Abstract

We derive an analytical expression describing the effect of phase modulation in two-wave mixing for dynamically recorded phase-shifted holograms in photorefractive materials. The temporal harmonic terms that arise from phase modulation are explicitly formulated for small modulation (as used in our experiments), allowing for pump depletion and an arbitrary value of the phase shift. The theory is experimentally verified for the particular case of an unshifted hologram in a photovoltaic LiNbO3 crystal and for the general case of an arbitrarily shifted hologram in a Bi12TiO20 crystal subject to an externally applied electric field, always for the 514.5-nm-wavelength laser light. In both cases the present analytical formulation permits material parameters to be computed that are self-consistent and in agreement with data in the literature.

© 1997 Optical Society of America

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  1. P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
    [CrossRef]
  2. R. Hofmeister, A. Yariv, A. Kewitsch, and S. Yagi, “Simple method of measuring the net photorefractive phase-shift and coupling constant,” Opt. Lett. 18, 488–490 (1993).
    [CrossRef]
  3. R. S. Cudney, G. D. Bacher, R. M. Pierce, and J. Feinberg, “Measurement of the photorefractive phase shift,” Opt. Lett. 17, 67–69 (1992).
    [CrossRef] [PubMed]
  4. A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
    [CrossRef] [PubMed]
  5. A. A. Freschi and J. Frejlich, “Adjustable phase control in stabilized interferometry,” Opt. Lett. 20, 635–637 (1995).
    [CrossRef] [PubMed]
  6. J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals,” Opt. Lett. 14, 1210–1212 (1989).
    [CrossRef] [PubMed]
  7. J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals: Errata,” Opt. Lett. 15, 1247 (1990).
    [CrossRef]
  8. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  9. M. Cronin-Golomb, “Analytic solution for photorefractive two beam coupling with time varying signal” in Photorefractive Materials, Effects and Devices, Vol. 17 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 142–145.
  10. Ph. Delaye, L. A. Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
    [CrossRef]
  11. E. Serrano, M. Carrascosa, and F. Agulló-López, “Analytical and numerical study of photorefractive kinetics at high modulation depths,” J. Opt. Soc. Am. B 13, 2587–2594 (1996).
    [CrossRef]
  12. J. Frejlich, “Real-time photorefractive hologram phase-shift measurement and self-diffraction effects,” Opt. Commun. 107, 260–264 (1994).
    [CrossRef]
  13. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  14. P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
    [CrossRef]
  15. R. Rupp, “Microphotometric investigations of thick refractive index gratings in photorefractive crystals,” Appl. Phys. B 41, 153–168 (1986).
    [CrossRef]
  16. J. P. Huignard, J.-P. Herriau, and F. Micheron, “Optical storage in LiNbO3:Fe with selective erasure capabilities,” Rev. Phys. Appl. 10, 417–423 (1975).
    [CrossRef]
  17. P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
    [CrossRef]
  18. E. Krätzig and O. F. Schirmer, “Photorefractive centers in electro-optic crystals,” in Photorefractive Materials and their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 131–166.
  19. L. Arizmendi and R. C. Powell, “Anisotropic self-diffraction in Mg-doped LiNbO3,” J. Appl. Phys. 61, 2128–2131 (1987).
    [CrossRef]
  20. L. Arizmendi, “Simple holographic method for determination of Li/Nb ratio and homogeneity of LiNbO3 crystals,” J. Appl. Phys. 64, 4654–4656 (1988).
    [CrossRef]
  21. A. Yariv, Optical Electronics, 3rd. ed. (Holt, Rinehard & Winston, New York, 1985), Chap. 9, p. 281.
  22. R. Sommerfeldt, L. Holtman, and E. Krätzig, “The light induced charge transport in LiNbO3:Mg, Fe crystals,” Ferroelectrics 92, 219–225 (1989).
    [CrossRef]
  23. P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, “Transport length, quantum efficiency and trap density measurement in Bi12SiO20,” J. Appl. Phys. 66, 247–251 (1989).
    [CrossRef]
  24. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
    [CrossRef]
  25. S. Bian and J. Frejlich, “Actively stabilized holographic recording for the measurement of photorefractive properties of a Ti-doped KNSBN crystal,” J. Opt. Soc. Am. B 12, 2060–2065 (1995).
    [CrossRef]
  26. T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985).
    [CrossRef]
  27. J. Frejlich and P. M. Garcia, “Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
    [CrossRef]
  28. S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 263–289.
    [CrossRef]
  29. A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
    [CrossRef]
  30. M. Horowitz, D. Kligler, and B. Fisher, “Time-dependent behavior of photorefractive two- and four-wave mixing,” J. Opt. Soc. Am. B 8, 2204–2217 (1991).
    [CrossRef]
  31. N. V. Kukhtarev, V. B. Markov, and S. G. Odulov, “Nonstationary energy exchange during interaction between two light beams in electrooptical crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).

1996 (1)

1995 (4)

P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
[CrossRef]

A. A. Freschi and J. Frejlich, “Adjustable phase control in stabilized interferometry,” Opt. Lett. 20, 635–637 (1995).
[CrossRef] [PubMed]

Ph. Delaye, L. A. Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

S. Bian and J. Frejlich, “Actively stabilized holographic recording for the measurement of photorefractive properties of a Ti-doped KNSBN crystal,” J. Opt. Soc. Am. B 12, 2060–2065 (1995).
[CrossRef]

1994 (1)

J. Frejlich, “Real-time photorefractive hologram phase-shift measurement and self-diffraction effects,” Opt. Commun. 107, 260–264 (1994).
[CrossRef]

1993 (1)

1992 (2)

R. S. Cudney, G. D. Bacher, R. M. Pierce, and J. Feinberg, “Measurement of the photorefractive phase shift,” Opt. Lett. 17, 67–69 (1992).
[CrossRef] [PubMed]

J. Frejlich and P. M. Garcia, “Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

1991 (1)

1990 (1)

1989 (5)

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals,” Opt. Lett. 14, 1210–1212 (1989).
[CrossRef] [PubMed]

P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

R. Sommerfeldt, L. Holtman, and E. Krätzig, “The light induced charge transport in LiNbO3:Mg, Fe crystals,” Ferroelectrics 92, 219–225 (1989).
[CrossRef]

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, “Transport length, quantum efficiency and trap density measurement in Bi12SiO20,” J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

1988 (1)

L. Arizmendi, “Simple holographic method for determination of Li/Nb ratio and homogeneity of LiNbO3 crystals,” J. Appl. Phys. 64, 4654–4656 (1988).
[CrossRef]

1987 (1)

L. Arizmendi and R. C. Powell, “Anisotropic self-diffraction in Mg-doped LiNbO3,” J. Appl. Phys. 61, 2128–2131 (1987).
[CrossRef]

1986 (2)

R. Rupp, “Microphotometric investigations of thick refractive index gratings in photorefractive crystals,” Appl. Phys. B 41, 153–168 (1986).
[CrossRef]

A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
[CrossRef] [PubMed]

1985 (2)

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

1982 (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

1980 (1)

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

1979 (1)

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

1975 (1)

J. P. Huignard, J.-P. Herriau, and F. Micheron, “Optical storage in LiNbO3:Fe with selective erasure capabilities,” Rev. Phys. Appl. 10, 417–423 (1975).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Agulló-López, F.

Arizmendi, L.

L. Arizmendi, “Simple holographic method for determination of Li/Nb ratio and homogeneity of LiNbO3 crystals,” J. Appl. Phys. 64, 4654–4656 (1988).
[CrossRef]

L. Arizmendi and R. C. Powell, “Anisotropic self-diffraction in Mg-doped LiNbO3,” J. Appl. Phys. 61, 2128–2131 (1987).
[CrossRef]

Bacher, G. D.

Bian, S.

Buse, K.

P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
[CrossRef]

Carrascosa, M.

Cescato, L.

Connors, L. M.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, “Analytic solution for photorefractive two beam coupling with time varying signal” in Photorefractive Materials, Effects and Devices, Vol. 17 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C.), pp. 142–145.

Cudney, R. S.

Delaye, Ph.

Ph. Delaye, L. A. Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

dos Santos, P. A. M.

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, “Transport length, quantum efficiency and trap density measurement in Bi12SiO20,” J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

Feinberg, J.

Fisher, B.

Foote, P. D.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Frejlich, J.

S. Bian and J. Frejlich, “Actively stabilized holographic recording for the measurement of photorefractive properties of a Ti-doped KNSBN crystal,” J. Opt. Soc. Am. B 12, 2060–2065 (1995).
[CrossRef]

P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
[CrossRef]

A. A. Freschi and J. Frejlich, “Adjustable phase control in stabilized interferometry,” Opt. Lett. 20, 635–637 (1995).
[CrossRef] [PubMed]

J. Frejlich, “Real-time photorefractive hologram phase-shift measurement and self-diffraction effects,” Opt. Commun. 107, 260–264 (1994).
[CrossRef]

J. Frejlich and P. M. Garcia, “Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals: Errata,” Opt. Lett. 15, 1247 (1990).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals,” Opt. Lett. 14, 1210–1212 (1989).
[CrossRef] [PubMed]

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, “Transport length, quantum efficiency and trap density measurement in Bi12SiO20,” J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
[CrossRef] [PubMed]

Freschi, A. A.

Garcia, P. M.

P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
[CrossRef]

J. Frejlich and P. M. Garcia, “Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals: Errata,” Opt. Lett. 15, 1247 (1990).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals,” Opt. Lett. 14, 1210–1212 (1989).
[CrossRef] [PubMed]

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, “Transport length, quantum efficiency and trap density measurement in Bi12SiO20,” J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

Günter, P.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Hall, T. J.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Herriau, J.-P.

J. P. Huignard, J.-P. Herriau, and F. Micheron, “Optical storage in LiNbO3:Fe with selective erasure capabilities,” Rev. Phys. Appl. 10, 417–423 (1975).
[CrossRef]

Hofmeister, R.

Holtman, L.

R. Sommerfeldt, L. Holtman, and E. Krätzig, “The light induced charge transport in LiNbO3:Mg, Fe crystals,” Ferroelectrics 92, 219–225 (1989).
[CrossRef]

Horowitz, M.

Huignard, J. P.

J. P. Huignard, J.-P. Herriau, and F. Micheron, “Optical storage in LiNbO3:Fe with selective erasure capabilities,” Rev. Phys. Appl. 10, 417–423 (1975).
[CrossRef]

Jaura, R.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect—a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Kamshilin, A. A.

A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
[CrossRef] [PubMed]

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

Kewitsch, A.

Kip, D.

P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
[CrossRef]

Kligler, D.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Krätzig, E.

R. Sommerfeldt, L. Holtman, and E. Krätzig, “The light induced charge transport in LiNbO3:Mg, Fe crystals,” Ferroelectrics 92, 219–225 (1989).
[CrossRef]

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

Kukhtarev, N. V.

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

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

Markov, V. B.

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

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

Micheron, F.

J. P. Huignard, J.-P. Herriau, and F. Micheron, “Optical storage in LiNbO3:Fe with selective erasure capabilities,” Rev. Phys. Appl. 10, 417–423 (1975).
[CrossRef]

Montmorillon, L. A.

Ph. Delaye, L. A. Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Odulov, S. G.

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

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

Petrov, M. P.

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 263–289.
[CrossRef]

Pierce, R. M.

Powell, R. C.

L. Arizmendi and R. C. Powell, “Anisotropic self-diffraction in Mg-doped LiNbO3,” J. Appl. Phys. 61, 2128–2131 (1987).
[CrossRef]

Roosen, G.

Ph. Delaye, L. A. Montmorillon, and G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Rupp, R.

R. Rupp, “Microphotometric investigations of thick refractive index gratings in photorefractive crystals,” Appl. Phys. B 41, 153–168 (1986).
[CrossRef]

Schirmer, O. F.

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

Serrano, E.

Sommerfeldt, R.

R. Sommerfeldt, L. Holtman, and E. Krätzig, “The light induced charge transport in LiNbO3:Mg, Fe crystals,” Ferroelectrics 92, 219–225 (1989).
[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. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 263–289.
[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. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Yagi, S.

Yariv, A.

Yeh, P.

P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

J. Frejlich and P. M. Garcia, “Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

Appl. Phys. B (1)

R. Rupp, “Microphotometric investigations of thick refractive index gratings in photorefractive crystals,” Appl. Phys. B 41, 153–168 (1986).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Ferroelectrics (2)

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

R. Sommerfeldt, L. Holtman, and E. Krätzig, “The light induced charge transport in LiNbO3:Mg, Fe crystals,” Ferroelectrics 92, 219–225 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, “2-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

J. Appl. Phys. (4)

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, “Transport length, quantum efficiency and trap density measurement in Bi12SiO20,” J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

L. Arizmendi and R. C. Powell, “Anisotropic self-diffraction in Mg-doped LiNbO3,” J. Appl. Phys. 61, 2128–2131 (1987).
[CrossRef]

L. Arizmendi, “Simple holographic method for determination of Li/Nb ratio and homogeneity of LiNbO3 crystals,” J. Appl. Phys. 64, 4654–4656 (1988).
[CrossRef]

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

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

Opt. Commun. (4)

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

P. M. Garcia, K. Buse, D. Kip, and J. Frejlich, “Self-stabilized holographic recording in LiNbO3:Fe crystals,” Opt. Commun. 117, 235–240 (1995).
[CrossRef]

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Other (4)

S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification,” in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 263–289.
[CrossRef]

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

A. Yariv, Optical Electronics, 3rd. ed. (Holt, Rinehard & Winston, New York, 1985), Chap. 9, p. 281.

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Figures (6)

Fig. 1
Fig. 1

Actively stabilized holographic recording and measurement setup: BS, beam splitter; M, mirror; PZT, piezoelectric-supported mirror; C, photorefractive crystal; G, glass plate; D’s, photodetectors; HSP, harmonic signal processor; LA, vectorial lock-in amplifier; OSC, oscillator at frequency ω; HV, high-voltage source for the PZT.

Fig. 2
Fig. 2

Evolution of VXIS2ω, VYISω, and VX/VYIS2ω/ISω data (points) and best fits for the VX/VY data to Eq. (33) (continuous curves) with β220 and I0=3.9 mW/cm2 with λ=514.5 nm. Two distinct fitted curves are observed for data around each discontinuity: the first one, A1, leads to γd/(4τsc)=1.8×10-3 s-1, whereas the second one, A2, gives γd/(4τsc)=1.5×10-3 s-1.

Fig. 3
Fig. 3

Evolution of VXIS2ω, VYISω, and VX/VYIS2ω/ISω data (points) and best fits for the VX/VY data to Eq. (33) (continuous curves) with β2=1/19 and I0=3.6 mW/cm2 with λ=514.5 nm, with the resulting that γd/(4τsc)=1.1×10-3 s-1.

Fig. 4
Fig. 4

Evolution of -1/tan ϕ (points) computed from the experimental data VX/VY and Eq. (26) as a function of the applied field E for the Bi12TiO20 sample with K=11.65 µm-1, β2=12, and I04 mW/cm2, with λ=514.5 nm. Fitting of the data to Eq. (35) leads to A, ls=0.023 µm for positive and B, ls=0.024 µm for negative values of E.

Fig. 5
Fig. 5

Evolution of -1/tan ϕ (open circles) computed from the experimental data for VX/VY and Eq. (26) as a function of the applied field E for the Bi12TiO20 sample with K=7.08 µm-1, β2=9, and I04 mW/cm2, with λ=514.5 nm. Fitting of the data to Eq. (35) leads to ls=0.027 µm; tan φ (open squares) is plotted as directly computed from the ratio VY/VX.

Fig. 6
Fig. 6

Plot of the exponential gain Γ as a function of the spatial frequency K (points) measured on the same Bi12TiO20 sample and its theoretical expression23 computed for the parameter ls =0.027 µm experimentally obtained with β2=12.8, for the 514.5-nm laser wavelength.

Tables (1)

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Table 1 Theoretically Computed and Measured Material Parameter Group for a 0.1 wt. % Fe-Doped LiNbO3 Crystal

Equations (66)

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R(z)=iκcos θm(z)S(z),
S(z)=iκ*cos θm*(z)R(z),
m(z)=2S*(z)R(z)I,
κm(z)=n1(z)k0=-1/2n¯3k0rEsc(z),
IR(z)I=IR(0)IR(0)+IS(0)exp(Γz),
IS(z)I=IS(0)exp(Γz)IR(0)+IS(0)exp(Γz),
Γ=4cos θI{κ}=4κ0sin ϕcos θ.
ψR(z)=ψR(0)=(γ/4)z+ψ(z),
ψS(z)=ψS(0)+(γ/4)z-ψ(z),
ψ(z)=12 tan ϕlnIR(0)exp-Γ2z+IS(0)expΓ2zI,
γ=4cos θR{κ}=4κ0cos ϕcos θ,
R(z)=iκcos θm(z)S(z),
S(z)=iκ*cos θm*(z)R(z),
m(z)=2S*(z)R(z)I
R(z)=R(0)RR(z)+S(0)exp(iψd sin ωt)RS(z),
S(z)=R(0)SR(z)+S(0)exp(iψd sin ωt)SS(z)=S+S(0)SS(z)[exp(iψd sin ωt)-1],
IS=IS+ISω2ψd sin ωt+IS2ωψd2/2 cos 2ωt,
ISω=-I{S*S(0)SS},
IS2ω=R{S*S(0)SS}-IS(0)|SS|2.
ψ=1/2Δkz,Δk=γ2IS(0)-IR(0)I,
ψR=ψR(0)+γ2IS(0)Iz,ψS=ψS(0)+γ2IR(0)Iz,
R=R(0)expiγ2IS(0)Iz,
S=S(0)expiγ2IR(0)Iz,
m=m(0)exp(iΔkz).
R=iγ4m(0)exp(iΔkz)S,
S=iγ4m*(0)exp(-iΔkz)R.
R=Rˆ exp(iΔkz/2),S=Sˆ exp(-iΔkz/2)
RR=IR(0)Iexpiγ2IS(0)Iz+IS(0)Iexp-iγ2IR(0)Iz,RR(0)=1,
SR=12m*(0)expiγ2IR(0)Iz-exp-iγ2IS(0)Iz,SR(0)=0.
η=|SR|2=|m(0)|2 sin2(γz/4).
ν=|m(0)|(γz/4),ξ=ψ=1/2Δkz,
RS=12m(0)expiγ2IS(0)Iz-exp-iγ2IR(0)Iz,
RS(0)=0,
SS=IS(0)Iexpiγ2IR(0)Iz+IR(0)Iexp-iγ2IS(0)Iz,SS(0)
=1.
S*S(0)SS=IS(0)IIS(0)+IR(0)exp-iγ2z,
|SS|2=1-η=1-|m(0)|2 sin2 (γz/4).
ISωI=IR(0)IS(0)I2sin(γ/2)z,
IS2ωI=-2IR(0)IS(0)I2IR(0)-IS(0)Isin2γ4z.
IS2ωISω=IR(0)-IS(0)Itanγ4z.
R=-S*,S=R*
RR=(1/I)[R(0)*R+S(0)S*],RR(0)=1,SR=(1/I)[-S(0)R*+R*(0)S],SR(0)=0.
RS=-SR*=(1/I)[S*(0)R-R(0)S*],
RS(0)=0,
SS=RR*=(1/I)[R(0)R*+S*(0)S],
SS(0)=1.
η=|SR|2=|RS|2=2IR(0)IS(0)IcoshΓ2z-cosγ2zIR(0)exp-Γ2z+IS(0)expΓ2z.
R=R(0)RR+S(0)RS,
S=R(0)SR+S(0)SS
|RR|2+|SR|2=|RS|2+|SS|2=1.
S*S(0)SS=IS(0)IR(0)exp-iγ2z+IS(0)expΓ2zIR(0)exp-Γ2z+IS(0)expΓ2z,
|SS|2=1-η=IR(0)2 exp-Γ2z+IS(0)2 expΓ2z+2IR(0)IS(0)cosγ2zIR(0)exp-Γ2z+IS(0)expΓ2zI.
ISωI=IR(0)IS(0)I2IIR(0)exp-Γ2z+IS(0)expΓ2zsinγ2z,
IS2ωI=-IR(0)IS(0)I2IR(0)exp-Γ2z-IS(0)expΓ2z+IS(0)-IR(0)cosγ2zIR(0)exp-Γ2z+IS(0)expΓ2z.
IS2ωISω=-1sinγ2zIR(0)Iexp-Γ2z-IS(0)IexpΓ2z+IS(0)I-IR(0)Icosγ2z.
IS=|IR(0)η+IS(0)1-η exp(iψd sin ωt)exp(iφ)|2.
tan ϕ=-sinγ2zIS(0)I-IR(0)IcoshΓ2z-cosγ2z+sinhΓ2z.
IS(0)I-IR(0)Itan φ tanγ4z=-1forϕ=0.
tan φ tan ϕ=-1forz0.
ISω=-IS(0)IR(0)1/2η(1-η)1/2 sin φ,
IS2ω=IS(0)IR(0)1/2η(1-η)1/2 cos φ,
IS2ωISω=-1tan φ.
IS2ω/ISω=β2-1β2+1tan{γd/4[1-exp(-t/τsc)]}
γd4τsc=πne3r33κ33ph2λ33st0 cos θI0A,
Acos θcos θ(1-R)[1-exp(-αd)]1-R exp(-αd),
-1tan ϕ=EDEED2(1+K2ls2)+K2ls2E2.

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