Abstract

We explore theoretically and experimentally how applying an electric field to a photorefractive crystal affects the recording and the readout of a hologram. We present a unified theory that describes several electric-field-related mechanisms relevant to photorefractive crystals, including amplitude coupling, phase coupling, linear and nonlinear electro-optic effects, and the piezoelectric effect. We analyze the influence of these different effects on the Bragg selectivity and the diffraction efficiency and derive general analytical expressions describing the Bragg detuning effects. Finally, we compare the theory with experiments that we have performed in a strontium barium niobate crystal by recording and retrieving holograms in the presence of an applied electric field.

© 1995 Optical Society of America

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    [CrossRef]
  7. P. Xie, Y.-H. Hong, J.-H. Dai, and Y. Zhu, "Theoretical and experimental studies of fanning effects in photorefractive crystals," J. Appl. Phys. 74, 813–818 (1993).
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    [CrossRef]
  9. M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
    [CrossRef]
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  11. A. Kewitsch, M. Segev, A. Yariv, and R. R. Neurgaonkar, "Electric-field mutliplexing/demultiplexing of volume holograms in photorefractive media," Opt. Lett. 18, 534–536 (1993).
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  13. Y. Qiao, S. Orlov, D. Psaltis, and R. R. Neurgaonkar, "Electrical fixing of photorefractive holograms in Sr0.75Ba0.25Nb2O6," Opt. Lett. 18, 1004–1006 (1993).
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    [CrossRef]
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  25. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–960 (1979).
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  28. M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Trapping the grating envelope in bulk photorefractive media," Opt. Lett. 19, 1415–1417 (1994).
    [CrossRef] [PubMed]
  29. L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
    [CrossRef]
  30. T. Kubota, "The bending of interference fringes inside a hologram," Opt. Acta 26, 731–743 (1979).
    [CrossRef]
  31. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  32. 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, 885–901 (1984).
    [CrossRef]
  33. M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Evolution and propagation of grating envelopes during erasure in bulk photorefractive media," submitted to J. Opt. Soc. Am. B.
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    [CrossRef] [PubMed]
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    [CrossRef]
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  37. J. P. Wilde, R. De Vré, M. Jeganathan, and L. Hesselink, "Electric field control of image-bearing volume holograms stored in photorefractive media," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 98–99, paper CTuK26.
  38. S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, "Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate," IEEE J. Quantum Electron. 23, 2116–2121 (1987).
    [CrossRef]
  39. S. Tao, D. R. Selviah, and J. E. Midwinter, "Optimum replay angle for maximum diffraction efficiency of holographic gratings in Fe:LiNbO3 crystals," in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1993), paper FRG11/1(4).
  40. S. Tao, Z. H. Song, and D. R. Selviah, "Bragg-shifting of holographic gratings in photorefractive Fe:LiNbO3 crystals," Opt. Commun. 108, 144–152 (1994).
    [CrossRef]
  41. A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
    [CrossRef]
  42. J. P. Wilde, "Growth and characterization of strontium barium niobate crystals for multiplex photorefractive holography," Ph.D. dissertation (Stanford University, Stanford, Calif., 1992).

1994

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

R. De Vré, 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, 910–912 (1994).
[CrossRef] [PubMed]

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Trapping the grating envelope in bulk photorefractive media," Opt. Lett. 19, 1415–1417 (1994).
[CrossRef] [PubMed]

S. Tao, Z. H. Song, and D. R. Selviah, "Bragg-shifting of holographic gratings in photorefractive Fe:LiNbO3 crystals," Opt. Commun. 108, 144–152 (1994).
[CrossRef]

1993

1992

1991

1989

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

1988

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

J. Ma, L. Liu, S. Wu, and Z. Wang, "Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals," Appl. Phys. Lett. 53, 826–828 (1988).
[CrossRef]

1987

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, "Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate," IEEE J. Quantum Electron. 23, 2116–2121 (1987).
[CrossRef]

1986

A. A. Izvanov, A. E. Mandel, N. D. Khat'kov, and S. M. Shandarov, "Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals," Optoelectron. Instrum. Data Processing 2, 80–84 (1986).

J. M. C. Jonathan, R. W. Hellwarth, and G. Roosen, "Effect of applied electric field on the buildup and decay of photorefractive gratings," IEEE J. Quantum Electron. QE-22, 1936–1940 (1986).
[CrossRef]

1985

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

1984

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, 885–901 (1984).
[CrossRef]

1979

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

T. Kubota, "The bending of interference fringes inside a hologram," Opt. Acta 26, 731–743 (1979).
[CrossRef]

1977

S. I. Stepanov, A. A. Kamshilin, and M. P. Petrov, "Electrically controlled optical diffraction by volume holograms in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 3, 89–93 (1977) [Sov. Tech. Phys. Lett. 3, 36–38 (1977)].

1976

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 2, 1114 (1976) [Sov. Tech. Phys. Lett. 2, 438–440 (1976)].

1974

1972

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

1969

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

Amodei, J. J.

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

Bashaw, M. C.

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Trapping the grating envelope in bulk photorefractive media," Opt. Lett. 19, 1415–1417 (1994).
[CrossRef] [PubMed]

L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Evolution and propagation of grating envelopes during erasure in bulk photorefractive media," submitted to J. Opt. Soc. Am. B.

Bernasconi, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Bhalla, A. S.

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

Bize, D.

Brubaker, R. M.

Burns, G.

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

Cory, W. K.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Cross, L. E.

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

Dacol, F. H.

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

Dai, J.-H.

P. Xie, Y.-H. Hong, J.-H. Dai, and Y. Zhu, "Theoretical and experimental studies of fanning effects in photorefractive crystals," J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Ducharme, S.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, "Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate," IEEE J. Quantum Electron. 23, 2116–2121 (1987).
[CrossRef]

Duelli, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Ewbank, M. D.

R. A. Vasquez, F. R. Vachss, R. R. Neurgaonkar, and M. D. Ewbank, "Large photorefractive coupling coefficient in a thin cerium-doped strontium barium niobate crystal," J. Opt. Soc. Am. B 8, 1932–1941 (1991).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

Fainman, Y.

Feinberg, J.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, "Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate," IEEE J. Quantum Electron. 23, 2116–2121 (1987).
[CrossRef]

Ford, J. E.

Garret, M. H.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Goonesekera, A.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Gu, C.

Günter, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

P. Günter and M. Zgonik, "Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena," Opt. Lett. 16, 1826–1828 (1991).
[CrossRef] [PubMed]

Guo, R.

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[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, 885–901 (1984).
[CrossRef]

Hellwarth, R. W.

J. M. C. Jonathan, R. W. Hellwarth, and G. Roosen, "Effect of applied electric field on the buildup and decay of photorefractive gratings," IEEE J. Quantum Electron. QE-22, 1936–1940 (1986).
[CrossRef]

Hesselink, L.

R. De Vré, 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, 910–912 (1994).
[CrossRef] [PubMed]

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Trapping the grating envelope in bulk photorefractive media," Opt. Lett. 19, 1415–1417 (1994).
[CrossRef] [PubMed]

L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

J. P. Wilde and L. Hesselink, "Electric-field-controlled diffraction in photorefractive strontium barium niobate," Opt. Lett. 17, 853–855 (1992).
[CrossRef] [PubMed]

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

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Evolution and propagation of grating envelopes during erasure in bulk photorefractive media," submitted to J. Opt. Soc. Am. B.

J. P. Wilde, R. De Vré, M. Jeganathan, and L. Hesselink, "Electric field control of image-bearing volume holograms stored in photorefractive media," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 98–99, paper CTuK26.

Hong, J.

Hong, J. H.

Hong, Y.-H.

P. Xie, Y.-H. Hong, J.-H. Dai, and Y. Zhu, "Theoretical and experimental studies of fanning effects in photorefractive crystals," J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Izvanov, A. A.

A. A. Izvanov, A. E. Mandel, N. D. Khat'kov, and S. M. Shandarov, "Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals," Optoelectron. Instrum. Data Processing 2, 80–84 (1986).

Jeganathan, M.

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Trapping the grating envelope in bulk photorefractive media," Opt. Lett. 19, 1415–1417 (1994).
[CrossRef] [PubMed]

R. De Vré, 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, 910–912 (1994).
[CrossRef] [PubMed]

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Evolution and propagation of grating envelopes during erasure in bulk photorefractive media," submitted to J. Opt. Soc. Am. B.

J. P. Wilde, R. De Vré, M. Jeganathan, and L. Hesselink, "Electric field control of image-bearing volume holograms stored in photorefractive media," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 98–99, paper CTuK26.

Jonathan, J. M. C.

J. M. C. Jonathan, R. W. Hellwarth, and G. Roosen, "Effect of applied electric field on the buildup and decay of photorefractive gratings," IEEE J. Quantum Electron. QE-22, 1936–1940 (1986).
[CrossRef]

Jones, B. E.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Kamshilin, A. A.

S. I. Stepanov, A. A. Kamshilin, and M. P. Petrov, "Electrically controlled optical diffraction by volume holograms in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 3, 89–93 (1977) [Sov. Tech. Phys. Lett. 3, 36–38 (1977)].

Kestigan, M.

Kewitsch, A.

Khat'kov, N. D.

A. A. Izvanov, A. E. Mandel, N. D. Khat'kov, and S. M. Shandarov, "Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals," Optoelectron. Instrum. Data Processing 2, 80–84 (1986).

Knyaz'kov, A.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Kogelnik, H.

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

Kozhevnikov, N.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Kubota, T.

T. Kubota, "The bending of interference fringes inside a hologram," Opt. Acta 26, 731–743 (1979).
[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, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 2, 1114 (1976) [Sov. Tech. Phys. Lett. 2, 438–440 (1976)].

Kulikov, V.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Kuz'minov, Y.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Lee, S. H.

Liphardt, M.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Liu, L.

J. Ma, L. Liu, S. Wu, and Z. Wang, "Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals," Appl. Phys. Lett. 53, 826–828 (1988).
[CrossRef]

Ma, J.

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, Y. Taketomi, D. Bize, and R. R. Neurgaonkar, "Multiplex holography in strontium barium niobate with applied field," J. Opt. Soc. Am. A 9, 1183–1192 (1992).
[CrossRef]

J. Ma, L. Liu, S. Wu, and Z. Wang, "Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals," Appl. Phys. Lett. 53, 826–828 (1988).
[CrossRef]

Mandel, A. E.

A. A. Izvanov, A. E. Mandel, N. D. Khat'kov, and S. M. Shandarov, "Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals," Optoelectron. Instrum. Data Processing 2, 80–84 (1986).

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, 949–960 (1979).
[CrossRef]

Mathey, P.

Midwinter, J. E.

S. Tao, D. R. Selviah, and J. E. Midwinter, "Optimum replay angle for maximum diffraction efficiency of holographic gratings in Fe:LiNbO3 crystals," in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1993), paper FRG11/1(4).

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, 885–901 (1984).
[CrossRef]

Neurgaonkar, R. R.

Y. Qiao, S. Orlov, D. Psaltis, and R. R. Neurgaonkar, "Electrical fixing of photorefractive holograms in Sr0.75Ba0.25Nb2O6," Opt. Lett. 18, 1004–1006 (1993).
[CrossRef] [PubMed]

A. Kewitsch, M. Segev, A. Yariv, and R. R. Neurgaonkar, "Selective page-addressable fixing of volume holograms in Sr0.75Ba0.25Nb2O6 crystals," Opt. Lett. 18, 1262–1264 (1993).
[CrossRef] [PubMed]

A. Kewitsch, M. Segev, A. Yariv, and R. R. Neurgaonkar, "Electric-field mutliplexing/demultiplexing of volume holograms in photorefractive media," Opt. Lett. 18, 534–536 (1993).
[CrossRef] [PubMed]

J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, Y. Taketomi, D. Bize, and R. R. Neurgaonkar, "Multiplex holography in strontium barium niobate with applied field," J. Opt. Soc. Am. A 9, 1183–1192 (1992).
[CrossRef]

R. A. Vasquez, F. R. Vachss, R. R. Neurgaonkar, and M. D. Ewbank, "Large photorefractive coupling coefficient in a thin cerium-doped strontium barium niobate crystal," J. Opt. Soc. Am. B 8, 1932–1941 (1991).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, "Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate," IEEE J. Quantum Electron. 23, 2116–2121 (1987).
[CrossRef]

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

Nolte, D. D.

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, 949–960 (1979).
[CrossRef]

Orlov, S.

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, 885–901 (1984).
[CrossRef]

Pauliat, G.

Petrov, M. P.

S. I. Stepanov, A. A. Kamshilin, and M. P. Petrov, "Electrically controlled optical diffraction by volume holograms in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 3, 89–93 (1977) [Sov. Tech. Phys. Lett. 3, 36–38 (1977)].

Polozkov, N.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Psaltis, D.

Qiao, Y.

Redfield, S.

Roosen, G.

G. Pauliat, P. Mathey, and G. Roosen, "Influence of piezoelectricity on the photorefractive effect," J. Opt. Soc. Am. B 8, 1942–1946 (1991).
[CrossRef]

J. M. C. Jonathan, R. W. Hellwarth, and G. Roosen, "Effect of applied electric field on the buildup and decay of photorefractive gratings," IEEE J. Quantum Electron. QE-22, 1936–1940 (1986).
[CrossRef]

Rytz, D.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Saxena, R.

Schlesser, R.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Segev, M.

Selviah, D. R.

S. Tao, Z. H. Song, and D. R. Selviah, "Bragg-shifting of holographic gratings in photorefractive Fe:LiNbO3 crystals," Opt. Commun. 108, 144–152 (1994).
[CrossRef]

S. Tao, D. R. Selviah, and J. E. Midwinter, "Optimum replay angle for maximum diffraction efficiency of holographic gratings in Fe:LiNbO3 crystals," in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1993), paper FRG11/1(4).

Sergushchenko, S.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Shandarov, S. M.

A. A. Izvanov, A. E. Mandel, N. D. Khat'kov, and S. M. Shandarov, "Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals," Optoelectron. Instrum. Data Processing 2, 80–84 (1986).

Solymar, L.

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, 885–901 (1984).
[CrossRef]

Song, Z. H.

S. Tao, Z. H. Song, and D. R. Selviah, "Bragg-shifting of holographic gratings in photorefractive Fe:LiNbO3 crystals," Opt. Commun. 108, 144–152 (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, 949–960 (1979).
[CrossRef]

Staebler, D. L.

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, A. A. Kamshilin, and M. P. Petrov, "Electrically controlled optical diffraction by volume holograms in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 3, 89–93 (1977) [Sov. Tech. Phys. Lett. 3, 36–38 (1977)].

Takacs, J. M.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Taketomi, Y.

Tao, S.

S. Tao, Z. H. Song, and D. R. Selviah, "Bragg-shifting of holographic gratings in photorefractive Fe:LiNbO3 crystals," Opt. Commun. 108, 144–152 (1994).
[CrossRef]

S. Tao, D. R. Selviah, and J. E. Midwinter, "Optimum replay angle for maximum diffraction efficiency of holographic gratings in Fe:LiNbO3 crystals," in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1993), paper FRG11/1(4).

Thaxter, J. B.

Vachss, F. R.

Vasquez, R. A.

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, 949–960 (1979).
[CrossRef]

Vré, R. De

R. De Vré, 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, 910–912 (1994).
[CrossRef] [PubMed]

J. P. Wilde, R. De Vré, M. Jeganathan, and L. Hesselink, "Electric field control of image-bearing volume holograms stored in photorefractive media," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 98–99, paper CTuK26.

Wang, Q.

Wang, Z.

J. Ma, L. Liu, S. Wu, and Z. Wang, "Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals," Appl. Phys. Lett. 53, 826–828 (1988).
[CrossRef]

Whu, X.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Wilde, J. P.

R. De Vré, 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, 910–912 (1994).
[CrossRef] [PubMed]

J. P. Wilde and L. Hesselink, "Electric-field-controlled diffraction in photorefractive strontium barium niobate," Opt. Lett. 17, 853–855 (1992).
[CrossRef] [PubMed]

J. P. Wilde, R. De Vré, M. Jeganathan, and L. Hesselink, "Electric field control of image-bearing volume holograms stored in photorefractive media," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 98–99, paper CTuK26.

J. P. Wilde, "Growth and characterization of strontium barium niobate crystals for multiplex photorefractive holography," Ph.D. dissertation (Stanford University, Stanford, Calif., 1992).

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, 885–901 (1984).
[CrossRef]

Wu, S.

J. Ma, L. Liu, S. Wu, and Z. Wang, "Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals," Appl. Phys. Lett. 53, 826–828 (1988).
[CrossRef]

Xie, P.

P. Xie, Y.-H. Hong, J.-H. Dai, and Y. Zhu, "Theoretical and experimental studies of fanning effects in photorefractive crystals," J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Yariv, A.

Yeh, P.

C. Gu, J. Hong, and P. Yeh, "Diffraction properties of momentum-mismatched gratings in photorefractive media," J. Opt. Soc. Am. B 9, 1473–1479 (1992).
[CrossRef]

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

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.

Zgonik, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

P. Günter and M. Zgonik, "Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena," Opt. Lett. 16, 1826–1828 (1991).
[CrossRef] [PubMed]

Zhang, L.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Zhu, Y.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

P. Xie, Y.-H. Hong, J.-H. Dai, and Y. Zhu, "Theoretical and experimental studies of fanning effects in photorefractive crystals," J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. Ma, L. Liu, S. Wu, and Z. Wang, "Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals," Appl. Phys. Lett. 53, 826–828 (1988).
[CrossRef]

Bell Syst. Tech. J.

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

Ferroelectrics

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

IEEE J. Quantum Electron.

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

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, "Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate," IEEE J. Quantum Electron. 23, 2116–2121 (1987).
[CrossRef]

J. M. C. Jonathan, R. W. Hellwarth, and G. Roosen, "Effect of applied electric field on the buildup and decay of photorefractive gratings," IEEE J. Quantum Electron. QE-22, 1936–1940 (1986).
[CrossRef]

J. Appl. Phys.

P. Xie, Y.-H. Hong, J.-H. Dai, and Y. Zhu, "Theoretical and experimental studies of fanning effects in photorefractive crystals," J. Appl. Phys. 74, 813–818 (1993).
[CrossRef]

D. L. Staebler and J. J. Amodei, "Coupled-wave analysis of holographic storage in LiNbO3," J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, and J. Feinberg, "Photorefractive properties of strontium barium niobate," J. Appl. Phys. 62, 374–380 (1987).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Acta

T. Kubota, "The bending of interference fringes inside a hologram," Opt. Acta 26, 731–743 (1979).
[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, 885–901 (1984).
[CrossRef]

Opt. Commun.

S. Tao, Z. H. Song, and D. R. Selviah, "Bragg-shifting of holographic gratings in photorefractive Fe:LiNbO3 crystals," Opt. Commun. 108, 144–152 (1994).
[CrossRef]

Opt. Lett.

P. Günter and M. Zgonik, "Clamped-unclamped electro-optic coefficient dilemma in photorefractive phenomena," Opt. Lett. 16, 1826–1828 (1991).
[CrossRef] [PubMed]

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Trapping the grating envelope in bulk photorefractive media," Opt. Lett. 19, 1415–1417 (1994).
[CrossRef] [PubMed]

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

J. H. Hong and R. Saxena, "Diffraction efficiency of volume holograms written by coupled beams," Opt. Lett. 16, 180–182 (1991).
[PubMed]

R. De Vré, 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, 910–912 (1994).
[CrossRef] [PubMed]

A. Kewitsch, M. Segev, A. Yariv, and R. R. Neurgaonkar, "Electric-field mutliplexing/demultiplexing of volume holograms in photorefractive media," Opt. Lett. 18, 534–536 (1993).
[CrossRef] [PubMed]

J. P. Wilde and L. Hesselink, "Electric-field-controlled diffraction in photorefractive strontium barium niobate," Opt. Lett. 17, 853–855 (1992).
[CrossRef] [PubMed]

Y. Qiao, S. Orlov, D. Psaltis, and R. R. Neurgaonkar, "Electrical fixing of photorefractive holograms in Sr0.75Ba0.25Nb2O6," Opt. Lett. 18, 1004–1006 (1993).
[CrossRef] [PubMed]

A. Kewitsch, M. Segev, A. Yariv, and R. R. Neurgaonkar, "Selective page-addressable fixing of volume holograms in Sr0.75Ba0.25Nb2O6 crystals," Opt. Lett. 18, 1262–1264 (1993).
[CrossRef] [PubMed]

Opt. Quantum Electron.

L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

Optoelectron. Instrum. Data Processing

A. A. Izvanov, A. E. Mandel, N. D. Khat'kov, and S. M. Shandarov, "Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals," Optoelectron. Instrum. Data Processing 2, 80–84 (1986).

Phys. Rev. B

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garret, D. Rytz, Y. Zhu, and X. Whu, "Dielectric, elastic, piezoelectric, electrooptic, and elastooptic tensors of BaTiO3 crystal," Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

A. S. Bhalla, R. Guo, L. E. Cross, G. Burns, F. H. Dacol, and R. R. Neurgaonkar, "Measurements of strain and the optical indices in the ferroelectric Ba0.4Sr0.6Nb2O6: polarization effects," Phys. Rev. B 36, 2030–2035 (1987).
[CrossRef]

Pis'ma Zh. Tekh. Fiz.

S. I. Stepanov, A. A. Kamshilin, and M. P. Petrov, "Electrically controlled optical diffraction by volume holograms in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 3, 89–93 (1977) [Sov. Tech. Phys. Lett. 3, 36–38 (1977)].

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Pis'ma Zh. Tekh. Fiz. 2, 1114 (1976) [Sov. Tech. Phys. Lett. 2, 438–440 (1976)].

Science

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, and L. Zhang, "High-performance photorefractive polymers," Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Sov. Phys. Tech. Phys.

A. Knyaz'kov, N. Kozhevnikov, Y. Kuz'minov, V. Kulikov, N. Polozkov, and S. Sergushchenko, "Influence of an electric field on the diffraction efficiency of holograms in ceriumdoped barium-strontium niobate crystals," Sov. Phys. Tech. Phys. 29, 801–802 (1985).

Other

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, Berlin, 1989), Chap. 5, p. 141.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.

J. P. Wilde, R. De Vré, M. Jeganathan, and L. Hesselink, "Electric field control of image-bearing volume holograms stored in photorefractive media," in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 98–99, paper CTuK26.

S. Tao, D. R. Selviah, and J. E. Midwinter, "Optimum replay angle for maximum diffraction efficiency of holographic gratings in Fe:LiNbO3 crystals," in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1993), paper FRG11/1(4).

M. Jeganathan, M. C. Bashaw, and L. Hesselink, "Evolution and propagation of grating envelopes during erasure in bulk photorefractive media," submitted to J. Opt. Soc. Am. B.

J. P. Wilde, "Growth and characterization of strontium barium niobate crystals for multiplex photorefractive holography," Ph.D. dissertation (Stanford University, Stanford, Calif., 1992).

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Figures (13)

Fig. 1
Fig. 1

General writing and readout geometries: (a) transmission case, (b) reflection case. E0 is the applied field, K is the grating vector, and l is the crystal length.

Fig. 2
Fig. 2

Transmission geometry: grating amplitude m(z) and grating phase ψ(z) as a function of distance inside a SBN:61 crystal for six different fields (from 0 to 10 kV/cm). (a) rpp = 100, (b) rpp = 1/100 (Λg = 5.0 μm).

Fig. 3
Fig. 3

Reflection geometry: grating amplitude m(z) and grating phase ψ(z) as a function of distance inside a SBN:61 crystal for six different fields (from 0 to 10 kV/cm). (a) rpp = 100, (b) rpp = 1/100 (Λg = 0.2 μm).

Fig. 4
Fig. 4

Maximum diffraction efficiency as a function of applied field (E0W) for three grating spacings Λg: (a) 1.0 μm, (b) 2.5 μm, (c) 5.0 μm (transmission geometry, Eor = 0 kV/cm, and rpp = 1/100).

Fig. 5
Fig. 5

k-vector diagram representing the writing and the readout wave vectors in the transmission geometry. The hatched areas represent the spatial distribution of grating vectors KPC(z) that are present in the crystal owing to phase coupling.

Fig. 6
Fig. 6

Three-dimensional representation of the Bragg detuning parameter as a function of E0r and θ ̂ sig in an asymmetric transmission geometry, showing the simultaneous influence of the phase-coupling component and the electro-optic component in SBN:61 (rpp ≪ 1, θ ̂ ref = 0, E0W = 5 kV/cm). The plane (solid grid) represents ξ = 0.

Fig. 7
Fig. 7

Experimental setup: ND, neutral density.

Fig. 8
Fig. 8

Experimental (dotted curves) and theoretical (solid curves) diffraction efficiencies as functions of Δ θ ̂ ρ and of the Bragg detuning parameter ξ ̂ for holograms recorded at five different fields E0W; from top to bottom, 0, 2.5, 5.0, 7.5, and 10.0 kV/cm (rpp = 1/100, Λg = 5.0 μm).

Fig. 9
Fig. 9

Experimental data points and theoretical fit of the angular detuning Δ θ ̂ ρ as a function of the applied field (E0W) (rpp = 1/100, Λg = 5.0 μm).

Fig. 10
Fig. 10

Normalized diffraction efficiency of a grating written with extraordinary polarization and read with ordinary polarization in SBN:61 (Λg = 0.75 μm).

Fig. 11
Fig. 11

Measured angular detuning in degrees ( Δ θ ̂ pol ) as a function of the parameter X = ( Λ g / 2 n λ 0 ) sin 2 θ ̂ sig 180 / π. The angular coefficient of the linear fit yields |Δnb| = 0.027.

Fig. 12
Fig. 12

(a). Angular selectivity of a grating written at symmetric incidence in SBN:75 and then read at five different applied fields E0R equal to 0-4 kV/cm (Λg = 0.6 μm). (b) Angular selectivity of a grating written at asymmetric incidence in SBN:75 and then read at five different applied fields E0r equal to 0–4 kV/cm (Λg = 0.6 μm).

Fig. 13
Fig. 13

Electro-optic coefficient ( r ̂ 33 ) as a function of the field for Ce-doped SBN:75 (★, Λg = 0.6 μm; ▲, Λg = 0.75 μm; ◆, Λg = 1.0 μm).

Tables (2)

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Table 1 Values of the Physical Parameters for a Ce-Doped SBN:61 Photorefractive Crystal

Equations (72)

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E W ( r ) = A ref ( z ) exp ( i k ref r ) × ê ref + A sig ( z ) exp ( i k sig r ) ê sig ,
K = k sig k ref .
2 E W ( r ) + k 2 ( r ) E W ( r ) = 0 ,
k 2 ( r ) = k 0 2 i α k 0 + 2 k 0 π λ 0 × [ n 1 exp ( i ϕ ) A ref A sig * | A sig | 2 + | A ref | 2 exp ( i K r ) + c . c . ] ,
n 1 exp ( i ϕ ) = 1 2 n 3 r eff ζ ( K ) ( ê ref ê sig ) | E SC ( N ) | exp ( i ϕ ) .
| E SC ( N ) | exp ( i ϕ ) = i E Q ( E D i E 0 W ) E Q + E D i E 0 W ,
E D = | K | k B T e ,
E Q = e 0 r | K | N A ( 1 N A N D ) .
cos θ ref d A ref d z = i κ exp ( i ϕ ) | A sig | 2 A ref | A sig | 2 + | A ref | 2 α 2 A ref , cos θ sig d A sig d z = i κ exp ( i ϕ ) | A ref | 2 A sig | A sig | 2 + | A ref | 2 α 2 A sig ,
κ = π n 1 / λ 0 .
A ref ( z ) = [ I ref ( z ) ] 1 / 2 exp [ i ψ ref ( z ) ] , A sig ( z ) = [ I sig ( z ) ] 1 / 2 exp [ i ψ sig ( z ) ] ,
cos θ ref d I ref d z = 2 κ sin ϕ I sig I ref I sig + I ref α I ref , cos θ sig d I sig d z = 2 κ sin ϕ I ref I sig I sig + I ref α I sig , cos θ ref d ψ ref d z = κ cos ϕ I sig I sig + I ref , cos θ sig d ψ sig d z = κ cos ϕ I ref I sig + I ref .
n ( r ) = n + n 1 [ I ref ( z ) I sig ( z ) ] 1 / 2 I ref ( z ) + I sig ( z ) cos [ K PC ( z ) r + ϕ ] .
K PC ( z ) = K + [ ψ ( z ) z + K z ] ê z ,
ψ ( z ) = ψ ref ( z ) ψ sig ( z ) .
| cos θ ref | = | cos θ sig | = cos θ .
γ = 2 κ cos θ sin ϕ , β = κ cos θ cos ϕ .
I ref ( z ) = I ref ( 0 ) 1 + r pp 1 1 + r pp 1 exp ( γ z ) exp ( α z cos θ ) , I sig ( z ) = I sig ( 0 ) 1 + r pp 1 + r pp exp ( γ z ) exp ( α z cos θ ) , ψ ( z ) = β γ ln [ r pp + exp ( γ z ) ] [ 1 + r pp exp ( γ z ) ] ( 1 + r pp ) 2 ,
r pp = I ref ( 0 ) I sig ( 0 ) .
I ref ( z ) = { C + [ C 2 + B exp ( γ z ) ] 1 / 2 } exp ( α z cos θ ) , I sig ( z ) = { C + [ C 2 + B exp ( γ z ) ] 1 / 2 } exp ( α ( z l ) cos θ ) , ψ ( z ) = β z ,
B = I ref ( 0 ) I sig ( l ) I ref ( 0 ) + I sig ( l ) I sig ( l ) + I ref ( 0 ) exp ( γ l ) , C = 1 2 I sig 2 ( l ) I ref 2 ( 0 ) exp ( γ l ) I sig ( l ) + I ref ( 0 ) exp ( γ l ) .
r pp = I ref ( 0 ) I sig ( l ) .
m ( z ) = 2 [ I ref ( z ) I sig ( z ) ] 1 / 2 I ref ( z ) + I sig ( z ) .
m ( z ) = sech ( γ z ln r pp 2 ) , ψ ( z ) = 2 ( β / γ ) ln m ( z ) + constant .
m ( z ) = 2 ( r pp ) 1 / 2 exp ( γ z / 2 ) , ψ ( z ) = β z .
E R ( r ) = a ρ ( z ) exp ( i k ρ r ) + a σ ( z ) exp ( i k σ r ) ,
k σ = k ρ + K .
cos θ ρ d a ρ d z = i κ ̂ ( z ) exp ( i ϕ ) a σ exp [ i χ ( z ) z ] , cos θ σ d a σ d z = i κ ̂ ( z ) exp ( i ϕ ) a ρ exp [ i χ ( z ) z ] ,
χ ( z ) = k ρ z k σ z + ψ ( z ) z + K z ,
κ ̂ ( z ) = π λ 0 n 1 2 m ( z ) ,
â ρ ( z ) = a ρ ( z ) , â σ ( z ) = a σ ( z ) exp [ i χ ( z ) z ] ,
cos θ ρ d â ρ d z = i κ ̂ ( z ) exp ( i ϕ ) â σ , cos θ ρ [ d â σ d z i ξ ( z ) l â σ ] = i κ ̂ ( z ) exp ( i ϕ ) â ρ ,
ξ ( z ) = 2 ξ ̂ + l d ψ ( z ) d z
ξ ̂ = l 2 ( k ρ z k σ z + K z ) .
a σ ( ξ ̂ ) = i a ρ ( 0 ) exp ( i ϕ ) cos θ σ 0 l κ ̂ ( z ) × exp [ i ψ ( z ) ] exp ( i 2 ξ ̂ z l ) d z .
η ( ξ ̂ ) = | a σ ( ξ ̂ ) | 2 | a ρ ( 0 ) | 2 = [ π n 1 m ( 0 ) l 2 λ 0 cos θ σ ] 2 sinc 2 ξ ̂ .
Δ n ( z ) = n 1 2 m ( z ) exp [ i ψ ( z ) ] .
η ( ξ ̂ ) | T ξ ̂ { Δ n ( z ) rect ( z l 1 2 ) } | 2 | T ξ ̂ { Δ n ( z ) } * sinc ξ ̂ exp ( i ξ ̂ ) | 2 .
ξ ( z ) = 2 ξ ̂ l β 1 r pp 1 + r pp .
η = sin 2 ( π n 1 2 λ 0 cos θ 0 l m ( z ) d z ) ,
η = tanh 2 ( π n 1 2 λ 0 cos θ 0 l m ( z ) d z ) .
ξ ( z ) = 2 ξ ̂ + ξ PC ( z ) ,
ξ ̂ = ξ Kog ( Δ θ ρ , Δ λ ) + ξ field ( E 0 R , E 0 W ) , ξ PC ( z ) = l d ψ ( z ) d z .
ξ Kog ( Δ θ ρ , Δ λ ) = Δ θ ρ | K | l sin ( φ θ ρ ) 2 cos θ σ Δ λ | K | 2 l 8 π cos θ σ ,
K = 2 π λ 0 [ n ( θ ̂ sig , E 0 W ) sin θ sig ( θ ̂ sig , E 0 W ) n ( θ ̂ ref , E 0 W ) sin θ ref ( θ ̂ ref , E 0 W ) ] = 2 π λ 0 ( sin θ ̂ sig sin θ ̂ ref ) , K z = 2 π λ 0 [ n ( θ ̂ sig , E 0 W ) cos θ sig ( θ ̂ sig , E 0 W ) n ( θ ̂ ref , E 0 W ) cos θ ref ( θ ̂ ref , E 0 W ) ] , k ρ z = 2 π λ 0 n ( θ ̂ ref , E 0 R ) cos θ ref ( θ ̂ ref , E 0 R ) , K σ z = 2 π λ 0 n ( θ ̂ sig , E 0 R ) cos θ sig ( θ ̂ sig , E 0 R ) ,
ξ eo = ( l / 2 ) ( k ρ z k σ z + K z ) = ξ eo ( E 0 W , E 0 R , θ ̂ ref , θ ̂ sig ) .
ξ Δ n = l 2 d K z d n Δ n .
sin θ ref + n cos θ ref d θ ref d n = 0 , sin θ sig + n cos θ sig d θ sig d n = 0 ,
ξ Δ n = l 2 2 π λ 0 cos θ ref cos θ sig cos θ sig cos θ ref Δ n .
ξ Δ n = l 2 2 π λ 0 sin 2 θ ̂ sig sin 2 θ ̂ ref 2 n 2 Δ n .
Δ n e - pol = ½ n e 3 [ r ̂ 33 ( E 0 W ) E 0 W r ̂ 33 ( E 0 R ) E 0 R ] , Δ n o - pol = ½ n o 3 [ r ̂ 13 ( E 0 W ) E 0 W r ̂ 13 ( E 0 R ) E 0 R ] , Δ n b = n e n o ,
r ̂ l k ( E ) = r l k ( E ) + m p l m ( E ) d m k ( E ) ,
ξ eo T E = 2 π l λ 0 1 8 n e ( sin 2 θ ̂ ref sin 2 θ ̂ sig ) × [ r ̂ 33 ( E 0 R ) E 0 R r ̂ 33 ( E 0 W ) E 0 W ] , ξ eo T O = 2 π l λ 0 1 8 n o ( sin 2 θ ̂ ref sin 2 θ ̂ sig ) × [ r ̂ 13 ( E 0 R ) E 0 R r ̂ 13 ( E 0 W ) E 0 W ] , ξ eo R O = 2 π l λ 0 1 8 n o { ( sin 2 θ ̂ ref + sin 2 θ ̂ sig + 4 n o 2 ) × [ r ̂ 13 ( E 0 R ) E 0 R r ̂ 13 ( E 0 W ) E 0 W ] } , ξ eo R E = 2 π l λ 0 1 8 n o { 2 ( sin 2 θ ̂ ref + sin 2 θ ̂ sig ) × [ r ̂ 33 ( E 0 R ) E 0 R r ̂ 33 ( E 0 W ) E 0 W ] + 4 n o 2 [ r ̂ 13 ( E 0 R ) E 0 R r ̂ 13 ( E 0 W ) E 0 W ] } .
| Δ K K | = | Δ Λ g Λ g | = d 33 E 0 ,
ξ piezo = l 2 Δ K = l 2 d 33 ( E 0 W E 0 R ) 2 π Λ g .
ξ eo = l 2 2 π Λ g n o 2 2 r ̂ 13 E 0 , ξ piezo = l 2 2 π Λ g d 33 E 0 ,
ξ PC T ( z ) = l β tanh γ z ln r pp 2 , ξ PC R ( z ) = l β .
ξ = 2 π l λ 0 1 8 n e sin 2 θ ̂ sig r ̂ 33 ( E 0 W E 0 R ) l β .
ξ ̂ = l 2 d ψ d z = l κ cos ϕ 2 cos ϕ
Δ θ ̂ ρ ( E 0 W ) = κ cos ϕ cos θ n Λ g 2 π ,
r c = r ̂ 33 n o 3 n e 3 r ̂ 13 ,
| Δ n b | = 2 n λ 0 Λ g Δ θ ̂ pol sin 2 θ ̂ sig ,
X = Λ g sin 2 θ ̂ sig 2 n λ 0 180 π ,
ξ eo T E = 2 π l λ 0 n e 8 sin 2 θ ̂ sig r ̂ 33 ( E 0 R ) E 0 R .
r ̂ 33
r ̂ 13
ξ eo T E = 2 π l λ 0 n e 8 { ( sin 2 θ ̂ ref sin 2 θ ̂ sig ) × [ r ̂ 33 ( E 0 R ) E 0 R r ̂ 33 ( E 0 W ) E 0 W ] }
ξ eo R E = 2 π l λ 0 n o 8 { 2 ( sin 2 θ ̂ ref + sin 2 θ ̂ sig ) × [ r ̂ 33 ( E 0 R ) E 0 R r ̂ 33 ( E 0 W ) E 0 W ] + 4 n o 2 [ r ̂ 13 ( E 0 R ) E 0 R r ̂ 13 ( E 0 W ) E 0 W ] }
ξ PC T ( z ) = l β tanh γ z ln r PP 2
ξ piezo = l 2 d 33 ( E 0 W E 0 R ) 2 π Λ g
η max = sin 2 [ π n 1 2 λ 0 cos θ 0 l m ( z ) d z ]
η max = tanh 2 [ π n 1 2 λ 0 cos θ 0 l m ( z ) d z ]

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