Abstract

The diffraction from a thick photorefractive hologram is shown to be angular dependent, which originates mainly from the angle-dependent effective electro-optic coefficient of a photorefractive crystal. The angle dependency of the diffraction causes a nonuniform diffraction over the pixel positions or the spatial frequency contents of a hologram image in a page-oriented holographic system, resulting in a deteriorated reconstructed image. In addition, owing to the angular variations in diffraction, the wavelength-multiplexing scheme should be a better choice than angular one.

© 1995 Optical Society of America

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References

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  1. J. J. Amodei, D. L. Staebler, W. Stephens, “Holographic storage in doped barium sodium niobate (Ba2NaNb5O15),” Appl. Phys. Lett. 18, 507–509 (1971).
    [CrossRef]
  2. D. Psaltis, F. Mok, H. S. Li, “Nonvolatile storage in photorefractive crystals,” Opt. Lett. 19, 210–213 (1994).
    [CrossRef] [PubMed]
  3. F. H. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3 crystal,” Opt. Lett. 16, 605–607 (1991).
    [CrossRef] [PubMed]
  4. S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
    [CrossRef]
  5. F. T. S. Yu, S. Jutamulia, in Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992), Chap. 7, pp. 249–286.
  6. P. Gunter, J. P. Huignard, eds. Photorefractive Materials and Their Applications. I. (Springer-Verlag, New York, 1988), Chap. 2, p. 60.
  7. C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
    [CrossRef] [PubMed]
  8. M. C. Bashaw, A. Aharoni, L. Hesselink, “Alleviation of image distortion due to striations in a photorefractive medium by using a phase-conjugated reference wave,” Opt. Lett.1149–1151 (1992).
    [CrossRef] [PubMed]
  9. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
    [CrossRef]
  10. F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.
  11. J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Multibeam coupling in photorefractive SBN:Ce,” Opt. Lett. 13, 1020–1022 (1988).
    [CrossRef] [PubMed]
  12. D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
    [CrossRef]
  13. F. Vachss, L. Hesselink, “Nonlinear photorefractive response at high modulation depths,” J. Opt. Soc. Am. A 5, 690–701 (1988).
    [CrossRef]
  14. B. Fischer, M. Segev, “Photorefractive waveguide and nonlinear mode coupling effects,” Appl. Phys. Lett. 54, 684–686 (1989).
    [CrossRef]
  15. Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
  16. H. Kogelnik, “Coupled wave theory for thick holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  17. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).
  18. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystal,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  19. A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York1984), Chap. 7, pp. 232–233.
  20. A. M. Glass, D. Von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
  21. G. A. Rakujilc, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef]

1994

D. Psaltis, F. Mok, H. S. Li, “Nonvolatile storage in photorefractive crystals,” Opt. Lett. 19, 210–213 (1994).
[CrossRef] [PubMed]

D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
[CrossRef]

1993

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

1992

M. C. Bashaw, A. Aharoni, L. Hesselink, “Alleviation of image distortion due to striations in a photorefractive medium by using a phase-conjugated reference wave,” Opt. Lett.1149–1151 (1992).
[CrossRef] [PubMed]

G. A. Rakujilc, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef]

1991

C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
[CrossRef] [PubMed]

F. H. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3 crystal,” Opt. Lett. 16, 605–607 (1991).
[CrossRef] [PubMed]

1989

B. Fischer, M. Segev, “Photorefractive waveguide and nonlinear mode coupling effects,” Appl. Phys. Lett. 54, 684–686 (1989).
[CrossRef]

1988

1986

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

1983

C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

1974

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

1971

J. J. Amodei, D. L. Staebler, W. Stephens, “Holographic storage in doped barium sodium niobate (Ba2NaNb5O15),” Appl. Phys. Lett. 18, 507–509 (1971).
[CrossRef]

1969

H. Kogelnik, “Coupled wave theory for thick holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1966

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Aharoni, A.

M. C. Bashaw, A. Aharoni, L. Hesselink, “Alleviation of image distortion due to striations in a photorefractive medium by using a phase-conjugated reference wave,” Opt. Lett.1149–1151 (1992).
[CrossRef] [PubMed]

Amodei, J. J.

J. J. Amodei, D. L. Staebler, W. Stephens, “Holographic storage in doped barium sodium niobate (Ba2NaNb5O15),” Appl. Phys. Lett. 18, 507–509 (1971).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Bashaw, M. C.

M. C. Bashaw, A. Aharoni, L. Hesselink, “Alleviation of image distortion due to striations in a photorefractive medium by using a phase-conjugated reference wave,” Opt. Lett.1149–1151 (1992).
[CrossRef] [PubMed]

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Brady, D.

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Fainman, Y.

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

Fischer, B.

B. Fischer, M. Segev, “Photorefractive waveguide and nonlinear mode coupling effects,” Appl. Phys. Lett. 54, 684–686 (1989).
[CrossRef]

Glass, A. M.

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

Gu, C.

C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
[CrossRef] [PubMed]

Hesselink, L.

M. C. Bashaw, A. Aharoni, L. Hesselink, “Alleviation of image distortion due to striations in a photorefractive medium by using a phase-conjugated reference wave,” Opt. Lett.1149–1151 (1992).
[CrossRef] [PubMed]

F. Vachss, L. Hesselink, “Nonlinear photorefractive response at high modulation depths,” J. Opt. Soc. Am. A 5, 690–701 (1988).
[CrossRef]

Jutamulia, S.

F. T. S. Yu, S. Jutamulia, in Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992), Chap. 7, pp. 249–286.

Klancnik, E.

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

Klein, M. B.

C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lee, S. H.

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

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Leyva, V.

G. A. Rakujilc, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef]

Li, H. S.

Liu, L.

Ma, J.

McMillen, D. K.

F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.

Mok, F.

Mok, F. H.

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Negran, T. J.

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

Psaltis, D.

Rakujilc, G. A.

G. A. Rakujilc, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef]

Segev, M.

B. Fischer, M. Segev, “Photorefractive waveguide and nonlinear mode coupling effects,” Appl. Phys. Lett. 54, 684–686 (1989).
[CrossRef]

Shu, B.

Smith, R. C.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

Staebler, D. L.

J. J. Amodei, D. L. Staebler, W. Stephens, “Holographic storage in doped barium sodium niobate (Ba2NaNb5O15),” Appl. Phys. Lett. 18, 507–509 (1971).
[CrossRef]

Stephens, W.

J. J. Amodei, D. L. Staebler, W. Stephens, “Holographic storage in doped barium sodium niobate (Ba2NaNb5O15),” Appl. Phys. Lett. 18, 507–509 (1971).
[CrossRef]

Stoll, H. M.

Tackitt, M. C.

Vachss, F.

Valley, C.

C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

Von der Linde, D.

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

Wagner, K.

Wang, Z.

Wen, M.

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

Wu, S.

Wu, Z.

F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.

Xu, L.

Yang, Z.

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

Yariv, A.

G. A. Rakujilc, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef]

A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York1984), Chap. 7, pp. 232–233.

Yeh, P.

C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
[CrossRef] [PubMed]

A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York1984), Chap. 7, pp. 232–233.

Yin, S.

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

Yu, F. T. S.

D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
[CrossRef]

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

F. T. S. Yu, S. Jutamulia, in Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992), Chap. 7, pp. 249–286.

F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.

Zhang, J.

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

Zhao, D.

D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
[CrossRef]

Zhao, F.

D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
[CrossRef]

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.

Zhou, H.

D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
[CrossRef]

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.

Appl. Phys. Lett.

J. J. Amodei, D. L. Staebler, W. Stephens, “Holographic storage in doped barium sodium niobate (Ba2NaNb5O15),” Appl. Phys. Lett. 18, 507–509 (1971).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

B. Fischer, M. Segev, “Photorefractive waveguide and nonlinear mode coupling effects,” Appl. Phys. Lett. 54, 684–686 (1989).
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. C. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 71–74 (1966).
[CrossRef]

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

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Opt. Soc. Am. A

Microwave Opt. Tech. Lett.

D. Zhao, H. Zhou, F. Zhao, F. T. S. Yu, “Anisotropic intrasignal coupling in photorefractive LiNbO3,” Microwave Opt. Tech. Lett. 7, 483–486 (1994).
[CrossRef]

Opt. Lett.

C. Gu, P. Yeh, “Scattering due to randomly distributed charge particles in photorefractive crystals,” Opt. Lett. 16, 1572–1574 (1991).
[CrossRef] [PubMed]

G. A. Rakujilc, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef]

Opt. Commun.

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Yang, J. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

Opt. Eng.

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

C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

Opt. Lett.

Other

F. Zhao, H. Zhou, Z. Wu, F. T. S. Yu, D. K. McMillen, “Temperature dependence of light-induced scattering and noise suppression in Ce:Fe:LiNbO3,” submitted to Applied Optics.

F. T. S. Yu, S. Jutamulia, in Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992), Chap. 7, pp. 249–286.

P. Gunter, J. P. Huignard, eds. Photorefractive Materials and Their Applications. I. (Springer-Verlag, New York, 1988), Chap. 2, p. 60.

A. Yariv, P. Yeh, Optical Waves in Crystal (Wiley, New York1984), Chap. 7, pp. 232–233.

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Figures (6)

Fig. 1
Fig. 1

PR holographic recording configurations: (a) transmission type, (b) reflection type.

Fig. 2
Fig. 2

Relative diffraction efficiency (the vertical axis is in arbitrary units) as a function of angles θ1 and θ2 (the two horizontal axes are in units of degrees) with transmission-type SBN: (a) β = 0°, (b) β = 45°, (c) β = 90°.

Fig. 3
Fig. 3

Same as Fig. 2 but for transmission-type LiNbO3.

Fig. 4
Fig. 4

Same as Fig. 2 but for reflection-type SBN.

Fig. 5
Fig. 5

Same as Fig. 2 but for reflection-type LiNbO3.

Fig. 6
Fig. 6

Recording- and reconstructed-image intensity distribution over write-in angle θ1: (a) Input image. Relative intensity distribution of the reconstructed image (arbitrary units) for the following: (b) SBN, transmission, β = 0°, θ2 = 0°; (c) LiNbO3, transmission, β = 0°, θ2 = −15°; (d) SBN, reflection, β = 0°, θ2 = 20°; (e) LiNbO3, reflection, β = 45°, θ2 = 20°; (f) LiNbO3, transmission, β = 0°, θ2 = 0°; (g) LiNbO3, reflection, β = 0°, θ2 = 20°; (h) SBN, transmission, β = 45°, θ2 = 20°; (i) LiNbO3, reflection, β = 45°, θ2 = −20°.

Equations (10)

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

η [ π Δ n d λ ( c S c R ) 1 / 2 ] 2
Δ n = ( ½ ) n 3 r eff m E sc e S e R * ( t / τ r ) ,
r eff = { ½ n o 4 r 13 [ cos 2 α cos ( 2 β 2 ϕ ) ] + 4 n e 2 n o 2 r 51 × sin 2 ( β ϕ ) + ½ n e 4 r 33 [ cos 2 α + cos ( 2 β 2 ϕ ) ] } × cos ( β ϕ )
[ LiNbO 3 ( n o = 2.286 , n e = 2.20 ) ] r 51 = 33 , r 13 = 9.6 , r 33 = 31 ; [ SBN ( n o = 2.3117 , n e = 2.2987 ) ] r 51 = 42 , r 13 = 67 , r 33 = 1340 .
E sc = [ E o 2 + E d 2 ( 1 + E d / E q ) 2 + E o 2 / E q 2 ] 1 / 2 ,
E d k g = A sin α , E q k g 1 = B / sin α ,
= cos 2 ( β ϕ ) + sin 2 ( β ϕ )
E sc = [ E oph 2 cos 2 ( β ϕ ) + A 2 sin 2 α ( 1 + A sin 2 α / B ) 2 + ( E oph cos ( β ϕ ) sin α / B ) 2 ] 1 / 2 ,
η = c ( r eff E sc cos 2 α ) 2 / ( cos θ 1 cos θ 2 ) ,
BER 1 2 [ 1 erf ( x ) ] exp ( x 2 / 2 ) x 2 π ,

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