Abstract

We present a theoretical model in which the band-transport equations and the coupled-wave equations are considered to study the two thermal-fixing methods (simultaneous fixing and postfixing) in Fe:LiNbO3. We found that, in simultaneous fixing, the existing ionic-grating affects the writing of the electronic grating by reduction of the coupling gain, and the grating envelope of the fixed-index grating is quite uniform inside the photorefractive crystal in comparison with the method of postfixing. The resulting diffraction efficiency of the fixed-volume grating is dependent mainly on the initial intensity modulation of the two writing beams. A set of experiments is also presented.

© 1998 Optical Society of America

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  1. D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (1995).
    [CrossRef]
  2. J. F. Heanue, M. C. Bashaw, A. J. Daiber, R. Snyder, L. Hesselink, “Digital holographic storage system incorporating thermal fixing in lithium niobate,” Opt. Lett. 21, 1615–1617 (1996).
    [CrossRef] [PubMed]
  3. J. J. Amodei, W. Phillips, D. L. Staebler, “Improved electro-optic materials and fixing techniques for holographic recording,” Appl. Opt. 11, 390–396 (1972).
    [CrossRef] [PubMed]
  4. D. L. Staebler, W. J. Burke, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
    [CrossRef]
  5. L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
    [CrossRef]
  6. F. Micheron, G. Bismuch, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
    [CrossRef]
  7. S. Redfield, L. Hesselink, “Enhanced nondestructive holographic readout in strontium barium niobate,” Opt. Lett. 13, 880–882 (1988).
    [CrossRef] [PubMed]
  8. D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive process for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
    [CrossRef]
  9. A. Yariv, S. S. Orlov, G. A. Rakuljic, “Holographic storage dynamics in lithium niobate: theory and experiment,” J. Opt. Soc. Am. B 13, 2513–2523 (1996).
    [CrossRef]
  10. G. Montemezzani, M. Zgonik, P. Gunter, “Photorefractive charge compensation at elevated temperature and application to KNbO3,” J. Opt. Soc. Am B 10, 171–185 (1993).
    [CrossRef]
  11. A. Yariv, S. S. Orlov, G. A. Rakuljic, V. Leyva, “Holographic fixing, readout, and storage dynamics in photorefractive materials,” Opt. Lett. 20, 1334–1336 (1995).
    [CrossRef] [PubMed]
  12. S. Orlov, D. Psaltis, R. R. Neurgaonkar, “Dynamic electronic compensation of fixed gratings in photorefractive media,” Appl. Phys. Lett. 63, 2466–2468 (1993).
    [CrossRef]
  13. M. Carrascosa, F. Agulló-López, “Theoretical modeling of the fixing and developing of holographic gratings in LiNbO3,” J. Opt. Soc. Am. B 7, 2317–2322 (1990).
    [CrossRef]
  14. R. Matull, R. A. Rupp, “Microphotometric investigation of fixed holograms,” J. Phys. D 21, 1556–1565 (1988).
    [CrossRef]
  15. V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).
  16. P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
    [CrossRef]
  17. N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electro-optic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).
  18. M. Jeganathan, M. C. Bashaw, L. Hesselink, “Evolution and propagation of grating envelopes during erasure in bulk photorefractive media,” J. Opt. Soc. Am. B 12, 1370–1383 (1995).
    [CrossRef]
  19. P. Yeh, “Two-wave mixing in nonlinear media,” J. Quantum Electron. 25, 484–519 (1989).
    [CrossRef]
  20. H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
    [CrossRef]
  21. R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
    [CrossRef]
  22. M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
    [CrossRef]
  23. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  24. W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
    [CrossRef]
  25. E. Kratzig, R. Orlowski, “Light-induced charge transport in doped LiNbO3 and TiTaO3,” Ferroelectrics 27, 241–244 (1980).
    [CrossRef]

1996

1995

1993

S. Orlov, D. Psaltis, R. R. Neurgaonkar, “Dynamic electronic compensation of fixed gratings in photorefractive media,” Appl. Phys. Lett. 63, 2466–2468 (1993).
[CrossRef]

G. Montemezzani, M. Zgonik, P. Gunter, “Photorefractive charge compensation at elevated temperature and application to KNbO3,” J. Opt. Soc. Am B 10, 171–185 (1993).
[CrossRef]

1992

R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

1990

1989

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
[CrossRef]

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

1988

S. Redfield, L. Hesselink, “Enhanced nondestructive holographic readout in strontium barium niobate,” Opt. Lett. 13, 880–882 (1988).
[CrossRef] [PubMed]

R. Matull, R. A. Rupp, “Microphotometric investigation of fixed holograms,” J. Phys. D 21, 1556–1565 (1988).
[CrossRef]

1987

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

1981

H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
[CrossRef]

1980

E. Kratzig, R. Orlowski, “Light-induced charge transport in doped LiNbO3 and TiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

1979

M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
[CrossRef]

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

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

1977

W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
[CrossRef]

1976

N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electro-optic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).

1975

D. L. Staebler, W. J. Burke, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

1974

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive process for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

1972

F. Micheron, G. Bismuch, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

J. J. Amodei, W. Phillips, D. L. Staebler, “Improved electro-optic materials and fixing techniques for holographic recording,” Appl. Opt. 11, 390–396 (1972).
[CrossRef] [PubMed]

Agulló-López, F.

Amodei, J. J.

D. L. Staebler, W. J. Burke, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

J. J. Amodei, W. Phillips, D. L. Staebler, “Improved electro-optic materials and fixing techniques for holographic recording,” Appl. Opt. 11, 390–396 (1972).
[CrossRef] [PubMed]

Arizmendi, L.

R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
[CrossRef]

Bashaw, M. C.

Bismuch, G.

F. Micheron, G. Bismuch, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Burke, W. J.

D. L. Staebler, W. J. Burke, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

Cabrera, J. M.

R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

Carrascosa, M.

R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

M. Carrascosa, F. Agulló-López, “Theoretical modeling of the fixing and developing of holographic gratings in LiNbO3,” J. Opt. Soc. Am. B 7, 2317–2322 (1990).
[CrossRef]

Daiber, A. J.

Glass, A. M.

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive process for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Gunter, P.

G. Montemezzani, M. Zgonik, P. Gunter, “Photorefractive charge compensation at elevated temperature and application to KNbO3,” J. Opt. Soc. Am B 10, 171–185 (1993).
[CrossRef]

Heanue, J. F.

Hertel, P.

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Hesselink, L.

Jeganathan, M.

Josch, W.

W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
[CrossRef]

Kapphan, S.

H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
[CrossRef]

Kratzig, E.

H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
[CrossRef]

E. Kratzig, R. Orlowski, “Light-induced charge transport in doped LiNbO3 and TiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

Kukhtarev, N. K.

N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electro-optic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).

Kukhtarev, N. V.

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

Kulikov, V. V.

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

Leyva, V.

Markov, V. B.

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

Matull, R.

R. Matull, R. A. Rupp, “Microphotometric investigation of fixed holograms,” J. Phys. D 21, 1556–1565 (1988).
[CrossRef]

Micheron, F.

F. Micheron, G. Bismuch, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Mok, F.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (1995).
[CrossRef]

Montemezzani, G.

G. Montemezzani, M. Zgonik, P. Gunter, “Photorefractive charge compensation at elevated temperature and application to KNbO3,” J. Opt. Soc. Am B 10, 171–185 (1993).
[CrossRef]

Muller, R.

R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

Muller-Vogt, G.

M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
[CrossRef]

Munser, R.

M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
[CrossRef]

W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
[CrossRef]

Neurgaonkar, R. R.

S. Orlov, D. Psaltis, R. R. Neurgaonkar, “Dynamic electronic compensation of fixed gratings in photorefractive media,” Appl. Phys. Lett. 63, 2466–2468 (1993).
[CrossRef]

Odulov, S. G.

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

Orlov, S.

S. Orlov, D. Psaltis, R. R. Neurgaonkar, “Dynamic electronic compensation of fixed gratings in photorefractive media,” Appl. Phys. Lett. 63, 2466–2468 (1993).
[CrossRef]

Orlov, S. S.

Orlowski, R.

E. Kratzig, R. Orlowski, “Light-induced charge transport in doped LiNbO3 and TiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

Phillips, W.

Psaltis, D.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (1995).
[CrossRef]

S. Orlov, D. Psaltis, R. R. Neurgaonkar, “Dynamic electronic compensation of fixed gratings in photorefractive media,” Appl. Phys. Lett. 63, 2466–2468 (1993).
[CrossRef]

Rakuljic, G. A.

Redfield, S.

Ringhofer, K. H.

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Rogers, K. F.

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive process for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Rupp, R. A.

R. Matull, R. A. Rupp, “Microphotometric investigation of fixed holograms,” J. Phys. D 21, 1556–1565 (1988).
[CrossRef]

Ruppel, W.

W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
[CrossRef]

Snyder, R.

Sommerfeldt, R.

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Soskin, M. S.

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

Staebler, D. L.

D. L. Staebler, W. J. Burke, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

J. J. Amodei, W. Phillips, D. L. Staebler, “Improved electro-optic materials and fixing techniques for holographic recording,” Appl. Opt. 11, 390–396 (1972).
[CrossRef] [PubMed]

Stepanov, S. I.

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

Vinetskii, V. L.

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

Von der Linde, D.

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive process for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Vormann, H.

H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
[CrossRef]

Weber, G.

H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
[CrossRef]

Weyer, M.

M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
[CrossRef]

Wurfer, P.

M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
[CrossRef]

W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
[CrossRef]

Yariv, A.

Yeh, P.

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

Zgonik, M.

G. Montemezzani, M. Zgonik, P. Gunter, “Photorefractive charge compensation at elevated temperature and application to KNbO3,” J. Opt. Soc. Am B 10, 171–185 (1993).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

D. L. Staebler, W. J. Burke, J. J. Amodei, “Multiple storage and erasure of fixed holograms in Fe-doped LiNbO3,” Appl. Phys. Lett. 26, 182–184 (1975).
[CrossRef]

F. Micheron, G. Bismuch, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive process for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

S. Orlov, D. Psaltis, R. R. Neurgaonkar, “Dynamic electronic compensation of fixed gratings in photorefractive media,” Appl. Phys. Lett. 63, 2466–2468 (1993).
[CrossRef]

R. Muller, L. Arizmendi, M. Carrascosa, J. M. Cabrera, “Determination of H concentration in LiNbO3 by photorefractive fixing,” Appl. Phys. Lett. 60, 3212–3214 (1992).
[CrossRef]

Ferroelectrics

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

W. Josch, R. Munser, W. Ruppel, P. Wurfer, “The photovoltaic effect and the charge transport in LiNbO3,” Ferroelectrics 21, 623–625 (1977).
[CrossRef]

E. Kratzig, R. Orlowski, “Light-induced charge transport in doped LiNbO3 and TiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

J. Appl. Phys.

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
[CrossRef]

J. Opt. Soc. Am B

G. Montemezzani, M. Zgonik, P. Gunter, “Photorefractive charge compensation at elevated temperature and application to KNbO3,” J. Opt. Soc. Am B 10, 171–185 (1993).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D

R. Matull, R. A. Rupp, “Microphotometric investigation of fixed holograms,” J. Phys. D 21, 1556–1565 (1988).
[CrossRef]

J. Quantum Electron.

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

Opt. Lett.

Phys. Status Solidi A

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

M. Weyer, P. Wurfer, R. Munser, G. Muller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53, 171–180 (1979).
[CrossRef]

Sci. Am.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (1995).
[CrossRef]

Solid State Commun.

H. Vormann, G. Weber, S. Kapphan, E. Kratzig, “Hydrogen as origin of thermal fixing in LiNbO3,” Solid State Commun. 40, 543–545 (1981).
[CrossRef]

Sov. Phys. Solid State

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

Sov. Tech. Phys. Lett.

N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electro-optic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the writing of a photorefractive grating.

Fig. 2
Fig. 2

Initial intensity ratio r-dependent envelopes of the fixed-index gratings obtained with simultaneous fixing (dashed lines) and with postfixing (solid curves).

Fig. 3
Fig. 3

Initial intensity ratio r-dependent diffraction efficiency of the fixed-index gratings: (a) Simultaneous fixing. (b) Postfixing.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup.

Fig. 5
Fig. 5

Experimental results of the initial intensity ratio r-dependent diffraction efficiency of the fixed-index gratings.

Tables (1)

Tables Icon

Table 1 Values of the Parameters of LiNbO3 and the External Conditions

Equations (36)

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

n e t = N d + t + 1 e x e μ e n e E + μ e k B T   n e x + esL ph I N d - N d + ,
N d + t = sI + β N d - N d + - γ e N d + n e ,
n i t = - 1 e x e μ i n i E - μ i k B T   n i x ,
0 E x = e N d + - N a + n i - n i 0 - n e .
n e = n e 0 + n e 1 exp - iKx + cc ,
N d + = N a + N d 1 + exp - iKx + cc ,
n i = n i 0 + n i 1 exp - iKx + cc ,
E = E 0 + E e sc   exp - iKx + cc ,
N d 1 + t = C 1 N d 1 + + C 2 n i 1 + C 3 m ,
n i 1 t = - n i 1 ω i + D i K 2 + i μ i KE 0 - N d 1 + ω i ,
E e sc = ie K N d 1 + + n i 1 ,
C 1 = - ω e γ e N a - sI 0 + β N d N a D e K 2 + i μ e KE 0 - iKsL ph I 0 γ e N a γ e N a + D e K 2 + i μ e KE 0 , C 2 = - ω e γ e N a γ e N a + D e K 2 + i μ e KE 0 , C 3 = sI 0 D e K 2 - iKsL ph I 0 γ e N a γ e N a + D e K 2 + i μ e KE 0 N d - N a ,
ω e = e μ e n e 0 = e μ e sI + β N d - N a γ e N a
n = n 0 + Δ n = n 0 + n 1 exp i ϕ exp - iKx + cc ,
n 1 = - 1 2   n 0 3 γ eff | E sc | ,
A 1 z ,   t z = - i   π n 1 z ,   t λ   cos   θ exp - i ϕ A 2 z ,   t - α 2   cos   θ   A 1 z ,   t ,
A 2 z ,   t z = - i   π n 1 z ,   t λ   cos   θ exp i ϕ A 1 z ,   t - α 2   cos   θ   A 2 z ,   t ,
t   n 1 z ,   t = - n 1 z ,   t τ + i   n max m z ,   t τ ,
N d 1 + = - C 3 C 1   m .
E sc = - ie 0 K C 3 C 1   m .
I 1 z = I 1 0 1 + r - 1 1 + r - 1 exp γ z exp - α z ,
I 2 z = I 2 0 1 + r 1 + r   exp - γ z exp - α z ,
γ = 2 π n p λ   cos   θ sin   ϕ = π en 0 3 γ eff 0 K λ   cos   θ γ e N a KsL ph I 0 + isI 0 D e K 2 N d - N a ω e γ e N a + sI 0 + β N d N a   D e K 2 + i γ e N a KsL ph I 0 sin   ϕ ,
ϕ = tan - 1 sI 0 D e K 2 γ e N a KsL ph I 0 - tan - 1 γ e N a KsL ph I 0 e ω e γ e N a + sI 0 + β N d N a   D e K 2 , r = I 1 0 I 2 0 .
m z = 2 I 1 z I 2 z I 1 2 z + I 2 2 z = sech γ z - ln   r 2 .
n i 1 = - ω i ω i + D i K 2   N d 1 + = ω i C 3 m z ω i + D i K 2 C 1 .
N d 1 + = - ω i C 2 C 3 m z ω i + D i K 2 C 1 2 .
E sc = ie 0 K ω i C 1 - C 2 C 3 m z ω i + D i K 2 C 1 2 .
η = sin 2 0 d π n 0 3 | γ eff E sc | λ   cos   θ d z .
n i 1 = C 3 ω i C 1 - C 2 ω i + D i K 2 C 1   m ,
N d 1 + = - ω i + D i K 2 C 3 C 1 - C 2 ω i + D i K 2 C 1   m ,
E sc = - ie K D i K 2 C 3 C 1 - C 2 ω i + D i K 2 C 1   m .
m z = sech γ z - ln   r 2 ,
γ = π n 0 3 γ eff λ   cos   θ   | E sc | sin   ϕ .
N d 1 + = - C 2 1 C 1 1   n i 1 = - C 2 1 C 3 ω i C 1 1 C 1 - C 2 ω i + D i K 2 C 1   m .
E sc = ie K C 1 1 - C 2 1 C 3 ω i C 1 1 C 1 - C 2 ω i + D i K 2 C 1   m .

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