Abstract

The steady-state beam-coupling gain during two-wave mixing in photorefractive materials has been analyzed in the strong nonlinear regime (high modulation depths). Numerical simulations have been carried out for B12SiO20, for which detailed information on photorefractive parameters is already available. First the amplitude and the phase mismatch (with regard to the light) of the recorded index grating and consequently the coupling gain coefficient were obtained under an applied field E0=5 kV/cm. Then the evolution of the intensities of the two interfering beams during propagation was determined for several light-modulation depths. The energy exchange was considerably enhanced with regard to the linear regime. The light and index fringe profiles at large modulation m were also obtained. The bending for both kinds of fringe differed appreciably from that previously calculated with a linear approach to the material equations.

© 1998 Optical Society of America

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References

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  1. P. Gunter and J. P. Huignard, eds., Photorefractive Materials and Their Applications II (Springer-Verlag, Berlin, 1989).
  2. F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).
  3. T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
    [CrossRef]
  4. S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39 (1994).
    [CrossRef]
  5. B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).
  6. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
    [CrossRef]
  7. J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
    [CrossRef]
  8. J. Goltz, C. Denz, and T. Tschudi, “Dynamics of hologram readout in photorefractive crystals for broken Bragg-condition,” Opt. Commun. 68, 228 (1988).
    [CrossRef]
  9. R. de Vre, M. Jeganathan, J. P. Wilde, and L. Hesselink, “Effect of applied fields on the Bragg condition and the diffraction efficiency in photorefractive crystals,” Opt. Lett. 19, 910 (1994).
    [CrossRef] [PubMed]
  10. S. Tao, Z. H. Song, and D. R. Selviah, “Bragg shift of holographic gratings in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144 (1994).
    [CrossRef]
  11. K. Buse, S. Kamper, J. Frejlich, R. Pankrath, and K. H. Ringhofer, “Tilting of holograms in photorefractive Sr0.61Ba0.39Nb2O6 crystals by self-diffraction,” Opt. Lett. 20, 2249 (1995).
    [CrossRef]
  12. A. A. Freschi, P. M. Garcia, Y. Rasnik, J. Frejlich, and K. Buse, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Opt. Lett. 21, 152 (1996).
    [CrossRef] [PubMed]
  13. J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
    [CrossRef]
  14. Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
    [CrossRef]
  15. Ch. H. Kwak, S. Y. Park, and E. Lee, “Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal,” Opt. Commun. 115, 315 (1995).
    [CrossRef]
  16. M. R. Belic, D. Timotijevic, M. Petrovic, and M. V. Jaric, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. 123, 201 (1996).
    [CrossRef]
  17. Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
    [CrossRef]
  18. P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
    [CrossRef]
  19. L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660 (1988).
    [CrossRef] [PubMed]
  20. E. Serrano, V. Lopez, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11, 670 (1994);“Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875 (1994).
    [CrossRef]
  21. G. A. Brost, “Photorefractive grating formations at large modulation with alternating electric fields,” J. Opt. Soc. Am. B 9, 1454 (1992).
    [CrossRef]
  22. G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993).
    [CrossRef]
  23. J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
    [CrossRef]
  24. J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22 (1993).
    [CrossRef]
  25. Y. H. Lee and R. W. Hellwarth, “Spatial harmonics of photorefractive gratings in a barium titanate crystal,” J. Appl. Phys. 71, 916 (1992).
    [CrossRef]
  26. E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910 (1995).
    [CrossRef] [PubMed]
  27. E. Serrano, M. Carrascosa y, and F. Agulló-López, “Analytical and numerical study of the photorefractive kinetics at high modulation depth,” J. Opt. Soc. Am. B 13, 2587 (1996).
    [CrossRef]

1997 (2)

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
[CrossRef]

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

1996 (3)

1995 (4)

E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910 (1995).
[CrossRef] [PubMed]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
[CrossRef]

K. Buse, S. Kamper, J. Frejlich, R. Pankrath, and K. H. Ringhofer, “Tilting of holograms in photorefractive Sr0.61Ba0.39Nb2O6 crystals by self-diffraction,” Opt. Lett. 20, 2249 (1995).
[CrossRef]

Ch. H. Kwak, S. Y. Park, and E. Lee, “Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal,” Opt. Commun. 115, 315 (1995).
[CrossRef]

1994 (5)

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

R. de Vre, M. Jeganathan, J. P. Wilde, and L. Hesselink, “Effect of applied fields on the Bragg condition and the diffraction efficiency in photorefractive crystals,” Opt. Lett. 19, 910 (1994).
[CrossRef] [PubMed]

S. Tao, Z. H. Song, and D. R. Selviah, “Bragg shift of holographic gratings in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144 (1994).
[CrossRef]

E. Serrano, V. Lopez, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11, 670 (1994);“Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875 (1994).
[CrossRef]

1993 (2)

G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993).
[CrossRef]

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22 (1993).
[CrossRef]

1992 (2)

Y. H. Lee and R. W. Hellwarth, “Spatial harmonics of photorefractive gratings in a barium titanate crystal,” J. Appl. Phys. 71, 916 (1992).
[CrossRef]

G. A. Brost, “Photorefractive grating formations at large modulation with alternating electric fields,” J. Opt. Soc. Am. B 9, 1454 (1992).
[CrossRef]

1988 (2)

L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660 (1988).
[CrossRef] [PubMed]

J. Goltz, C. Denz, and T. Tschudi, “Dynamics of hologram readout in photorefractive crystals for broken Bragg-condition,” Opt. Commun. 68, 228 (1988).
[CrossRef]

1986 (1)

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

1985 (1)

P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

1984 (1)

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

1978 (1)

B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).

Agulló-López, F.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
[CrossRef]

E. Serrano, M. Carrascosa y, and F. Agulló-López, “Analytical and numerical study of the photorefractive kinetics at high modulation depth,” J. Opt. Soc. Am. B 13, 2587 (1996).
[CrossRef]

E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910 (1995).
[CrossRef] [PubMed]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
[CrossRef]

E. Serrano, V. Lopez, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11, 670 (1994);“Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875 (1994).
[CrossRef]

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).

Agulló-Rueda, F.

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).

Albers, J.

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

Alvarez-Bravo, J. V.

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22 (1993).
[CrossRef]

Arizmendi, L.

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22 (1993).
[CrossRef]

Au, L. B.

Belic, M. R.

M. R. Belic, D. Timotijevic, M. Petrovic, and M. V. Jaric, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. 123, 201 (1996).
[CrossRef]

Brost, G. A.

G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993).
[CrossRef]

G. A. Brost, “Photorefractive grating formations at large modulation with alternating electric fields,” J. Opt. Soc. Am. B 9, 1454 (1992).
[CrossRef]

Buse, K.

Cabrera, J. M.

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).

Carrascosa, M.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
[CrossRef]

E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910 (1995).
[CrossRef] [PubMed]

E. Serrano, V. Lopez, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11, 670 (1994);“Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875 (1994).
[CrossRef]

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22 (1993).
[CrossRef]

Carrascosa y, M.

de Vre, R.

Denz, C.

J. Goltz, C. Denz, and T. Tschudi, “Dynamics of hologram readout in photorefractive crystals for broken Bragg-condition,” Opt. Commun. 68, 228 (1988).
[CrossRef]

Frejlich, J.

Freschi, A. A.

Garcia, P. M.

Goltz, J.

J. Goltz, C. Denz, and T. Tschudi, “Dynamics of hologram readout in photorefractive crystals for broken Bragg-condition,” Opt. Commun. 68, 228 (1988).
[CrossRef]

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

Heaton, J. M.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

Hellwarth, R. W.

Y. H. Lee and R. W. Hellwarth, “Spatial harmonics of photorefractive gratings in a barium titanate crystal,” J. Appl. Phys. 71, 916 (1992).
[CrossRef]

Herden, A.

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

Hesselink, L.

Huignard, J. P.

P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Jaric, M. V.

M. R. Belic, D. Timotijevic, M. Petrovic, and M. V. Jaric, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. 123, 201 (1996).
[CrossRef]

Jeganathan, M.

Jeong, J. S.

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

Jiang, Y.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Kamper, S.

Klumb, H.

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Kwak, Ch. H.

Ch. H. Kwak, S. Y. Park, and E. Lee, “Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal,” Opt. Commun. 115, 315 (1995).
[CrossRef]

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

Laeri, F.

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

Lee, E.

Ch. H. Kwak, S. Y. Park, and E. Lee, “Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal,” Opt. Commun. 115, 315 (1995).
[CrossRef]

Lee, E.-H.

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

Lee, Y. H.

Y. H. Lee and R. W. Hellwarth, “Spatial harmonics of photorefractive gratings in a barium titanate crystal,” J. Appl. Phys. 71, 916 (1992).
[CrossRef]

Li, Y.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Lopez, V.

Magaña, L. F.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Mills, P. A.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

Murillo, J. G.

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Paige, E. G. S.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

Pankrath, R.

Park, S. Y.

Ch. H. Kwak, S. Y. Park, and E. Lee, “Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal,” Opt. Commun. 115, 315 (1995).
[CrossRef]

Petrovic, M.

M. R. Belic, D. Timotijevic, M. Petrovic, and M. V. Jaric, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. 123, 201 (1996).
[CrossRef]

Rajbenbach, H.

P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Rasnik, Y.

Refrégier, P.

P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Ringhofer, K. H.

Selviah, D. R.

S. Tao, Z. H. Song, and D. R. Selviah, “Bragg shift of holographic gratings in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144 (1994).
[CrossRef]

Serrano, E.

Solymar, L.

L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660 (1988).
[CrossRef] [PubMed]

P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

Song, Z. H.

S. Tao, Z. H. Song, and D. R. Selviah, “Bragg shift of holographic gratings in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144 (1994).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

Sturman, B. I.

B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).

Suh, H. H.

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

Sun, X.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Tao, S.

S. Tao, Z. H. Song, and D. R. Selviah, “Bragg shift of holographic gratings in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144 (1994).
[CrossRef]

Timotijevic, D.

M. R. Belic, D. Timotijevic, M. Petrovic, and M. V. Jaric, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. 123, 201 (1996).
[CrossRef]

Tschudi, T.

J. Goltz, C. Denz, and T. Tschudi, “Dynamics of hologram readout in photorefractive crystals for broken Bragg-condition,” Opt. Commun. 68, 228 (1988).
[CrossRef]

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

Wan, Q.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Wilde, J. P.

Wilson, T.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

Xu, K.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Yeon Park, S.

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

Zhao, H.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Zhou, Zh.

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Tschudi, A. Herden, J. Goltz, H. Klumb, F. Laeri, and J. Albers, “Image amplification by two- and four-wave mixing in BaTiO3 crystals,” IEEE J. Quantum Electron. QE-22, 1493 (1986).
[CrossRef]

J. Appl. Phys. (3)

P. Refrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Temporal evolution of the physical response during photorefractive grating formation and erasure for BSO,” J. Appl. Phys. 78, 5686 (1995).
[CrossRef]

Y. H. Lee and R. W. Hellwarth, “Spatial harmonics of photorefractive gratings in a barium titanate crystal,” J. Appl. Phys. 71, 916 (1992).
[CrossRef]

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

Opt. Acta (1)

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, and T. Wilson, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885 (1984).
[CrossRef]

Opt. Commun. (9)

J. Goltz, C. Denz, and T. Tschudi, “Dynamics of hologram readout in photorefractive crystals for broken Bragg-condition,” Opt. Commun. 68, 228 (1988).
[CrossRef]

S. Tao, Z. H. Song, and D. R. Selviah, “Bragg shift of holographic gratings in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144 (1994).
[CrossRef]

J. G. Murillo, L. F. Magaña, M. Carrascosa, and F. Agulló-López, “Effects of light modulation on grating phase-shifts in photorefractive recording,” Opt. Commun. 139, 81 (1997).
[CrossRef]

Ch. H. Kwak, S. Yeon Park, J. S. Jeong, H. H. Suh, and E.-H. Lee, “An analytical solution for large modulation effects in photorefractive two-wave couplings,” Opt. Commun. 105, 353 (1994).
[CrossRef]

Ch. H. Kwak, S. Y. Park, and E. Lee, “Intensity dependent two-wave mixing at large modulation depth in photorefractive BaTiO3 crystal,” Opt. Commun. 115, 315 (1995).
[CrossRef]

M. R. Belic, D. Timotijevic, M. Petrovic, and M. V. Jaric, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. 123, 201 (1996).
[CrossRef]

Zh. Zhou, X. Sun, Y. Li, Y. Jiang, H. Zhao, K. Xu, and Q. Wan, “Dynamic solutions of the photorefractive two-wave coupling at large modulation depths,” Opt. Commun. 132, 128 (1997).
[CrossRef]

G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96, 113 (1993).
[CrossRef]

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22 (1993).
[CrossRef]

Opt. Lett. (5)

Rep. Prog. Phys. (1)

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

B. I. Sturman, “Interaction of two light waves in a crystal caused by photoelectron diffusion and drift,” Sov. Phys. Tech. Phys. 23, 589 (1978).

Other (2)

P. Gunter and J. P. Huignard, eds., Photorefractive Materials and Their Applications II (Springer-Verlag, Berlin, 1989).

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, San Diego, Calif., 1994).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the experimental configuration.

Fig. 2
Fig. 2

Dependence of Γ sin φ on m as obtained from our numerical calculations (solid curve) corresponding to Λ=1 μm and E0=5 kV/cm. The dashed curve, derived from the phenomenological law f(m)/m=1+1.75 m4, is also included for comparison.

Fig. 3
Fig. 3

Evolution of the steady-state coupling coefficient Γ sin φ with penetration depth Z in the sample for various values of initial modulation depth m0 (Λ=1 μm and E0=5 kV/cm).

Fig. 4
Fig. 4

Evolution of steady-state coupling coefficient Γ with penetration depth Z in the sample for various values of initial modulation depth m0 and zero applied electric field (sin φ=1).

Fig. 5
Fig. 5

Evolution of the intensity of the two beams as they penetrate the sample for m0=0.9 E0=5 kV/cm (solid curves). The analytical solutions obtained by Heaton et al.7 (dashed curves) are included for comparison.

Fig. 6
Fig. 6

Variation of light modulation m along crystal thickness Z for various initial (Z=0) light-modulation values m0. Solid curves, full numerical approach; dashed curves, analytical linear solution.

Fig. 7
Fig. 7

Evolution of the intensity of the two beams as they penetrate the sample. Solid curves, full numerical solution as in Fig. 5; dashed curves, solution obtained by Heaton et al.,7 but with the nonlinear value associated with the initial modulation m0 used for coupling coefficient Γ sin φ.

Fig. 8
Fig. 8

Phase Δψ=ψ(x, y)-ψ(x, 0) (in rad) of the light pattern obtained for various values of the initial light modulation m0. Dashed curves, analytical solution obtained by Heaton et al.7; solid curves, the full numerical solution.

Fig. 9
Fig. 9

Phases (in rad) of the light (dashed curve) and index (solid curve) fringes for m0=0.9.

Tables (1)

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Table 1 Numerical Parameters for the Simulation

Equations (15)

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dA˜+dz+iκ*A˜-=0,
dA˜-dz+iκA˜+=0,
κ=n˜1ω2c cos θ,
n˜1=n3rEs A˜+ A˜-|A0|2 exp(iφ)
dI+(z)dz+Γ sin φ I+ I-I0=0,
dI-(z)dz-Γ sin φ I+ I-I0=0,
Γ=2πn3rEsλ cos θ.
dψ+dz+Γ cos φ I-2I0=0,
dψ-dz+Γ cos φ I+2I0=0.
dψdz-Γ cos φ I1+-I1-2I0=0,
I+(Z)=I01+r0 exp(ΓZ sin φ),
I-(Z)=r0I0 exp(ΓZ sin φ)1+r0 exp(ΓZ sin φ),
ψ(x, Z)=ψ(x, 0)+(Γ/2)Z cos φ,
x=-Γ cos φ2K Z+x0.
ψ(x, Z)=ψ(x, 0)+12 cot φ ln(1+r0)2 exp(ΓZ sin φ)[1+r0 exp(ΓZ sin φ)]2.

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