Abstract

We investigate in detail the grating properties of a recently discovered organic photorefractive polymer as a function of electric field by using two-beam coupling. Using an oblique-incidence geometry, we present measurements of index and absorption grating phase relative to the intensity interference pattern as well as measurements of the amplitude of both the absorption and index gratings. We find that in low electric fields a weak in-phase grating (possibly photochromic) and the low electro-optic coefficient prevent observation of a phase-shifted photorefractive grating. However, in moderate-to-high electric fields a much stronger photorefractive index grating with a phase shift approaching 90° dominates. The presence of an index grating with a 90° phase shift at high fields provides strong evidence that these polymers are indeed photorefractive.

© 1992 Optical Society of America

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References

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  1. K. Sutter, J. Hullinger, P. Günter, Solid State Commun. 74, 867 (1990).
    [CrossRef]
  2. S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), postdeadline paper PDP28-1, p. 359.
  3. S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, Phys. Rev. Lett. 66, 1846 (1991).
    [CrossRef] [PubMed]
  4. J. S. Schildkraut, Appl. Phys. Lett. 58, 340 (1991).
    [CrossRef]
  5. J. Feinberg, Phys. Today 41(10), 46 (1988).
    [CrossRef]
  6. SeeP. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II (Springer-Verlag, Berlin, 1988, 1989).
    [CrossRef]
  7. M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
    [CrossRef]
  8. D. Z. Anderson, D. M. Lininger, J. Feinberg, Opt. Lett. 12, 123 (1987).
    [CrossRef] [PubMed]
  9. D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635 (1989).
    [CrossRef]
  10. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  11. J. Feinberg, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 417.
  12. J.-P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
    [CrossRef]
  13. S. I. Stepanov, M. P. Petrov, Ref. 6, Vol. I, Chap. 9.
  14. G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
    [CrossRef]
  15. H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
    [CrossRef]
  16. M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
    [CrossRef]
  17. W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]
  18. V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
    [CrossRef]
  19. M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. B 43, 61 (1987).
    [CrossRef]
  20. M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
    [CrossRef]
  21. K. Sutter, P. Günter, J. Opt. Soc. Am. B 7, 2274 (1990).
    [CrossRef]
  22. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]
  23. R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
    [CrossRef] [PubMed]
  24. R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
    [CrossRef]
  25. See, for example, G. C. Valley, J. F. Lam, Ref. 6, Vol. I, Chap. 3.
  26. G. C. Valley, M. B. Klein, Opt. Eng. 22, 704 (1983).
    [CrossRef]
  27. A. Twarowski, J. Appl. Phys. 65, 2833 (1989),derived the Esc expected in the case of Onsager geminate recombination with a field-independent mobility.
    [CrossRef]
  28. N. V. Kukhtarev, V. B. Markov, M. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
    [CrossRef]
  29. P. N. Prasad, D. J. Williams, in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 7, p. 132.

1991 (3)

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

J. S. Schildkraut, Appl. Phys. Lett. 58, 340 (1991).
[CrossRef]

R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
[CrossRef]

1990 (3)

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[CrossRef]

K. Sutter, P. Günter, J. Opt. Soc. Am. B 7, 2274 (1990).
[CrossRef]

K. Sutter, J. Hullinger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

1989 (3)

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635 (1989).
[CrossRef]

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

A. Twarowski, J. Appl. Phys. 65, 2833 (1989),derived the Esc expected in the case of Onsager geminate recombination with a field-independent mobility.
[CrossRef]

1988 (3)

R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
[CrossRef] [PubMed]

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

J. Feinberg, Phys. Today 41(10), 46 (1988).
[CrossRef]

1987 (2)

1985 (1)

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

1983 (1)

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

1982 (1)

1981 (1)

J.-P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

1979 (2)

V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

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

1969 (1)

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

Amrhein, P.

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635 (1989).
[CrossRef]

D. Z. Anderson, D. M. Lininger, J. Feinberg, Opt. Lett. 12, 123 (1987).
[CrossRef] [PubMed]

Bacher, G. D.

Bjorklund, G. C.

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Bräuchle, C.

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. B 43, 61 (1987).
[CrossRef]

Burland, D. M.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Bylsma, R. B.

Cronin-Golomb, M.

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

Cudney, R. S.

Ducharme, S.

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

S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), postdeadline paper PDP28-1, p. 359.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Eich, M.

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

Eichler, H. J.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
[CrossRef]

Feinberg, J.

R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
[CrossRef]

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635 (1989).
[CrossRef]

J. Feinberg, Phys. Today 41(10), 46 (1988).
[CrossRef]

D. Z. Anderson, D. M. Lininger, J. Feinberg, Opt. Lett. 12, 123 (1987).
[CrossRef] [PubMed]

J. Feinberg, Opt. Lett. 7, 486 (1982).
[CrossRef] [PubMed]

J. Feinberg, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 417.

Gehrtz, M.

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. B 43, 61 (1987).
[CrossRef]

Glass, A. M.

Günter, P.

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[CrossRef]

K. Sutter, P. Günter, J. Opt. Soc. Am. B 7, 2274 (1990).
[CrossRef]

K. Sutter, J. Hullinger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
[CrossRef]

Huignard, J.-P.

J.-P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Hullinger, J.

K. Sutter, J. Hullinger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

Klein, M. B.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

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

Kogelnik, H.

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

Kondilenko, V.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Kukhtarev, N. V.

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

Lam, J. F.

See, for example, G. C. Valley, J. F. Lam, Ref. 6, Vol. I, Chap. 3.

Lininger, D. M.

Markov, V.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Markov, V. B.

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

Marrakchi, A.

J.-P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Moerner, W. E.

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

S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), postdeadline paper PDP28-1, p. 359.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Mullen, R. A.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

Odulov, S.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Olson, D. H.

Petrov, M. P.

S. I. Stepanov, M. P. Petrov, Ref. 6, Vol. I, Chap. 9.

Pierce, R. M.

Pinsl, J.

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. B 43, 61 (1987).
[CrossRef]

Pohl, D. W.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
[CrossRef]

Prasad, P. N.

P. N. Prasad, D. J. Williams, in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 7, p. 132.

Reck, B.

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

Rytz, D.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

Schildkraut, J. S.

J. S. Schildkraut, Appl. Phys. Lett. 58, 340 (1991).
[CrossRef]

Scott, J. C.

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

S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), postdeadline paper PDP28-1, p. 359.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Soskin, M.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

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

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, Ref. 6, Vol. I, Chap. 9.

Sutter, K.

K. Sutter, J. Hullinger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

K. Sutter, P. Günter, J. Opt. Soc. Am. B 7, 2274 (1990).
[CrossRef]

Twarowski, A.

A. Twarowski, J. Appl. Phys. 65, 2833 (1989),derived the Esc expected in the case of Onsager geminate recombination with a field-independent mobility.
[CrossRef]

Twieg, R. J.

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

S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), postdeadline paper PDP28-1, p. 359.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Valley, G. C.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

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

See, for example, G. C. Valley, J. F. Lam, Ref. 6, Vol. I, Chap. 3.

Vinetskii, V. L.

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

Walsh, C.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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]

Wechsler, B.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

Williams, D. J.

P. N. Prasad, D. J. Williams, in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 7, p. 132.

Willson, C. G.

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

Yoon, D. Y.

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

Zha, M. Z.

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, B. Wechsler, Annu. Rev. Mater. Sci. 18, 165 (1988).
[CrossRef]

Appl. Phys. B (1)

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. B 43, 61 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

J. S. Schildkraut, Appl. Phys. Lett. 58, 340 (1991).
[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, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[CrossRef]

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. 25, 635 (1989).
[CrossRef]

J. Appl. Phys. (3)

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

M. Eich, B. Reck, D. Y. Yoon, C. G. Willson, G. C. Bjorklund, J. Appl. Phys. 66, 3241 (1989).
[CrossRef]

A. Twarowski, J. Appl. Phys. 65, 2833 (1989),derived the Esc expected in the case of Onsager geminate recombination with a field-independent mobility.
[CrossRef]

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

Opt. Acta (1)

V. Kondilenko, V. Markov, S. Odulov, M. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Opt. Commun. (1)

J.-P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Opt. Eng. (1)

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

Opt. Lett. (3)

Phys. Rev. Lett. (1)

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

Phys. Today (1)

J. Feinberg, Phys. Today 41(10), 46 (1988).
[CrossRef]

Solid State Commun. (1)

K. Sutter, J. Hullinger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

Other (8)

S. Ducharme, J. C. Scott, R. J. Twieg, W. E. Moerner, OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), postdeadline paper PDP28-1, p. 359.

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

J. Feinberg, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 417.

W. E. Moerner, C. Walsh, J. C. Scott, S. Ducharme, D. M. Burland, G. C. Bjorklund, 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. I. Stepanov, M. P. Petrov, Ref. 6, Vol. I, Chap. 9.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings, Vol. 50 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1986).
[CrossRef]

See, for example, G. C. Valley, J. F. Lam, Ref. 6, Vol. I, Chap. 3.

P. N. Prasad, D. J. Williams, in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 7, p. 132.

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Figures (4)

Fig. 1
Fig. 1

Geometry used for writing the grating and determining the grating phase by using two-beam coupling. Edc is the externally applied dc poling field, and the space-charge Esc is in the direction of the grating wave vector Kg. The angles are defined in the text.

Fig. 2
Fig. 2

Transmitted powers for (a) beam 1 and (b) beam 2 as the grating is translated. The rate of translation is 3.2 μm/s. Motion begins at time 0 and stops at ≃2.1 s. These data were taken in the high-field regime (Eg,dc = 37 kV/cm), and the shape of the modulations indicates an index grating with 90° phase shift. Trace (b) has been offset downward by 0.02 V for clarity.

Fig. 3
Fig. 3

Phase shift of the index grating (relative to the intensity grating) as a function of applied electric field along the grating wave vector (symbols). At zero field the phase shift is near zero, indicating a nonphotorefractive grating. As the field increases, the phase of the index grating increases to 90° as the photorefractive mechanism becomes dominant. Possible sources of the scatter in the points are discussed in the text. Data are collected by using several samples. The solid curve is the phase shift appropriate for a conventional inorganic photorefractive material [Eq. (14)].

Fig. 4
Fig. 4

Normalized grating amplitudes for both the index (P) and absorption (A) gratings as a function of applied electric field along the grating wave vector for the dimensionless units of Eqs. (5). The amplitude of the absorption grating is unaffected by the applied field, whereas the index grating increases with the field and is more than 10 times greater than the absorption grating at high fields.

Equations (14)

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

n ( r ) = n 0 + Δ n cos ( K g · r ϕ p ) , α ( r ) = α 0 + Δ α cos ( K g · r ϕ A ) ,
E ( 1 R ) = E 01 R 1 exp [ i ( ω t k 1 · r ) ] , E ( 1 S ) = E 01 S 1 exp [ i ( ω t k 2 · r ) ] ,
R 1 = exp [ α 0 d / ( 2 cos Θ 1 ) ] ,
S 1 = D ( cos Θ 1 / cos Θ 2 ) 1 / 2 × [ i P exp ( i ϕ P ) + A exp ( i ϕ A ) ] ,
P = ( r ̂ · ŝ ) π d Δ n λ υ ( cos Θ 2 cos Θ 1 ) 1 / 2 , A = ( r ̂ · ŝ ) d Δ α 2 ( cos Θ 2 cos Θ 1 ) 1 / 2 ,
E ( 2 R ) = E 02 R 2 exp [ i ( ω t k 2 · r ) ] , E ( 2 S ) = E 02 S 2 exp [ i ( ω t k 2 · r ) ] ,
S 2 = D ( cos Θ 2 / cos Θ 1 ) 1 / 2 [ i P exp ( + i ϕ P ) + A exp ( + i ϕ A ) ,
E ( 1 T ) = R 1 E 02 D E 02 { ( cos Θ 2 / cos Θ 1 ) 1 / 2 [ i P exp ( + i ϕ P ) + A exp ( + i ϕ A ) ] } , E ( 2 T ) = R 2 E 02 D E 01 { ( cos Θ 1 / cos Θ 2 ) 1 / 2 [ i P exp ( i ϕ P ) + A exp ( i ϕ A ) ] } ,
P ( 1 ) = ( 1 / 2 ) n 0 0 cos Θ 1 × [ R 1 2 E 01 2 D R 1 E 01 E 02 ( cos Θ 2 / cos Θ 1 ) 1 / 2 × ( 2 A cos ϕ A 2 P sin ϕ P ) ] , P ( 2 ) = ( 1 / 2 ) n 0 0 cos Θ 2 × [ R 2 2 E 02 2 D R 2 E 01 E 02 ( cos Θ 1 / cos Θ 2 ) 1 / 2 × ( 2 A cos ϕ A + 2 P sin ϕ P ) ] ,
P ( + ) = P g [ ( P t 1 + P t 2 P g ) 2 A cos ϕ A ] ,
P ( ) = P g [ ( P t 1 P t 2 P g ) + 2 P sin ϕ P ] ,
P ( + ) ( ξ ) = P g { 1.09 2 A cos [ ϕ A + 2 π ξ cos ( Θ g ) / Λ g ] } ,
P ( ) ( ξ ) = P g { 0.29 + 2 P sin [ ϕ P + 2 π ξ cos ( Θ g ) / Λ g ] } ,
phase ( E sc ) = phase [ m ( E g , dc + i E d ) 1 + E d / E q i E g , dc / E q ] ,

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