. B. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

Knox, W. H.

Koehler, S. D.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[Crossref]

Kost, A.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
[Crossref]

Kuzyk, M. G.

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, J. Opt. Soc. Am. B 7, 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]

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]

Layva, V.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
[Crossref]

Matray, T. J.

Miller, R. D.

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

Millerd, J. E.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

Moerner, W. E.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

C. A. Walsh and W. E. Moerner, J. Opt. Soc. Am. B 9, 1642 (1992); J. Opt. Soc. Am. B 10, 753 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, and W. E. Moerner, Appl. Phys. Lett. 61, 2967 (1992); W. E. Moerner, C. A. Walsh, S. M. Silence, R. J. Twieg, T. J. Matray, J. C. Scott, V. Y. Lee, R. D. Miller, F. Hache, D. M. Burland, and G. C. Bjorklund, Proc. Mat. Res. Soc. 277, 121 (1992).
[Crossref]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
[Crossref] [PubMed]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

Mullen, R. A.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

Nolte, D. D.

Ochoa, E.

Olson, D. H.

Padias, A. B.

K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
[Crossref]

Partovi, A.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976), p. 144.

Peyghambarian, N.

K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
[Crossref]

Prasad, P. N.

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[Crossref]

Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992).
[Crossref]

Rytz, D.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

Schildkraut, J. S.

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[Crossref]

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[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]

Scott, J. C.

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

S. M. Silence, C. A. Walsh, J. C. Scott, and W. E. Moerner, Appl. Phys. Lett. 61, 2967 (1992); W. E. Moerner, C. A. Walsh, S. M. Silence, R. J. Twieg, T. J. Matray, J. C. Scott, V. Y. Lee, R. D. Miller, F. Hache, D. M. Burland, and G. C. Bjorklund, Proc. Mat. Res. Soc. 277, 121 (1992).
[Crossref]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
[Crossref] [PubMed]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

Silence, S. M.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

S. M. Silence, C. A. Walsh, J. C. Scott, and W. E. Moerner, Appl. Phys. Lett. 61, 2967 (1992); W. E. Moerner, C. A. Walsh, S. M. Silence, R. J. Twieg, T. J. Matray, J. C. Scott, V. Y. Lee, R. D. Miller, F. Hache, D. M. Burland, and G. C. Bjorklund, Proc. Mat. Res. Soc. 277, 121 (1992).
[Crossref]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

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]

Smith, B. A.

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

Sohn, J. E.

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, J. Opt. Soc. Am. B 7, 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]

Soskin, M.

N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
[Crossref]

Stählein, M.

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

Tamura, K.

K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
[Crossref]

Torkelson, J. M.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
[Crossref]

Trend, J. E.

Twarowski, A.

A. Twarowski, J. Appl. Phys. 65, 2833 (1989).
[Crossref]

Twieg, R. J.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
[Crossref] [PubMed]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

Vachss, F.

Valley, G. C.

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

G. C. Valley and M. B. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
[Crossref]

Volksen, W.

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

Walsh, C.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

Walsh, C. A.

M. C. J. M. Donckers, S. M. Silence, C. A. Walsh, F. Hache, D. M. Burland, W. E. Moerner, and R. J. Twieg, Opt. Lett. 18, 1044 (1993).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, T. J. Matray, R. J. Twieg, F. Hache, G. C. Bjorklund, and W. E. Moerner, Opt. Lett. 17, 1107 (1992).
[Crossref] [PubMed]

C. A. Walsh and W. E. Moerner, J. Opt. Soc. Am. B 9, 1642 (1992); J. Opt. Soc. Am. B 10, 753 (1993).
[Crossref]

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[Crossref]

S. M. Silence, C. A. Walsh, J. C. Scott, and W. E. Moerner, Appl. Phys. Lett. 61, 2967 (1992); W. E. Moerner, C. A. Walsh, S. M. Silence, R. J. Twieg, T. J. Matray, J. C. Scott, V. Y. Lee, R. D. Miller, F. Hache, D. M. Burland, and G. C. Bjorklund, Proc. Mat. Res. Soc. 277, 121 (1992).
[Crossref]

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

Wechsler, B.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

Williams, D. J.

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[Crossref]

D. J. Williams, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), Chap. II-7.

Wong, G. K.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
[Crossref]

Wu, J. W.

Yacoby, Y.

Yang, J.

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
[Crossref]

Yariv, A.

Zhang, Y.

Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992).
[Crossref]

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[Crossref]

Ann. Rev. Mater. Sci. (1)

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, Ann. Rev. Mater. Sci. 18, 165 (1988), and references therein.
[Crossref]

Appl. Phys. Lett. (7)

M. Stählein, D. M. Burland, M. Ebert, R. D. Miller, B. A. Smith, R. J. Twieg, W. Volksen, and C. A. Walsh, Appl. Phys. Lett. 61, 1626 (1992).
[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]

S. M. Silence, C. A. Walsh, J. C. Scott, and W. E. Moerner, Appl. Phys. Lett. 61, 2967 (1992); W. E. Moerner, C. A. Walsh, S. M. Silence, R. J. Twieg, T. J. Matray, J. C. Scott, V. Y. Lee, R. D. Miller, F. Hache, D. M. Burland, and G. C. Bjorklund, Proc. Mat. Res. Soc. 277, 121 (1992).
[Crossref]

Y. Cui, Y. Zhang, P. N. Prasad, J. S. Schildkraut, and D. J. Williams, Appl. Phys. Lett. 61, 2132 (1992).
[Crossref]

K. Tamura, A. B. Padias, H. K. Hall, and N. Peyghambarian, Appl. Phys. Lett. 60, 1803 (1992).
[Crossref]

A. Partovi, A. Kost, E. M. Garmire, G. C. Valley, and M. B. Klein, Appl. Phys. Lett. 56, 1089 (1990).
[Crossref]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, Appl. Phys. Lett. 57, 2776 (1990).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[Crossref]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 and 961 (1979).
[Crossref]

J. Appl. Phys. (2)

A. Twarowski, J. Appl. Phys. 65, 2833 (1989).
[Crossref]

J. S. Schildkraut and A. V. Buettner, J. Appl. Phys. 72, 1888 (1992).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (6)

Opt. Eng. (1)

G. C. Valley and M. B. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

Opt. Lett. (3)

Phys. Rev. B (1)

Y. Zhang, Y. Cui, and P. N. Prasad, Phys. Rev. B 46, 9900 (1992).
[Crossref]

Phys. Rev. Lett. (1)

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
[Crossref] [PubMed]

Polym. Commun. (1)

H. L. Hampsch, J. Yang, G. K. Wong, and J. M. Torkelson, Polym. Commun. 30, 40 (1989).
[Crossref]

Other (7)

B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976), p. 144.

J. Feinberg, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 417.
[Crossref]

D. J. Williams, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), Chap. II-7.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, and R. J. Twieg, in Nonlinear Optical Properties of Organic Materials IV, K. D. Singer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1560, 278 (1991).
[Crossref]

S. M. Silence, F. Hache, M. Donckers, C. A. Walsh, D. M. Burland, G. C. Bjorklund, R. J. Twieg, and W. E. Moerner, in Nonlinear Optical Properties of Advanced Materials, S. Etemad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1852, 253 (1993).
[Crossref]

S. M. Silence, M. C. J. M. Donckers, C. A. Walsh, D. M. Burland, R. J. Twieg, and W. E. Moerner, “Optical properties of poly(N-vinylcarbazole)-based guest–host photorefractive polymer systems,” Appl. Opt. (to be published).

See P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications[Springer-Verlag, Berlin, 1988 (Vol. I); 1989 (Vol. II)].
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Tilted grating geometry used for the PR measurements. The wave vector of the grating written by beams 1 and 2 (angles of incidence θ1 and θ2, defined inside the sample) is directed along KG, which forms an angle θG with the direction of the external bias field EB. PR gratings produced at 1KG are read out with beam 3 (diffracted into beam 4), and PR gratings produced at 2KG are read out with beam 3 (diffracted into beam 4).

Fig. 2
Fig. 2

Esco2 determined from ηp (filled circles) and ηs (open circles) for PVK:FDEANST:TNF with Eqs. (4) and (5) (n3r13 = −1.7 pm/V), shown as a function of θG (bottom axis) and KG (top axis). The solid curve is the square of the projection of EB along the grating wave vector.

Fig. 3
Fig. 3

Illustration of the enhancement of the PR diffraction efficiency induced by dynamic orientation. The diffraction efficiencies ηs and ηp predicted by the simple electro-optic theory (circles) from Eqs. (4) and (5) and the diffraction efficiencies ηs and ηp predicted by the orientational enhancement theory (squares) from Eqs. (23) and (24) are shown as a function of θG (bottom axis) and KG (top axis). The space-charge field Esco is assumed to reach its maximum value Esco = EB cos θG; λ = 676 nm, d = 125 μm, and the values of n3r33, n3r33 = (1/3)/n3r33, C, and A are given in Appendix A.

Fig. 4
Fig. 4

Ratio of the diffraction efficiency for p- and s-polarized probe beams shown as a function of θG for PVK:FDEANST:TNF (filled circles), bisA-NAT:DEH (open square), and bisA-NPDA:DEH (open triangle). The dashed line is the predicted ratio from the simple electro-optic theory [Eq. (6), assuming that r33 = 3r13], and the solid line is the ratio predicted by the orientational enhancement theory for the 1KG grating [Eq. (25)] for the experimentally measured value of C/A = −4.6.

Fig. 5
Fig. 5

Diffraction efficiency for light phase matched for scattering from the 1KG component of the PR grating (open circles) and the 2KG component (closed circles) for PVK:FDEANST:TNF at EB = 40 V/μm. The grating is written and the 1KG component probed at λ0 = 676 nm and the 2KG component is probed at λ0 = 782 nm. The writing beams are turned on at t = 0, and both the writing beams and the external field are turned off at t = 10 s. η1K decays to its pre-(t = 0) baseline after 30 s, while η2K remains well above baseline for much longer times.

Fig. 6
Fig. 6

Values of CEO(1 + δ) (filled circles) and CBR(2δ) (open circles) determined by interferometric measurements shown as a function of the frequency of the applied ac field. The solid curves are fits to the data with δ = f−0.23. (b) Value of for PVK:FDEANST:TNF determined by capacitance measurements shown on a log–log scale over the full measurement range and on a linear–linear scale over the frequency range of the interferometric measurements. The line is a fit to the data with a power-law function assumed for the frequency dependence with the exponent −0.23.

Equations (40)

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Δ χ = · ( R · E sco K ˆ G ) · ,
R = [ 0 0 r 13 0 0 r 13 0 0 r 33 0 r 13 0 r 13 0 0 0 0 0 ] .
η = | H ( e ˆ 4 * · e ˆ 3 ) ( e ˆ 4 * · Δ χ · e ˆ 3 ) | 2 ,
η s , simple EO = ( H n 4 r 13 cos θ G E sco ) 2 .
η p , simple EO = { H n 4 cos ( θ 2 θ 1 ) E sco × [ r 13 cos θ 1 cos θ 2 cos θ G + r 13 sin ( θ 1 + θ 2 ) sin θ G + r 33 sin θ 1 sin θ 2 cos θ G ] } 2 .
( η p η s ) simple EO = cos 2 ( θ 2 θ 1 ) [ cos θ 1 cos 2 + sin ( θ 1 + θ 2 ) tan θ G + ( r 33 r 13 ) sin θ 1 sin θ 2 ] 2 ,
Δ χ z z ( 1 , BR ) ( ω ; ω ) = N ( α ( ω ) α ( ω ) ) ( 2 45 ) ( μ E pole k B T ) 2 C BR E pole 2 ,
Δ χ y y ( 1 , BR ) ( ω ; ω ) = Δ χ x x ( 1 , BR ) ( ω ; ω ) A BR E pole 2 = ( 1 / 2 ) Δ χ z z ( 1 , BR ) ( ω ; ω ) = ( 1 / 2 ) C BR E pole 2 ,
Δ n z , BR = ( 1 / 2 n ) C BR E pole 2 = ( 1 / 2 n ) C BR E T 2 ,
Δ n x , BR = ( 1 / 4 n ) C BR E pole 2 = ( 1 / 4 n ) C BR E T 2 ,
Δ χ z z z ( 2 ) ( ω ; ω , 0 ) = N β 333 μ 5 k B T E pole ,
Δ χ x x z ( 2 ) ( ω ; ω , 0 ) = N β 333 μ 15 k B T E pole .
Δ n z , EO = ( 1 / 2 n ) Δ χ z z z ( 2 ) E T ( 1 / 2 n ) C EO E pole E T = ( 1 / 2 n ) C EO E T 2 ,
Δ n x , EO = ( 1 / 2 n ) Δ χ x x z ( 2 ) E T ( 1 / 2 n ) A EO E pole E T = ( 1 / 6 n ) C EO E pole E T = ( 1 / 6 n ) C EO E T 2 ,
Δ χ = [ A 0 0 0 A 0 0 0 C ] E T 2 ,
E T ( r ) = [ E sc ( r ) sin θ G ] x ˆ + [ E B + E sc ( r ) cos θ G ] z ˆ ,
θ p = arctan [ E sc ( r ) sin θ G E B + E sc ( r ) cos θ G ] .
U = [ cos θ p 0 sin θ p 0 1 0 sin θ p 0 cos θ p ] .
Δ χ lab = [ A cos 2 θ p + C sin 2 θ p 0 ( C A ) cos θ p sin θ p 0 A 0 ( C A ) cos θ p sin θ p 0 A sin 2 θ p + C cos 2 θ p ] × E T 2 .
Δ χ = [ A + ( C A ) γ 2 sin 2 θ G 0 ( C A ) [ γ sin θ G ( γ 2 / 2 ) sin 2 θ G ] 0 A 0 ( C A ) [ γ sin θ G ( γ 2 / 2 ) sin 2 θ G ] 0 C ( C A ) γ 2 sin 2 θ G ] E T 2 .
E T 2 ( r ) = E sco 2 exp ( 2 i K G · r ) + E B 2 + 2 E B E sco exp ( i K G · r ) cos θ G .
Δ χ 1 K = [ 2 A cos θ G 0 ( C A ) sin θ G 0 2 A cos θ G 0 ( C A ) sin θ G 0 2 C cos θ G ] × E B E sco exp ( i K G · r ) .
η s , 1 K = [ H E B E sco ( 2 A cos θ G ) ] 2 ,
η p , 1 K = { H E B E sco cos ( θ 2 θ 1 ) × [ 2 A cos θ 1 cos θ 2 cos θ G + ( C A ) sin ( θ 1 + θ 2 ) sin θ G + 2 C sin θ 1 sin θ 2 cos θ G ] } 2 .
( η p η s ) 1 K = cos 2 ( θ 2 θ 1 ) [ cos θ 1 cos θ 2 + 1 2 ( C A 1 ) sin ( θ 1 + θ 2 ) tan θ G + C A sin θ 1 sin θ 2 ] 2 .
Δ χ 2 K = [ A + ( C A ) sin 2 θ G 0 ( C A ) ( 1 / 2 ) sin 2 θ G 0 A 0 ( C A ) ( 1 / 2 ) sin 2 θ G 0 C + ( A C ) sin 2 θ G ] × E sco 2 exp ( i 2 K G · r ) .
n s , 2 K = ( H E sco 2 A ) 2 ,
η p , 2 K = cos 2 ( θ 2 θ 1 ) { H E sco 2 [ A cos θ 1 cos θ 2 + ( C A ) cos ( θ 1 + θ 2 ) sin 2 θ G + ( 1 / 2 ) ( C A ) sin ( θ 1 + θ 2 ) sin 2 θ G + C sin θ 1 sin θ 2 ] } 2 .
( η p η s ) 2 K = cos 2 ( θ 2 θ 1 ) [ cos θ 1 cos θ 2 + ( C A 1 ) cos ( θ 1 + θ 2 ) sin 2 θ G + ( 1 2 ) ( C A 1 ) cos ( θ 1 + θ 2 ) sin 2 2 θ G + ( C A ) sin θ 1 sin θ 2 ] 2 .
C = C EO + C BR = [ ( 2.12 ± 0.06 ) + ( 4.11 ± 1.0 ) ] × 10 19 m 2 / V 2 ,
A = A E O + C BR = [ ( 0.71 ± 0.02 ) + ( 2.06 ± 0.5 ) ] × 10 19 m 2 / V 2 .
Δ ϕ = 2 2 S ac , rms S full , p p ,
Δ n = ( λ 0 2 π ) ( cos θ d ) Δ ϕ ,
Δ n = Δ n x + ( Δ n z Δ n x ) sin 2 θ .
Δ n = 1 2 n [ ( 1 + 2 sin 2 θ ) C EO 3 E pole E T + ( 3 sin 2 θ 1 ) C BR 2 E pole 2 ] ,
Δ n = 1 2 n { ( 1 + 2 sin 2 θ ) C EO 3 × [ E dc + δ ( Ω ) E ac sin Ω t ] ( E dc + E ac sin Ω t ) + ( 3 sin 2 θ 1 ) C BR 2 [ E dc + δ ( Ω ) E ac sin Ω t ] × [ E dc + δ ( Ω ) E ac sin Ω t ] } .
{ [ C EO 3 ( 1 + δ ) C BR 2 ( 2 δ ) ] + [ 2 C EO 3 ( 1 + δ ) 3 C BR 2 ( 2 δ ) ] sin 2 θ } E dc = 2 n 2 λ cos θ π V ac S ac , rms 1 f S full , p p .
C EO = ( 2.12 ± 0.06 ) × 10 19 m 2 / V 2 ,
C BR = ( 4.1 ± 1.0 ) × 10 19 m 2 / V 2 ,
n 3 r 33 = C EO E dc n = 5.0 pm / V .

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