Abstract

Polarization conversion that is photoinduced by means of spatially oscillating photovoltaic currents in bulk LiNbO3:Fe is studied both experimentally and theoretically. We measured nearly complete ordinary-to-extraordinary conversion for input ordinary beam diameters greater than ∼200 μm and almost no conversion for beam diameters less than ∼60 μm. The extraordinary light was scattered perpendicular to the optic axis into a bow-tie-shaped distribution. To analyze the effect, we use the bulk photovoltaic model to derive coupled-wave equations for arbitrary-direction two-beam coupling (one ordinary wave, one extraordinary wave) and multiple-beam coupling (one ordinary wave, multiple extraordinary waves). We include the effect of beam diameter by using an overlap integral of the interacting beam profiles. The theory correctly models both the experimental three-dimensional distribution of extraordinary scattered light and the total polarization conversion as a function of beam diameter.

© 1992 Optical Society of America

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  1. E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).
  2. E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3: Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).
  3. A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photovoltaic process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [Crossref]
  4. V. I. Belinicher and B. I. Sturman, “The photogalvanic effect in media lacking a center of symmetry,” Sov. Phys. Usp. 23, 199–223 (1980).
    [Crossref]
  5. B. Sturman, “The photogalvanic effect—a new mechanism of nonlinear wave interaction in electrooptic crystals,” Sov. J. Quantum Electron. 10, 276–278 (1980).
    [Crossref]
  6. A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
    [Crossref]
  7. R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
    [Crossref]
  8. S. G. Odoulov, “Anisotropic scattering in photorefractive crystals: comment,” J. Opt. Soc. Am. B 4, 1333–1334 (1987).
    [Crossref]
  9. S. G. Odoulov, “Vectorial interactions in photovoltaic media,” Ferroelectrics 91, 213–225 (1989).
    [Crossref]
  10. S. G. Odoulov and M. S. Soskin, “Amplification, oscillation, and light-induced scattering in photorefractive crystals,” in Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), pp. 5–44.
    [Crossref]
  11. E. Kratzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
    [Crossref]
  12. E. Kratzig and O. F. Schirmer, “Photorefractive centers in electro-optic crystals,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 131–166.
    [Crossref]
  13. N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [Crossref]
  14. B. I. Sturman, “Photovoltaic effect, diffusion and drift of nonequilibrium electrons having finite mean free paths,” Sov. Phys. JETP 56, 1116–1121 (1982).
  15. B. Sturman, “Dynamic holography effects in ferroelectrics induced by spatially oscillating photovoltaic currents,” J. Opt. Soc. Am. B 8, 1333–1340 (1991).
    [Crossref]
  16. R. von Baltz, Ch. Lingerfelder, and R. Rupp, “Nonlocal photovoltaic response function for the interpretation of hologram writing in ferroelectric crystals,” Appl. Phys. A 32, 13–18 (1983).
    [Crossref]
  17. L. Young, M. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
    [Crossref]
  18. M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
    [Crossref]
  19. R. A. Rupp and F. W. Drees, “Light-induced scattering in photorefractive crystals,” Appl. Phys. B 39, 223–229 (1986).
    [Crossref]
  20. G. Zhang, Q.-X. Li, P.-P. Ho, S. Liu, Z. K. Wu, and R. R. Alfano, “Dependence of specklon size on the laser beam size via photo-induced light-scattering in LiNbO3:Fe,” Appl. Opt. 25, 2955–2959 (1986).
    [Crossref]
  21. S. G. Odoulov, K. Belabaev, and I. Kiseleva, “Degenerate stimulated parametric scattering in LiTaO3,” Opt. Lett. 10, 31–33 (1985).
    [Crossref] [PubMed]
  22. G. Zhang, Q. X. Li, P. P. Ho, R. R. Alfano, S. Liu, and Z. Wu, “Degenerate stimulated parametric scattering in LiNbO3: Fe,” J. Opt. Soc. Am. B 4, 882–885 (1987).
    [Crossref]
  23. N. V. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3in external electric field,” Opt. Commun. 23, 338–343 (1987).
    [Crossref]
  24. N. V. Kukhtarev, V. B. Markov, and S. G. Odoulov, “Nonstationary energy exchange during interaction between two light beams in electrooptic crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).
  25. J. M. Heaton and L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–408 (1985).
    [Crossref]
  26. L. Solymar and J. M. Heaton, “Transient energy transfer in photorefractive materials; an analytic solution,” Opt. Commun. 51, 76–78 (1985).
    [Crossref]
  27. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, London, 1957).
  28. A. R. Billings, Tensor Properties of Materials (Wiley, London, 1969).

1991 (1)

1989 (1)

S. G. Odoulov, “Vectorial interactions in photovoltaic media,” Ferroelectrics 91, 213–225 (1989).
[Crossref]

1987 (4)

A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
[Crossref]

S. G. Odoulov, “Anisotropic scattering in photorefractive crystals: comment,” J. Opt. Soc. Am. B 4, 1333–1334 (1987).
[Crossref]

G. Zhang, Q. X. Li, P. P. Ho, R. R. Alfano, S. Liu, and Z. Wu, “Degenerate stimulated parametric scattering in LiNbO3: Fe,” J. Opt. Soc. Am. B 4, 882–885 (1987).
[Crossref]

N. V. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3in external electric field,” Opt. Commun. 23, 338–343 (1987).
[Crossref]

1986 (2)

1985 (4)

S. G. Odoulov, K. Belabaev, and I. Kiseleva, “Degenerate stimulated parametric scattering in LiTaO3,” Opt. Lett. 10, 31–33 (1985).
[Crossref] [PubMed]

J. M. Heaton and L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–408 (1985).
[Crossref]

L. Solymar and J. M. Heaton, “Transient energy transfer in photorefractive materials; an analytic solution,” Opt. Commun. 51, 76–78 (1985).
[Crossref]

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[Crossref]

1983 (2)

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3: Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

R. von Baltz, Ch. Lingerfelder, and R. Rupp, “Nonlocal photovoltaic response function for the interpretation of hologram writing in ferroelectric crystals,” Appl. Phys. A 32, 13–18 (1983).
[Crossref]

1982 (1)

B. I. Sturman, “Photovoltaic effect, diffusion and drift of nonequilibrium electrons having finite mean free paths,” Sov. Phys. JETP 56, 1116–1121 (1982).

1980 (3)

V. I. Belinicher and B. I. Sturman, “The photogalvanic effect in media lacking a center of symmetry,” Sov. Phys. Usp. 23, 199–223 (1980).
[Crossref]

B. Sturman, “The photogalvanic effect—a new mechanism of nonlinear wave interaction in electrooptic crystals,” Sov. J. Quantum Electron. 10, 276–278 (1980).
[Crossref]

N. V. Kukhtarev, V. B. Markov, and S. G. Odoulov, “Nonstationary energy exchange during interaction between two light beams in electrooptic crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).

1979 (3)

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

L. Young, M. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[Crossref]

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

1978 (2)

E. Kratzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
[Crossref]

E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).

1974 (1)

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photovoltaic process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[Crossref]

Alaverdyan, S. A.

E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).

Alfano, R. R.

Avakyan, E. M.

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3: Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).

Belabaev, K.

Belabaev, K. G.

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3: Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).

Belinicher, V. I.

V. I. Belinicher and B. I. Sturman, “The photogalvanic effect in media lacking a center of symmetry,” Sov. Phys. Usp. 23, 199–223 (1980).
[Crossref]

Billings, A. R.

A. R. Billings, Tensor Properties of Materials (Wiley, London, 1969).

Drees, F. W.

R. A. Rupp and F. W. Drees, “Light-induced scattering in photorefractive crystals,” Appl. Phys. B 39, 223–229 (1986).
[Crossref]

El Guibaly, F.

L. Young, M. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[Crossref]

Gaylord, T. K.

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[Crossref]

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

Glass, A. M.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photovoltaic process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[Crossref]

Heaton, J. M.

L. Solymar and J. M. Heaton, “Transient energy transfer in photorefractive materials; an analytic solution,” Opt. Commun. 51, 76–78 (1985).
[Crossref]

J. M. Heaton and L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–408 (1985).
[Crossref]

Ho, P. P.

Ho, P.-P.

Kiseleva, I.

Kratzig, E.

E. Kratzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
[Crossref]

E. Kratzig and O. F. Schirmer, “Photorefractive centers in electro-optic crystals,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 131–166.
[Crossref]

Kukhtarev, N. V.

N. V. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3in external electric field,” Opt. Commun. 23, 338–343 (1987).
[Crossref]

N. V. Kukhtarev, V. B. Markov, and S. G. Odoulov, “Nonstationary energy exchange during interaction between two light beams in electrooptic crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).

Kukhtarov, N. V.

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Li, Q. X.

Li, Q.-X.

Lingerfelder, Ch.

R. von Baltz, Ch. Lingerfelder, and R. Rupp, “Nonlocal photovoltaic response function for the interpretation of hologram writing in ferroelectric crystals,” Appl. Phys. A 32, 13–18 (1983).
[Crossref]

Liu, S.

Lun, E.

L. Young, M. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[Crossref]

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

Markov, V.

N. V. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3in external electric field,” Opt. Commun. 23, 338–343 (1987).
[Crossref]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, and S. G. Odoulov, “Nonstationary energy exchange during interaction between two light beams in electrooptic crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

L. Young, M. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[Crossref]

Negran, T. J.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photovoltaic process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[Crossref]

Nonikov, A.

A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
[Crossref]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, London, 1957).

Odoulov, S.

N. V. Kukhtarev, V. Markov, and S. Odoulov, “Transient energy transfer during hologram formation in LiNbO3in external electric field,” Opt. Commun. 23, 338–343 (1987).
[Crossref]

A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
[Crossref]

Odoulov, S. G.

S. G. Odoulov, “Vectorial interactions in photovoltaic media,” Ferroelectrics 91, 213–225 (1989).
[Crossref]

S. G. Odoulov, “Anisotropic scattering in photorefractive crystals: comment,” J. Opt. Soc. Am. B 4, 1333–1334 (1987).
[Crossref]

S. G. Odoulov, K. Belabaev, and I. Kiseleva, “Degenerate stimulated parametric scattering in LiTaO3,” Opt. Lett. 10, 31–33 (1985).
[Crossref] [PubMed]

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3: Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

N. V. Kukhtarev, V. B. Markov, and S. G. Odoulov, “Nonstationary energy exchange during interaction between two light beams in electrooptic crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

S. G. Odoulov and M. S. Soskin, “Amplification, oscillation, and light-induced scattering in photorefractive crystals,” in Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), pp. 5–44.
[Crossref]

Oleinick, O.

A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
[Crossref]

Rupp, R.

R. von Baltz, Ch. Lingerfelder, and R. Rupp, “Nonlocal photovoltaic response function for the interpretation of hologram writing in ferroelectric crystals,” Appl. Phys. A 32, 13–18 (1983).
[Crossref]

Rupp, R. A.

R. A. Rupp and F. W. Drees, “Light-induced scattering in photorefractive crystals,” Appl. Phys. B 39, 223–229 (1986).
[Crossref]

Sarkisov, V. Kh.

E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).

Schirmer, O. F.

E. Kratzig and O. F. Schirmer, “Photorefractive centers in electro-optic crystals,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 131–166.
[Crossref]

Solymar, L.

J. M. Heaton and L. Solymar, “Transient energy transfer during hologram formation in photorefractive crystals,” Opt. Acta 32, 397–408 (1985).
[Crossref]

L. Solymar and J. M. Heaton, “Transient energy transfer in photorefractive materials; an analytic solution,” Opt. Commun. 51, 76–78 (1985).
[Crossref]

Soskin, M. S.

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

S. G. Odoulov and M. S. Soskin, “Amplification, oscillation, and light-induced scattering in photorefractive crystals,” in Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1989), pp. 5–44.
[Crossref]

Sturman, B.

B. Sturman, “Dynamic holography effects in ferroelectrics induced by spatially oscillating photovoltaic currents,” J. Opt. Soc. Am. B 8, 1333–1340 (1991).
[Crossref]

A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
[Crossref]

B. Sturman, “The photogalvanic effect—a new mechanism of nonlinear wave interaction in electrooptic crystals,” Sov. J. Quantum Electron. 10, 276–278 (1980).
[Crossref]

Sturman, B. I.

B. I. Sturman, “Photovoltaic effect, diffusion and drift of nonequilibrium electrons having finite mean free paths,” Sov. Phys. JETP 56, 1116–1121 (1982).

V. I. Belinicher and B. I. Sturman, “The photogalvanic effect in media lacking a center of symmetry,” Sov. Phys. Usp. 23, 199–223 (1980).
[Crossref]

Tumanyan, K. M.

E. M. Avakyan, S. A. Alaverdyan, K. G. Belabaev, V. Kh. Sarkisov, and K. M. Tumanyan, “Characteristics of the induced optical inhomogeniety on LiNbO3crystals doped with iron ions,” Sov. Phys. Solid State 20, 1401–1403 (1978).

Vinetskii, V. L.

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

von Baltz, R.

R. von Baltz, Ch. Lingerfelder, and R. Rupp, “Nonlocal photovoltaic response function for the interpretation of hologram writing in ferroelectric crystals,” Appl. Phys. A 32, 13–18 (1983).
[Crossref]

von der Linde, D.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photovoltaic process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[Crossref]

Weis, R. S.

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[Crossref]

Wu, Z.

Wu, Z. K.

Young, L.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

L. Young, M. G. Moharam, F. El Guibaly, and E. Lun, “Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect,” J. Appl. Phys. 50, 4201–4207 (1979).
[Crossref]

Zhang, G.

Appl. Opt. (1)

Appl. Phys. A (2)

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[Crossref]

R. von Baltz, Ch. Lingerfelder, and R. Rupp, “Nonlocal photovoltaic response function for the interpretation of hologram writing in ferroelectric crystals,” Appl. Phys. A 32, 13–18 (1983).
[Crossref]

Appl. Phys. B (1)

R. A. Rupp and F. W. Drees, “Light-induced scattering in photorefractive crystals,” Appl. Phys. B 39, 223–229 (1986).
[Crossref]

Appl. Phys. Lett. (1)

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photovoltaic process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[Crossref]

Ferroelectrics (4)

A. Nonikov, S. Odoulov, O. Oleinick, and B. Sturman, “Beam-coupling, four-wave mixing, and optical oscillation due to spatially oscillating photovoltaic currents in lithium niobate crystals,” Ferroelectrics 75, 295–315 (1987).
[Crossref]

N. V. Kukhtarov, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystal. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

S. G. Odoulov, “Vectorial interactions in photovoltaic media,” Ferroelectrics 91, 213–225 (1989).
[Crossref]

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[Crossref]

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[Crossref]

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

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

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (11)

Fig. 1
Fig. 1

(a) Experimental configuration for polarization-conversion measurement. (b) Scattering geometry and polarization.

Fig. 2
Fig. 2

Transmitted light for beam diameter d0 = 140 μm: (a) total, (b) ordinary, (c) extraordinary transmission; (d) optical multichannel analyzer measurement of extraordinary component.

Fig. 3
Fig. 3

Geometry of interacting ordinary and extraordinary waves.

Fig. 4
Fig. 4

Grating formed by ordinary- and extraordinary-wave interaction.

Fig. 5
Fig. 5

Plot of (K · êo)2 for the case koŷ (ordinary-wave propagation along y).

Fig. 6
Fig. 6

Illustration of how overlap between the ordinary pump beam and the extraordinary scattered beam decreases as the waves propagate at different angles. The beam separation at the point y is r = x 2 + z 2 .

Fig. 7
Fig. 7

Two-wave conversion efficiency as a function of extraordinary-beam azimuthal angle ϕe with θe = 90° (extraordinary wave in the xy plane). The beam diameter d0 is a parameter, and for all cases β131Aph = 103 A/m.

Fig. 8
Fig. 8

Energy transfer as a function of position inside crystal for one ordinary wave and three extraordinary waves.

Fig. 9
Fig. 9

Comparison of experimental and calculated extraordinary light distribution on a screen 20 mm from the crystal for (a) 67 μm, (b) 140 μm, and (c) 253 μm. In all sets the top plot is the experimental optical multichannel analyzer measured data and lower plots are the theoretical two-wave (one ordinary wave, one extraordinary wave) efficiency surface and contour computed with β131Aph = 103 A/m and m0 = 0.001.

Fig. 10
Fig. 10

Comparison of experimental, two-wave theoretical, and multiple-wave theoretical extraordinary light distribution on a screen 20 mm from the crystal for d0 = 202 μm. (a) Experimental optical multichannel analyzer measured data, (b) two-wave efficiency with the extraordinary wave scanned to yield the surface, and (c) multiple-wave intensity distribution with one extraordinary wave at each grid point (441 extraordinary waves). In calculations β131Aph = 103 A/m and m0 = 0.001.

Fig. 11
Fig. 11

Polarization conversion as function of beam diameter. Theoretical curves are calculated using 1 ordinary wave, 16 extraordinary waves, β131Aph = 103 A/m, and m0 = 0.001.

Equations (44)

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E = A o ( y ) exp ( i k o · r ) + A e ( y ) exp ( i k e · r ) ,
J j = ( β j k l S + i β j k l A ) E k E l * ,
J x = β 222 S ( E x E y * + c . c . ) + β 131 S ( E x E z * + c . c . ) i β 131 A ( E x E z * c . c . ) ,
J y = β 222 S ( | E x | 2 | E y | 2 ) + β 131 S ( E y E z * + c . c . ) i β 131 A ( E y E z * c . c . ) ,
J z = β 311 S ( | E x | 2 + | E y | 2 ) + β 333 S | E z | 2 ,
E sc = ( J s o · K ̂ ) σ ph K ̂ ,
Δ ( 1 ɛ ) j k = r j k l E l sc ,
2 E j + ( ω 2 / c 2 ) [ ( ɛ 0 + Δ ɛ ) E ] j = 0 ,
ɛ 0 = [ ɛ o 0 0 0 ɛ o 0 0 0 ɛ E ] ,
Δ ɛ [ ɛ o 2 ( r 22 E y sc r 13 E z sc ) ɛ o 2 r 22 E x sc ɛ o ɛ E r 42 E x sc ɛ o 2 r 22 E x sc ɛ o 2 ( r 22 E y sc + r 13 E z sc ) ɛ o ɛ E r 42 E y sc ɛ o ɛ E r 42 E x sc ɛ o ɛ E r 42 E y sc ɛ E 2 r 33 E z sc ] ,
2 E j ( 2 i k o y d A o j d y k o 2 A o j ) exp ( i k o · r ) + ( 2 i k e y d A e j d y k e 2 A e j ) exp ( i k e · r ) .
( J s o · K ̂ ) E x pm = ( β 131 S + i β 131 A ) ( K ̂ x ê o x 2 + K ̂ y ê o x ê o y ) × | A o | 2 A e exp ( i k e · r ) , ( J s o · K ̂ ) E y pm = ( β 131 S + i β 131 A ) ( K ̂ x ê o x ê o y + K ̂ y ê o y 2 ) × | A o | 2 A e exp ( i k e · r ) , ( J s o · K ̂ ) E z pm = ( β 131 S i β 131 A ) ( K ̂ x ê o x + K ̂ n ê o y ) × | A e | 2 A o exp ( i k o · r ) ,
k o y ê o x d A o d y = ω 2 ɛ o ɛ E r 42 K ̂ x 2 c 2 σ ph ( K ̂ x ê o x + K ̂ y ê o y ) × ( i β 131 S β 131 A ) | A e | 2 A o ,
k o y ê o y d A o d y = ω 2 ɛ o ɛ E r 42 K ̂ y 2 c 2 σ ph ( K ̂ x ê o x + K ̂ y ê o y ) × ( i β 131 S β 131 A ) | A e | 2 A o ,
k e y d A e d y = ω 2 ɛ o ɛ E r 42 ( K ̂ · ê o ) 2 2 c 2 σ ph ( i β 131 S + β 131 A ) | A o | 2 A e .
k o y d A o d y = ω 2 ɛ o ɛ E r 42 ( K ̂ · ê o ) 2 2 c 2 σ ph ( i β 131 S β 131 A ) | A e | 2 A o ,
k e y d A e d y = ω 2 ɛ o ɛ E r 42 ( K ̂ · ê o ) 2 2 c 2 σ ph ( i β 131 S + β 131 A ) | A o | 2 A e .
cos ξ o d I o d y = Γ I e I o + I e I o α I o , cos ξ e d I e d y = Γ I o I o + I e I e α I e ,
Γ = 2 ω n o n e r 42 β 131 A ( K ̂ · ê o ) 2 c 3 o κ ph
d d y ( I o cos ξ o + I e cos ξ e ) α ( I o + I e ) = 0 .
Γ [ I o / ( I o + I e ) ] > α .
I o ( y ) = I o ( 0 ) + I e ( 0 ) 1 + m 0 exp ( Γ y y ) exp ( α y y ) , I e ( y ) = I o ( 0 ) + I e ( 0 ) 1 + m 0 1 exp ( Γ y y ) exp ( α y y ) ,
O ( x , z ) = i ( x , z ) i ( x x , z z ) d x d z i ( x , z ) i ( x , z ) d x d z ,
O ( r ) = exp ( r 2 / r 0 2 ) .
Γ eff ( y ) = O [ r ( y ) ] Γ ,
η = I e ( L ) cos ξ e I o ( 0 ) cos ξ o + I e ( 0 ) cos ξ e .
E = A o ( y ) exp ( i k o · r ) + n = 1 N A e n ( y ) exp ( i k e n · r ) .
2 E j ( 2 i k o y d A o j d y k o 2 A o j ) exp ( i k o · r ) + n = 1 N ( 2 i k e n y d A e n j d y k e n 2 A e n j ) exp ( i k e n · r ) .
( J s o · K ̂ ) E x pm = ( β 131 S + i β 131 A ) n ( K ̂ n x ê o x 2 + K ̂ n y ê o x ê o y ) × | A o | 2 A e n exp ( i k e n · r ) , ( J s o · K ̂ ) E y pm = ( β 131 S + i β 131 A ) n ( K ̂ n x ê o x ê o y + K ̂ n y ê o y 2 ) × | A o | 2 A e n exp ( i k e n · r ) , ( J s o · K ̂ ) E z pm = ( β 131 S i β 131 A ) n ( K ̂ n x ê o x + K ̂ n y ê o y ) × | A e n | 2 A o exp ( i k o · r ) + β 333 S n m n ( K ̂ n m · ) 2 | A e m | 2 A e n × exp ( i k e n · r ) ,
k o y d A o d y = ω 2 ɛ o ɛ E r 42 2 c 2 σ ph ( i β 131 S β 131 A ) n = 1 N ( K ̂ n · ê o ) 2 | A e n | 2 A o , k e n y d A e n d y = ω 2 2 c 2 σ ph [ ɛ 0 ɛ E r 42 ( i β 131 S + β 131 A ) × ( K ̂ n · ê o ) 2 | A o | 2 A e n ɛ E 2 r 33 i β 333 S m n × ( K ̂ n m · ) 2 | A e m | 2 A e n , ] , n = 1 , 2 , , N .
cos ξ o d I o d y = n Γ n I e n I o + n I e n I o α I o , cos ξ e n d I e n d y = Γ n I o I o + n I e n I e n α I e n , n = 1 , 2 , , N ,
Γ n = 2 ω n o n e r 42 β 131 A ( K ̂ n · ê o ) 2 c 2 0 κ ph .
Γ n , eff ( y ) = O [ r n ( y ) ] Γ n , n = 1 , 2 , , N ,
T j k l = T j k l ,
T j k l = a j m a k n a l p T m n p ,
( 001 ) ± 1 / 3 = [ 1 / 2 ± 3 / 2 0 3 / 2 1 / 2 0 0 0 1 ] ,
( 100 ) m = [ 1 0 0 0 1 0 0 0 1 ] .
J j = ( β j k l S + i β j k l A ) E k E l * .
β S = [ 0 β 222 S β 131 S β 222 S 0 0 β 131 S 0 0 β 222 S 0 0 0 β 222 S β 131 S 0 β 131 S 0 β 311 S 0 0 0 β 311 S 0 0 0 β 333 S ] ,
β A = [ 0 0 β 131 A 0 0 0 β 131 A 0 0 0 0 0 0 0 β 131 A 0 β 131 A 0 0 0 0 0 0 0 0 0 0 ] .
E = A 1 exp ( i k 1 · r ) + A 2 exp ( i k 2 · r ) ,
J s o , x = 2 β 222 S ( | A 1 x | | A 2 y | + | A 2 x | | A 1 y | ) cos ( K · r + φ 12 ) + 2 ( | A 1 x | | A 2 z | + | A 1 z | | A 2 x | ) [ β 131 S cos ( K · r + φ 12 ) β 131 A sin ( K · r + φ 12 ) ] ,
J s o , y = 2 β 222 S ( | A 1 x | | A 2 x | | A 1 y | | A 2 y | ) cos ( K · r + φ 12 ) + 2 ( | A 1 y | | A 2 z | + | A 1 z | | A 2 y | ) [ β 131 S cos ( K · r + φ 12 ) β 131 A sin ( K · r + φ 12 ) ] ,
J s o , z = 2 [ β 311 S ( | A 1 x | | A 2 x | + | A 1 y | | A 2 y | ) + β 333 S | A 1 z | | A 2 z | ] cos ( K · r + φ 12 ) ,

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