Abstract

Vectorial Kukhtarev equations modified for the nonvolatile holographic recording in doubly doped crystals are analyzed, in which the bulk photovoltaic effect and the external electrical field are both considered. On the basis of small modulation approximation, both the analytic solution to the space-charge field with time in the recording phase and in the readout phase are deduced. The analytic solutions can be easily simplified to adapt the one-center model, and they have the same analytic expressions given those when the grating vector is along the optical axis. Based on the vectorial analyses of the band transport model an optimal recording direction is given to maximize the refractive index change in doubly doped LiNbO3:Fe:Mn crystals.

© 2007 Optical Society of America

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  1. K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in doubly doped lithium niobate crystals," Nature 339, 665-668 (1998).
  2. L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
    [CrossRef]
  3. A. Adibi, K. Buse, and D. Psaltis, "Two-center holographic recording," J. Opt. Soc. Am. B 18, 584-601 (2001).
    [CrossRef]
  4. L. Solymar, D. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).
  5. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Systems (Springer-Verlag, 1991).
  6. B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
    [CrossRef]
  7. K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
    [CrossRef]
  8. G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
    [CrossRef]
  9. B. Sturman, V. Fridkin, and G. Breach, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric materials (Science Publishers, 1992).
  10. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61 of Topics in Applied Physics (Springer-Verlag, 1988).
  11. G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
    [CrossRef]
  12. Y. Fainman, E. Klancnik, and S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. (Bellingham) 25, 228-234 (1986).
  13. P. M. Johansen, "Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain," IEEE J. Quantum Electron. 25, 530-539 (1989).
    [CrossRef]
  14. D. W. Wilson, E. N. Glytisi, N. F. Hartman, and T. K. Gaylord, "Beam diameter threshold for polarization conversion photoinduced by spatially oscillating bulk photovoltaic currents in LiNbO3:Fe," J. Opt. Soc. Am. B 9, 1714-1725 (1992).
    [CrossRef]
  15. H. Zhou, F. Zhao, and F. T. S. Yu, "Angle-dependent diffraction efficiency in a thick photorefractive hologram," Appl. Opt. 34, 1303-1309 (1995).
    [CrossRef] [PubMed]
  16. C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
    [CrossRef]
  17. Y. Liu, L. Liu, and C. Zhou, "Prescription for optimizing holograms in LiNbO3:Fe:Mn," Opt. Lett. 25, 551-553 (2000).
    [CrossRef]
  18. O. Momtahan and A. Adibi, "Global optimization of sensitivity and dynamic range for two-center holographic recording," J. Opt. Soc. Am. B 20, 449-461 (2003).
    [CrossRef]
  19. J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3: analyses under the two-center model," Appl. Phys. B 79, 351-358 (2004).
    [CrossRef]
  20. 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]
  21. A. M. Glass, D. Von der Linde, and T. J. Negran, "High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3," Appl. Phys. Lett. 25, 233-235 (1974).
    [CrossRef]
  22. N. Kukhtarev, V. Markov, and S. Odoulov, "Transient energy transfer during hologram formation in LiNbO3 in external electric field," Opt. Commun. 23, 338-343 (1977).
    [CrossRef]
  23. D. A. Temple and C. Warde, "Anisotropic scattering in photorefractive crystals," J. Opt. Soc. Am. B 3, 337-341 (1986).
    [CrossRef]
  24. S. I. Karabekian and V. V. Obukhovsky, "Nondiagonal component of linear photovoltaic tensor in dopped LiNbO3 and LiTaO3 crystals," YERPHI 1370, 1-10 (1992).

2004 (1)

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3: analyses under the two-center model," Appl. Phys. B 79, 351-358 (2004).
[CrossRef]

2003 (1)

2002 (1)

2001 (2)

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

A. Adibi, K. Buse, and D. Psaltis, "Two-center holographic recording," J. Opt. Soc. Am. B 18, 584-601 (2001).
[CrossRef]

2000 (1)

1999 (2)

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

1998 (1)

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in doubly doped lithium niobate crystals," Nature 339, 665-668 (1998).

1997 (1)

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

1995 (1)

1992 (2)

1991 (1)

C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
[CrossRef]

1989 (1)

P. M. Johansen, "Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain," IEEE J. Quantum Electron. 25, 530-539 (1989).
[CrossRef]

1986 (2)

Y. Fainman, E. Klancnik, and S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. (Bellingham) 25, 228-234 (1986).

D. A. Temple and C. Warde, "Anisotropic scattering in photorefractive crystals," J. Opt. Soc. Am. B 3, 337-341 (1986).
[CrossRef]

1980 (1)

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]

1977 (1)

N. Kukhtarev, V. Markov, and S. Odoulov, "Transient energy transfer during hologram formation in LiNbO3 in external electric field," Opt. Commun. 23, 338-343 (1977).
[CrossRef]

1974 (1)

A. M. Glass, D. Von der Linde, and T. J. Negran, "High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3," Appl. Phys. Lett. 25, 233-235 (1974).
[CrossRef]

Adibi, A.

Agulló-López, F.

G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
[CrossRef]

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

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]

Breach, G.

B. Sturman, V. Fridkin, and G. Breach, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric materials (Science Publishers, 1992).

Buse, K.

A. Adibi, K. Buse, and D. Psaltis, "Two-center holographic recording," J. Opt. Soc. Am. B 18, 584-601 (2001).
[CrossRef]

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in doubly doped lithium niobate crystals," Nature 339, 665-668 (1998).

Caballero, O.

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3: analyses under the two-center model," Appl. Phys. B 79, 351-358 (2004).
[CrossRef]

Cabrera, J. M.

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3: analyses under the two-center model," Appl. Phys. B 79, 351-358 (2004).
[CrossRef]

Calvo, G. F.

G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
[CrossRef]

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

Carnicero, J.

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3: analyses under the two-center model," Appl. Phys. B 79, 351-358 (2004).
[CrossRef]

Carrascosa, M.

J. Carnicero, O. Caballero, M. Carrascosa, and J. M. Cabrera, "Superlinear photovoltaic currents in LiNbO3: analyses under the two-center model," Appl. Phys. B 79, 351-358 (2004).
[CrossRef]

G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
[CrossRef]

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

Fainman, Y.

Y. Fainman, E. Klancnik, and S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. (Bellingham) 25, 228-234 (1986).

Fridkin, V.

B. Sturman, V. Fridkin, and G. Breach, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric materials (Science Publishers, 1992).

Gaylord, T. K.

Glass, A. M.

A. M. Glass, D. Von der Linde, and T. J. Negran, "High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3," Appl. Phys. Lett. 25, 233-235 (1974).
[CrossRef]

Glytisi, E. N.

Grunnet-Jepsen, A.

L. Solymar, D. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Gu, C.

C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
[CrossRef]

Günter, P.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61 of Topics in Applied Physics (Springer-Verlag, 1988).

Guo, Y.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Hartman, N. F.

Hong, J.

C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
[CrossRef]

Huignard, J.-P.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61 of Topics in Applied Physics (Springer-Verlag, 1988).

Johansen, P. M.

P. M. Johansen, "Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain," IEEE J. Quantum Electron. 25, 530-539 (1989).
[CrossRef]

Kamenov, V. P.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Kamshilin, A. A.

G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
[CrossRef]

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Karabekian, S. I.

S. I. Karabekian and V. V. Obukhovsky, "Nondiagonal component of linear photovoltaic tensor in dopped LiNbO3 and LiTaO3 crystals," YERPHI 1370, 1-10 (1992).

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Systems (Springer-Verlag, 1991).

Klancnik, E.

Y. Fainman, E. Klancnik, and S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. (Bellingham) 25, 228-234 (1986).

Kukhtarev, N.

N. Kukhtarev, V. Markov, and S. Odoulov, "Transient energy transfer during hologram formation in LiNbO3 in external electric field," Opt. Commun. 23, 338-343 (1977).
[CrossRef]

Lee, S. H.

Y. Fainman, E. Klancnik, and S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. (Bellingham) 25, 228-234 (1986).

Li, G.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Li, H.-Y.

C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
[CrossRef]

Li, J.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Liu, B.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Liu, L.

Y. Liu, L. Liu, and C. Zhou, "Prescription for optimizing holograms in LiNbO3:Fe:Mn," Opt. Lett. 25, 551-553 (2000).
[CrossRef]

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Liu, Y.

Markov, V.

N. Kukhtarev, V. Markov, and S. Odoulov, "Transient energy transfer during hologram formation in LiNbO3 in external electric field," Opt. Commun. 23, 338-343 (1977).
[CrossRef]

Momtahan, O.

Montemezzani, G.

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

Negran, T. J.

A. M. Glass, D. Von der Linde, and T. J. Negran, "High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3," Appl. Phys. Lett. 25, 233-235 (1974).
[CrossRef]

Nippolainen, E.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Obukhovsky, V. V.

S. I. Karabekian and V. V. Obukhovsky, "Nondiagonal component of linear photovoltaic tensor in dopped LiNbO3 and LiTaO3 crystals," YERPHI 1370, 1-10 (1992).

Odoulov, S.

N. Kukhtarev, V. Markov, and S. Odoulov, "Transient energy transfer during hologram formation in LiNbO3 in external electric field," Opt. Commun. 23, 338-343 (1977).
[CrossRef]

Paivasaari, K.

G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
[CrossRef]

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

Petrov, M. P.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Systems (Springer-Verlag, 1991).

Podivilov, E. V.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Prokofiev, V. V.

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Psaltis, D.

A. Adibi, K. Buse, and D. Psaltis, "Two-center holographic recording," J. Opt. Soc. Am. B 18, 584-601 (2001).
[CrossRef]

K. Buse, A. Adibi, and D. Psaltis, "Non-volatile holographic storage in doubly doped lithium niobate crystals," Nature 339, 665-668 (1998).

C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
[CrossRef]

Ringhofer, K. H.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Shamonina, E.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

Shao, L.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Solymar, L.

L. Solymar, D. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Stepanov, S. I.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Systems (Springer-Verlag, 1991).

Sturman, B.

K. Paivasaari, A. A. Kamshilin, V. V. Prokofiev, B. Sturman, G. F. Calvo, M. Carrascosa, and F. Agulló-López, "Linear phase demodulation in photorefractive crystals with nonlocal response," J. Appl. Phys. 90, 3135-3141 (2001).
[CrossRef]

B. Sturman, V. Fridkin, and G. Breach, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric materials (Science Publishers, 1992).

Sturman, B. I.

G. F. Calvo, B. I. Sturman, F. Agulló-López, M. Carrascosa, A. A. Kamshilin, and K. Paivasaari, "Grating translation technique for vectorial beam coupling and its applications to linear signal detection," J. Opt. Soc. Am. B 19, 1564-1574 (2002).
[CrossRef]

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, "Theory of photorefractive vectorial coupling in cubic crystals," Phys. Rev. E 60, 3332-3352 (1999).
[CrossRef]

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]

Temple, D. A.

Von der Linde, D.

A. M. Glass, D. Von der Linde, and T. J. Negran, "High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3," Appl. Phys. Lett. 25, 233-235 (1974).
[CrossRef]

Warde, C.

Webb, D.

L. Solymar, D. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

Wilson, D. W.

Yan, X.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Yeh, P.

C. Gu, J. Hong, H.-Y. Li, D. Psaltis, and P. Yeh, "Dynamics of grating formation in photovoltaic media," J. Appl. Phys. 69, 1167-1172 (1991).
[CrossRef]

Yin, Y.

L. Liu, B. Liu, X. Yan, L. Shao, G. Li, Y. Yin, J. Li, and Y. Guo, "Photorefractive miniaturized integration of optical 3D systems," J. Opt. A Pure Appl. Opt. 1, 220-224 (1999).
[CrossRef]

Yu, F. T. S.

Zgonik, M.

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997).
[CrossRef]

Zhao, F.

Zhou, C.

Zhou, H.

Appl. Opt. (1)

Appl. Phys. B (1)

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Figures (4)

Fig. 1
Fig. 1

Holographic recording configurations.

Fig. 2
Fig. 2

Hologram strength versus time for a typical 633 nm recording in LiNbO 3 crystal doped with 0.075 wt . % Fe 2 O 3 and 0.01 wt . % MnO by transmission geometry with 15° included angle in crystal. Initially, 90% of the Mn traps are filled with electrons. Sensitizing and recording intensities are 20 and 500 mW cm 2 , respectively. The absorption of both recording and sensitizing beams is neglected in this simulation. The dotted curve represents analysis solution and the solid curve represents numerical solution.

Fig. 3
Fig. 3

Variation of parameters with the direction of grating wave vector in two-center recording for o–o holographic recording. The grating is recorded in LiNbO 3 crystal doped with 0.075 wt . % Fe 2 O 3 and 0.01 wt . % MnO by transmission geometry with 15° included angle in crystal. Initially, 90% of the Mn traps are filled with electrons. Sensitizing and recording intensities are 20 and 500 mW cm 2 , respectively. The readout beams keep the same polarization states and the same directions as recording beams. The absorption and scattering of both recording and sensitizing beams is neglected in this simulation. (a) Steady-state space-charge field, (b) effective electro-optic coefficient, (c) refractive index change.

Fig. 4
Fig. 4

Variation of parameters with the direction of grating wave vector in two-center recording for e–e holographic recording. The grating is recorded in LiNbO 3 crystal doped with 0.075 wt . % Fe 2 O 3 and 0.01 wt . % MnO by transmission geometry with 15° included angle in crystal. Initially, 90% of the Mn traps are filled with electrons. Sensitizing and recording intensities are 20 and 500 mW cm 2 , respectively. The readout beams keep the same polarization states and the same directions as recording beams. The absorption and scattering of both recording and sensitizing beams is neglected in this simulation. (a) Steady-state space-charge field, (b) effective electro-optic coefficient, (c) refractive index change.

Tables (1)

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Table 1 Description of the Parameters Used in the Notation in This Paper a

Equations (86)

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N D + t = S D H I H ( N D N D + ) γ D n N D + ,
N S + t = ( S S L I L + S S H I H + β t s ) ( N S N S + ) γ S n N S + ,
n t = N D + t + N S + t + 1 e J ,
J = e n μ E s c + e D n + J p h D H + J p h S H + J p h S L ,
( ϵ E s c ) = e ( N D + + N S + N A n ) ,
E = A r e ̂ r exp i ( k r r + φ r ) + A s e ̂ s exp i ( k s r + φ s ) ,
I L ( r ) = I L s + I L r + 2 e ̂ s e ̂ r I L s I L r cos ( K r + φ )
= I L 0 [ 1 + m e ̂ s e ̂ r cos ( K r + φ ) ]
= I L 0 + 1 2 I L 1 e ̂ s e ̂ r exp i ( K r + φ ) + c.c. ,
J p h j = ( β j k l S + β j k l A ) E k E l * ,
J p h = κ p h I ( N N + ) .
κ p h = ( β j k l S + β j k l A ) E k E l * I ( N N + ) .
J p h D H = κ D H I H ( N D N D + ) e ̂ z ,
J p h S H = κ S H I H ( N S N S + ) e ̂ z .
J p h S L = ( κ S L 0 I L 0 + 1 2 κ S L 1 I L 1 exp i ( K r + φ ) + c.c ) ( N S N S + )
= ( κ S L 0 I L 0 + 1 2 m I L 0 κ S L 1 exp i ( K r + φ ) + c.c ) ( N S N S + ) ,
E s c = E 0 + 1 2 E s c 1 exp ( i K r ) + c.c ,
d N D 0 + d t = S D H I H ( N D N D 0 + ) γ D n 0 N D 0 + ,
d N S 0 + d t = ( S S L I L 0 + S S H I H + β t s ) ( N S N S 0 + ) γ S n 0 N S 0 + ,
N D 0 + + N S 0 + = N A + n 0 ,
d N D 1 + d t = S D H I H N D 1 + γ D ( N D 1 + n 0 + N D 0 + n 1 ) ,
d N S 1 + d t = ( S S L I L 0 + S S H I H + β t s ) N S 1 + + m S S L I L 0 e ̂ s e ̂ r ( N S N S 0 + ) γ S ( N S 1 + n 0 + N S 0 + n 1 ) ,
d n 1 d t = d N D 1 + d t + d N S 1 + d t + 1 e K J 1 ,
J 1 = ( e n 0 μ E s c 1 + e n 1 μ E 0 + i e n 1 D K κ D H I H N D 1 + e ̂ z κ S H I H N S 1 + e ̂ z κ S L 0 I L 0 N S 1 + + m κ S L 1 I L 0 ( N S N S 0 + ) ) ,
i K ( ϵ E s c 1 ) = e ( N D 1 + + N S 1 + n 1 ) .
× E s c = ( i K × E s c 1 ) exp ( i K r ) = 0 ;
E s c 1 K .
E s c 1 = i e N D 1 + + N S 1 + K ϵ K K .
J 1 = [ i e 2 n 0 μ K K ϵ K ( N D 1 + + N S 1 + ) + e n 1 μ E 0 + i e n 1 D K κ D H I H N D 1 + e ̂ z κ S H I H N S 1 + e ̂ z κ S L 0 I L 0 N S 1 + + m κ S L 1 I L 0 ( N S N S 0 + ) ] .
N S 0 + = S S L I L 0 + S S H I H + β t s S S L I L 0 + S S H I H + β t s + γ s n 0 N s ,
N D 0 + = S D H I H S D H I H + γ D n 0 N D ,
n 0 = 1 2 N A { [ Γ D ( N A N D ) + Γ S ( N A N S ) ] 2 + 4 N A Γ S Γ D ( N S + N D N A ) [ Γ D ( N A N D ) + Γ S ( N A N S ) ] } .
Γ S = S S L I L 0 + S S H I H + β t s γ S ,
Γ D = S D H I H γ D .
E S s c 1 = m E S S ( E 0 + N D 0 + N D E p h D H + i E D + i E S D ) S S L I L 0 S S L I L 0 + S S H I H + β t s e ̂ s e ̂ r + E S S E p h S L 1 E S S + E S D + E D i ( E 0 + N D 0 + N D E p h D H + N S 0 + N S E p h S H + N S 0 + N S E p h S L 0 ) n ̂ ,
E D s c 1 = m E S D ( N S 0 + N S E p h S H + N S 0 + N S E p h S L 0 + i E S S ) S S L I L 0 S S L I L 0 + S S H I H + β t s e ̂ s e ̂ r E S D E p h S L 1 E S S + E S D + E D i ( E 0 + N D 0 + N D E p h D H + N S 0 + N S E p h S H + N S 0 + N S E p h S L 0 ) n ̂ ,
E s c 1 = E S s c 1 + E D s c 1 = m [ E S S ( E 0 + N D 0 + N D E p h D H + i E D ) E S D N S 0 + N S ( E p h S H + E p h S L 0 ) ] S S L I L 0 S S L I L 0 + S S H I H + β t s e ̂ s e ̂ r + ( E S D + E S S ) E p h S L 1 E S S + E S D + E D i ( E 0 + N D 0 + N D E p h D H + N S 0 + N S E p h S H + N S 0 + N S E p h S L 0 ) n ̂ ,
E D = K D K K μ K K = k B T e K ;
E 0 = K μ E 0 K μ K K ;
E S D = e K K ϵ K N D 0 + ( 1 N D 0 + N D ) ;
E S S = e K K ϵ K N S 0 + ( 1 N S 0 + N S ) ;
E p h D H = κ D H I H K e ̂ z e n 0 K μ K K ( N D N D 0 + ) ;
E p h S H = κ S H I H K e ̂ z e n 0 K μ K K ( N S N S 0 + ) ;
E p h S L 0 = I L 0 K κ S L 0 e n 0 K μ K K ( N S N S 0 + ) ;
E p h S L 1 = I L 0 K κ S L 1 e n 0 K μ K K ( N S N S 0 + ) .
n 0 = n 00 exp ( t τ r 3 ) ,
N S 0 + = N S ( N S N S 0 + ) exp ( t τ r 3 ) ,
N D 0 + = N A N S + ( N S N S 0 + ) exp ( t τ r 3 ) ,
n 00 = ( S S L I L r + β t s ) ( N S N S 0 + ) γ S N S γ D ( N A N S ) ,
τ r 3 = γ S N S γ D ( N A N S ) ( S S L I L r + β t s ) γ D ( N A N S ) .
E s c 1 = E M E s c 1 + i E p h S L r 0 E S s c 1 + ( E D i E 0 ) E D s c 1 E M + E R + N A N S 0 + N A N S ( E D i E 0 ) n ̂ ,
E M = γ D ( N A N S ) K μ K K ;
E R = e K K ϵ K ( N S N S 0 + ) ;
E p h S L r 0 = I L r K κ S L r 0 e n 00 K μ K K ( N S N s 0 + ) ;
Δ n = 1 2 n 0 3 e ̂ r [ ϵ r ( r e ̂ s c ) ϵ r ] e ̂ s n 0 3 n λ E s c = 1 2 n 0 3 r e f f E s c ,
β 311 : β 333 : β 222 : β 131 : β 131 A = 1 : 0.67 : 0.014 : 0.011 : 0.2 .
E = A r exp i ( k r r + φ r ) + A s exp i ( k s r + φ s ) ,
J p h j = ( β j k l S + β j k l A ) E k E l * .
J p h = β 0 + 1 2 β 1 exp i ( K r + φ ) + c.c. ;
β 0 = [ β 222 S ( A r x A r y + A s x A s y ) + β 131 S ( A r x A r z + A s x A s z ) ] e ̂ x
+ [ β 222 S ( A r x 2 A r y 2 + A s x 2 A s y 2 ) + β 131 S ( A r y A r z + A s y A s z ) ] e ̂ y
+ [ β 311 S ( A r x 2 + A r y 2 + A s x 2 + A s y 2 ) + β 333 S ( A r z 2 + A s z 2 ) ] e ̂ z ,
β 1 = 2 [ β 222 S ( A r x A s y + A r y A s x ) + β 131 S ( A r x A s z + A r z A s x ) + i β 131 A ( A r z A s x A r x A s z ) ] e ̂ x
+ 2 [ β 222 S ( A r x A s x A r y A s y ) + β 131 S ( A r y A s z + A r z A s y ) + i β 131 S ( A r z A s y A r y A s z ) ] e ̂ y
+ 2 [ β 311 S ( A r x A s x + A r y A s y ) + β 333 S A r y A s z ] e ̂ z ,
n 1 = A N D 1 + + B N S 1 + + C ,
A = S D H I H + γ D n 0 e n 0 K μ K K ϵ K + i 1 e κ D H I H K e ̂ z γ S N S 0 + + γ D N D 0 + + K D K i K μ E 0 ,
B = S S L I L 0 + S S H I H + β t s + γ S n 0 e n 0 K μ K K ϵ K + i 1 e κ S H I H K e ̂ z + i 1 e I L 0 K κ S L 0 γ S N S 0 + + γ D N D 0 + + K D K i K μ E 0 ,
C = m S S L I L 0 e ̂ s e ̂ r + i 1 e m I L 0 K κ S L 1 γ S N S 0 + + γ D N D 0 + + K D K i K μ E 0 ( N s N s 0 + ) .
N D 1 + = C D 1 exp ( t τ r 1 ) + C D 2 exp ( t τ r 2 ) + D 2 S 3 D 3 S 1 D 1 S 1 D 2 S 2 ,
N S 1 + = S 1 D 1 + G 2 D 2 C D 1 exp ( t τ r 1 ) + S 1 D 1 G 2 D 2 C D 2 exp ( t τ r 2 ) + D 3 S 2 D 1 S 3 D 1 S 1 D 2 S 2 ,
D 1 = ( S D H I H + γ D n 0 + γ D A N D 0 + ) ,
D 2 = γ D B N D 0 + ,
D 3 = γ D C N D 0 + ,
S 1 = ( S S L I L 0 + S S H I H + β t s + γ S n 0 + γ S B N S 0 + ) ,
S 2 = γ S A N S 0 + ,
S 3 = m S S L I L 0 e ̂ s e ̂ r ( N S N S 0 + ) γ S C N S 0 + ,
G = ( S 1 D 1 ) 2 + 4 D 2 S 2 ,
τ r 1 = 2 ( S 1 + D 1 + G ) ,
τ r 2 = 2 ( S 1 + D 1 G ) ,
C D 1 = 2 D 2 ( D 1 S 3 D 3 S 2 ) ( S 1 D 1 G ) ( D 3 S 1 D 2 S 3 ) 2 G ( D 1 S 1 D 2 S 2 ) ,
C D 2 = ( S 1 D 1 + G ) ( D 3 S 1 D 2 S 3 ) 2 D 2 ( D 1 S 3 D 3 S 2 ) 2 G ( D 1 S 1 D 2 S 2 ) .
n 1 = n 1 exp ( t τ r 3 ) ,
N S 1 + = N S 1 + exp ( t τ r 3 ) ,
N D 1 + = N D 1 + ( N D 1 + N D 1 + ) exp ( t τ r 3 ) .
N D 1 + = γ D N D 0 + 1 e n 0 τ r 3 K μ K K ϵ K + i 1 e τ r 3 I L r K k S L r 0 ( KDK + i K μ E 0 ) N S 1 + ( 1 γ D n 0 τ r 3 γ D N D 0 + 1 e n 0 τ r 3 K μ K K ϵ K ( KDK + i K μ E 0 ) ) N D 1 + γ D n 0 τ r 3 ( 1 e N D 0 + K μ K K ϵ K ( KDK + i K μ E 0 ) ) ( 1 γ D n 0 τ r 3 γ D N D 0 + 1 e n 0 τ r 3 K μ K K ϵ K ( KDK + i K μ E 0 ) ) .

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