Abstract

The polarization properties of diffraction from volume phase gratings in photorefractive sillenite crystals such as bismuth silicon oxide (Bi12SiO20), bismuth germanium oxide (Bi12GeO20), and bismuth titanium oxide (Bi12TiO20) are strongly modified by the presence of concomitant natural optical activity and electric-field-induced linear birefringence. A set of coupled-wave equations that characterize the Bragg regime has been derived for the 〈110〉 and the 〈001〉 crystallographic orientations typically employed in volume holographic storage and multiwave-mixing applications. The predicted anisotropic behavior of the grating diffraction is experimentally confirmed, and a significant efficiency improvement is shown to occur for proper choice of the operating mode and the probe beam polarization in a given configuration.

© 1986 Optical Society of America

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  1. B. Aurivillius and L. G. Sillen, “Polymorphy of bismuth trioxide,” Nature 155, 305–306 (1945).
    [Crossref]
  2. J. P. Huignard and F. Micheron, “High-sensitivity read–write volume holographic storage in Bi12SiO20and Bi12GeO20crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
    [Crossref]
  3. J. P. Huignard, J. P. Herriau, and T. Valentin, “Time average holographic interferometry with photoconductive electrooptic Bi12SiO20crystals,” Appl. Opt. 16(11), 2796–2798 (1977).
    [Crossref] [PubMed]
  4. B. A. Horwitz and F. J. Corbett, “The PROM—theory and applications for the Pockels readout optical modulator,” Opt. Eng. 17, 353–364 (1978).
    [Crossref]
  5. A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
    [Crossref]
  6. S. McCahon, S. Kim, and A. R. Tanguay, “Optically modulated linear-array total-internal-reflection spatial light modulator,” J. Opt. Soc. Am. A 1, 1314 (A) (1984).
  7. V. Markov, S. Odulov, and M. Soskin, “Dynamic holography and optical image processing,” Opt. Laser Technol. 11, 95–99 (1979).
    [Crossref]
  8. J. O. White and A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
    [Crossref]
  9. J. P. Huignard, J. P. Herriau, P. Aubourg, and E. Spitz, “Phase-conjugate wavefront generation via real-time holography in Bi12SiO20crystals,” Opt. Lett. 4, 21–23 (1979).
    [Crossref]
  10. J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
    [Crossref]
  11. J. P. Herriau, A. Delboulbe, B. Loiseaux, and J. P. Huignard, “Commutateur optique bidimensionnel par reseaux holographiques photoinduits,” J. Opt. (Paris) 15, 314–318 (1984).
    [Crossref]
  12. H. Rajbenbach and J. P. Huignard, “Self-induced coherent oscillations with photorefractive Bi12SiO20amplifier,” Opt. Lett. 10, 137–139 (1985).
    [Crossref] [PubMed]
  13. J. P. Herriau, J. P. Huignard, and P. Aubourg, “Some polarization properties of volume holograms in Bi12SiO20crystals and applications,” Appl. Opt. 17, 1851–1852 (1978).
    [Crossref] [PubMed]
  14. M. P. Petrov, T. G. Pencheva, and S. I. Stepanov, “Light diffraction from volume phase holograms in electrooptic photorefractive crystals,” J. Opt. (Paris) 12, 287–292 (1981).
    [Crossref]
  15. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [Crossref]
  16. P. St and J. Russell, “Optical volume holography,” Phys. Rep. 71, 209–312 (1981).
    [Crossref]
  17. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [Crossref]
  18. A. Yariv and J. Lotspeich, “Coupled-mode analysis of light propagation in optically active crystals,” J. Opt. Soc. Am. 72, 273–277 (1982).
    [Crossref]
  19. M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction in photorefractive ferroelectrics,” Ferroelectrics 21, 631–633 (1978).
    [Crossref]
  20. M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Image polarization characteristics storage in birefringent crystals,” Opt. Commun. 21, 297–300 (1977).
    [Crossref]
  21. M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction from the volume holograms in electrooptic birefringent crystals,” Opt. Commun. 29, 44–48 (1979).
    [Crossref]
  22. T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, “Selective properties of volume phase holograms in photorefractive crystals.” Opt. Commun. 40, 175–178 (1982).
    [Crossref]
  23. M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
    [Crossref]
  24. N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
    [Crossref]
  25. K. Rokushima and J. Yamakita, “Analysis of anisotropic dielectric gratings,” J. Opt. Soc. Am. 73, 901–908 (1983).
    [Crossref]
  26. A. Marrakchi, J. P. Huignard, and P. Gunter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20crystals,” Appl. Phys. 24, 131–138 (1981).
    [Crossref]
  27. A. R. Tanguay, P. Chavel, T. C. Strand, C. S. Wu, and B. H. Soffer, “Polarization properties of the variable-grating-mode liquid-crystal device,” Opt. Lett. 9(5), 174–176 (1984).
    [Crossref] [PubMed]
  28. M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).
  29. A. R. Tanguay, “The Czochralski growth and optical properties of bismuth silicon oxide,” Ph.D. dissertion (Yale University, New Haven, Conn., 1977).
  30. R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
    [Crossref]
  31. A. R. Tanguay, “Polarization properties of birefringent phase gratings,” J. Opt. Soc. Am. 72, (12), 1832 (1982).
  32. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Sec. 4.9.
  33. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [Crossref]
  34. V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
    [Crossref]
  35. N. V. Kukhtarev, V. B. Markov, and S. G. Odulov, “Nonstationary energy exchange during interaction between two light beams in electro-optical crystals,” Sov. Phys. Tech. Phys. 25, 1109–1114 (1980).
  36. V. N. Astratov, V. A. Ilinskii, and M. B. Melnikov, “Effect of preliminary optical excitation of traps on charge transfer of Bi12GeO20crystals,” Sov. Phys. Solid State 25, 1244–1247 (1983).
  37. Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [Crossref]
  38. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985), Sec. IV.
    [Crossref]
  39. B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 4, Sec. 4.8.
  40. B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 6, Sec. 6.5.
  41. L. Thylen and D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982).
    [Crossref] [PubMed]
  42. R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. (to be published).
  43. F. Vachss and L. Hesselink, “Holographic beam coupling in generally retarding media,” J. Opt. Soc. Am. A 1, 1221 (1984).
  44. S. I. Stepanov and M. P. Petrov, “Photorefractive crystals of the Bi12SiO20type for interferometry, wavefront conjugation, and processing of nonstationary images,” Opt. Acta 31, 1335–1343 (1984).
    [Crossref]

1985 (5)

A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[Crossref]

H. Rajbenbach and J. P. Huignard, “Self-induced coherent oscillations with photorefractive Bi12SiO20amplifier,” Opt. Lett. 10, 137–139 (1985).
[Crossref] [PubMed]

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985), Sec. IV.
[Crossref]

1984 (7)

A. R. Tanguay, P. Chavel, T. C. Strand, C. S. Wu, and B. H. Soffer, “Polarization properties of the variable-grating-mode liquid-crystal device,” Opt. Lett. 9(5), 174–176 (1984).
[Crossref] [PubMed]

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[Crossref]

J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[Crossref]

J. P. Herriau, A. Delboulbe, B. Loiseaux, and J. P. Huignard, “Commutateur optique bidimensionnel par reseaux holographiques photoinduits,” J. Opt. (Paris) 15, 314–318 (1984).
[Crossref]

S. McCahon, S. Kim, and A. R. Tanguay, “Optically modulated linear-array total-internal-reflection spatial light modulator,” J. Opt. Soc. Am. A 1, 1314 (A) (1984).

F. Vachss and L. Hesselink, “Holographic beam coupling in generally retarding media,” J. Opt. Soc. Am. A 1, 1221 (1984).

S. I. Stepanov and M. P. Petrov, “Photorefractive crystals of the Bi12SiO20type for interferometry, wavefront conjugation, and processing of nonstationary images,” Opt. Acta 31, 1335–1343 (1984).
[Crossref]

1983 (2)

K. Rokushima and J. Yamakita, “Analysis of anisotropic dielectric gratings,” J. Opt. Soc. Am. 73, 901–908 (1983).
[Crossref]

V. N. Astratov, V. A. Ilinskii, and M. B. Melnikov, “Effect of preliminary optical excitation of traps on charge transfer of Bi12GeO20crystals,” Sov. Phys. Solid State 25, 1244–1247 (1983).

1982 (4)

L. Thylen and D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982).
[Crossref] [PubMed]

A. R. Tanguay, “Polarization properties of birefringent phase gratings,” J. Opt. Soc. Am. 72, (12), 1832 (1982).

T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, “Selective properties of volume phase holograms in photorefractive crystals.” Opt. Commun. 40, 175–178 (1982).
[Crossref]

A. Yariv and J. Lotspeich, “Coupled-mode analysis of light propagation in optically active crystals,” J. Opt. Soc. Am. 72, 273–277 (1982).
[Crossref]

1981 (4)

A. Marrakchi, J. P. Huignard, and P. Gunter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

M. P. Petrov, T. G. Pencheva, and S. I. Stepanov, “Light diffraction from volume phase holograms in electrooptic photorefractive crystals,” J. Opt. (Paris) 12, 287–292 (1981).
[Crossref]

P. St and J. Russell, “Optical volume holography,” Phys. Rep. 71, 209–312 (1981).
[Crossref]

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

1980 (2)

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

J. O. White and A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[Crossref]

1979 (6)

J. P. Huignard, J. P. Herriau, P. Aubourg, and E. Spitz, “Phase-conjugate wavefront generation via real-time holography in Bi12SiO20crystals,” Opt. Lett. 4, 21–23 (1979).
[Crossref]

V. Markov, S. Odulov, and M. Soskin, “Dynamic holography and optical image processing,” Opt. Laser Technol. 11, 95–99 (1979).
[Crossref]

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

V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction from the volume holograms in electrooptic birefringent crystals,” Opt. Commun. 29, 44–48 (1979).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
[Crossref]

1978 (3)

B. A. Horwitz and F. J. Corbett, “The PROM—theory and applications for the Pockels readout optical modulator,” Opt. Eng. 17, 353–364 (1978).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction in photorefractive ferroelectrics,” Ferroelectrics 21, 631–633 (1978).
[Crossref]

J. P. Herriau, J. P. Huignard, and P. Aubourg, “Some polarization properties of volume holograms in Bi12SiO20crystals and applications,” Appl. Opt. 17, 1851–1852 (1978).
[Crossref] [PubMed]

1977 (2)

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Image polarization characteristics storage in birefringent crystals,” Opt. Commun. 21, 297–300 (1977).
[Crossref]

J. P. Huignard, J. P. Herriau, and T. Valentin, “Time average holographic interferometry with photoconductive electrooptic Bi12SiO20crystals,” Appl. Opt. 16(11), 2796–2798 (1977).
[Crossref] [PubMed]

1976 (1)

J. P. Huignard and F. Micheron, “High-sensitivity read–write volume holographic storage in Bi12SiO20and Bi12GeO20crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

1969 (1)

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

1965 (1)

R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
[Crossref]

1945 (1)

B. Aurivillius and L. G. Sillen, “Polymorphy of bismuth trioxide,” Nature 155, 305–306 (1945).
[Crossref]

Astratov, V. N.

V. N. Astratov, V. A. Ilinskii, and M. B. Melnikov, “Effect of preliminary optical excitation of traps on charge transfer of Bi12GeO20crystals,” Sov. Phys. Solid State 25, 1244–1247 (1983).

Athale, R. A.

J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[Crossref]

Aubourg, P.

Aurivillius, B.

B. Aurivillius and L. G. Sillen, “Polymorphy of bismuth trioxide,” Nature 155, 305–306 (1945).
[Crossref]

Carnahan, B.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 4, Sec. 4.8.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 6, Sec. 6.5.

Chavel, P.

Corbett, F. J.

B. A. Horwitz and F. J. Corbett, “The PROM—theory and applications for the Pockels readout optical modulator,” Opt. Eng. 17, 353–364 (1978).
[Crossref]

Delboulbe, A.

J. P. Herriau, A. Delboulbe, B. Loiseaux, and J. P. Huignard, “Commutateur optique bidimensionnel par reseaux holographiques photoinduits,” J. Opt. (Paris) 15, 314–318 (1984).
[Crossref]

Dovgalenko, G. E.

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[Crossref]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985), Sec. IV.
[Crossref]

Goodman, J. M.

J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[Crossref]

Gunter, P.

A. Marrakchi, J. P. Huignard, and P. Gunter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

Herriau, J. P.

Hesselink, L.

F. Vachss and L. Hesselink, “Holographic beam coupling in generally retarding media,” J. Opt. Soc. Am. A 1, 1221 (1984).

Horwitz, B. A.

B. A. Horwitz and F. J. Corbett, “The PROM—theory and applications for the Pockels readout optical modulator,” Opt. Eng. 17, 353–364 (1978).
[Crossref]

Huignard, J. P.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

H. Rajbenbach and J. P. Huignard, “Self-induced coherent oscillations with photorefractive Bi12SiO20amplifier,” Opt. Lett. 10, 137–139 (1985).
[Crossref] [PubMed]

J. P. Herriau, A. Delboulbe, B. Loiseaux, and J. P. Huignard, “Commutateur optique bidimensionnel par reseaux holographiques photoinduits,” J. Opt. (Paris) 15, 314–318 (1984).
[Crossref]

A. Marrakchi, J. P. Huignard, and P. Gunter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

J. P. Huignard, J. P. Herriau, P. Aubourg, and E. Spitz, “Phase-conjugate wavefront generation via real-time holography in Bi12SiO20crystals,” Opt. Lett. 4, 21–23 (1979).
[Crossref]

J. P. Herriau, J. P. Huignard, and P. Aubourg, “Some polarization properties of volume holograms in Bi12SiO20crystals and applications,” Appl. Opt. 17, 1851–1852 (1978).
[Crossref] [PubMed]

J. P. Huignard, J. P. Herriau, and T. Valentin, “Time average holographic interferometry with photoconductive electrooptic Bi12SiO20crystals,” Appl. Opt. 16(11), 2796–2798 (1977).
[Crossref] [PubMed]

J. P. Huignard and F. Micheron, “High-sensitivity read–write volume holographic storage in Bi12SiO20and Bi12GeO20crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

Ilinskii, V. A.

V. N. Astratov, V. A. Ilinskii, and M. B. Melnikov, “Effect of preliminary optical excitation of traps on charge transfer of Bi12GeO20crystals,” Sov. Phys. Solid State 25, 1244–1247 (1983).

Johnson, R. V.

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. (to be published).

Kamshilin, A. A.

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction from the volume holograms in electrooptic birefringent crystals,” Opt. Commun. 29, 44–48 (1979).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction in photorefractive ferroelectrics,” Ferroelectrics 21, 631–633 (1978).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Image polarization characteristics storage in birefringent crystals,” Opt. Commun. 21, 297–300 (1977).
[Crossref]

Khomenko, A. V.

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

Kim, S.

S. McCahon, S. Kim, and A. R. Tanguay, “Optically modulated linear-array total-internal-reflection spatial light modulator,” J. Opt. Soc. Am. A 1, 1314 (A) (1984).

Kogelnik, H.

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

Kondilenko, V.

V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
[Crossref]

Krasin’kova, M. V.

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

Kukhtarev, N. V.

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[Crossref]

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

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

Kulikov, V. V.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
[Crossref]

Kung, S. -Y.

J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[Crossref]

Leonberger, F. J.

J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[Crossref]

Loiseaux, B.

J. P. Herriau, A. Delboulbe, B. Loiseaux, and J. P. Huignard, “Commutateur optique bidimensionnel par reseaux holographiques photoinduits,” J. Opt. (Paris) 15, 314–318 (1984).
[Crossref]

Lotspeich, J.

Luther, H. A.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 4, Sec. 4.8.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 6, Sec. 6.5.

Marakhonov, V. I.

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

Markov, V.

V. Markov, S. Odulov, and M. Soskin, “Dynamic holography and optical image processing,” Opt. Laser Technol. 11, 95–99 (1979).
[Crossref]

V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
[Crossref]

Markov, V. B.

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

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

Marrakchi, A.

A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[Crossref]

A. Marrakchi, J. P. Huignard, and P. Gunter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

McCahon, S.

S. McCahon, S. Kim, and A. R. Tanguay, “Optically modulated linear-array total-internal-reflection spatial light modulator,” J. Opt. Soc. Am. A 1, 1314 (A) (1984).

Melnikov, M. B.

V. N. Astratov, V. A. Ilinskii, and M. B. Melnikov, “Effect of preliminary optical excitation of traps on charge transfer of Bi12GeO20crystals,” Sov. Phys. Solid State 25, 1244–1247 (1983).

Micheron, F.

J. P. Huignard and F. Micheron, “High-sensitivity read–write volume holographic storage in Bi12SiO20and Bi12GeO20crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

Miridonov, S. V.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
[Crossref]

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985), Sec. IV.
[Crossref]

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Nitsche, R.

R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
[Crossref]

Odulov, S.

V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
[Crossref]

V. Markov, S. Odulov, and M. Soskin, “Dynamic holography and optical image processing,” Opt. Laser Technol. 11, 95–99 (1979).
[Crossref]

Odulov, S. G.

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

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

Pencheva, T. G.

T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, “Selective properties of volume phase holograms in photorefractive crystals.” Opt. Commun. 40, 175–178 (1982).
[Crossref]

M. P. Petrov, T. G. Pencheva, and S. I. Stepanov, “Light diffraction from volume phase holograms in electrooptic photorefractive crystals,” J. Opt. (Paris) 12, 287–292 (1981).
[Crossref]

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, “Photorefractive crystals of the Bi12SiO20type for interferometry, wavefront conjugation, and processing of nonstationary images,” Opt. Acta 31, 1335–1343 (1984).
[Crossref]

T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, “Selective properties of volume phase holograms in photorefractive crystals.” Opt. Commun. 40, 175–178 (1982).
[Crossref]

M. P. Petrov, T. G. Pencheva, and S. I. Stepanov, “Light diffraction from volume phase holograms in electrooptic photorefractive crystals,” J. Opt. (Paris) 12, 287–292 (1981).
[Crossref]

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction from the volume holograms in electrooptic birefringent crystals,” Opt. Commun. 29, 44–48 (1979).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction in photorefractive ferroelectrics,” Ferroelectrics 21, 631–633 (1978).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Image polarization characteristics storage in birefringent crystals,” Opt. Commun. 21, 297–300 (1977).
[Crossref]

Psaltis, D.

A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[Crossref]

Rajbenbach, H.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

H. Rajbenbach and J. P. Huignard, “Self-induced coherent oscillations with photorefractive Bi12SiO20amplifier,” Opt. Lett. 10, 137–139 (1985).
[Crossref] [PubMed]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Rokushima, K.

Russell, J.

P. St and J. Russell, “Optical volume holography,” Phys. Rep. 71, 209–312 (1981).
[Crossref]

Shlyagin, M. G.

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

Sillen, L. G.

B. Aurivillius and L. G. Sillen, “Polymorphy of bismuth trioxide,” Nature 155, 305–306 (1945).
[Crossref]

Soffer, B. H.

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Soskin, M.

V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
[Crossref]

V. Markov, S. Odulov, and M. Soskin, “Dynamic holography and optical image processing,” Opt. Laser Technol. 11, 95–99 (1979).
[Crossref]

Soskin, M. S.

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

Spitz, E.

St, P.

P. St and J. Russell, “Optical volume holography,” Phys. Rep. 71, 209–312 (1981).
[Crossref]

Starkov, V. N.

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[Crossref]

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, “Photorefractive crystals of the Bi12SiO20type for interferometry, wavefront conjugation, and processing of nonstationary images,” Opt. Acta 31, 1335–1343 (1984).
[Crossref]

T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, “Selective properties of volume phase holograms in photorefractive crystals.” Opt. Commun. 40, 175–178 (1982).
[Crossref]

M. P. Petrov, T. G. Pencheva, and S. I. Stepanov, “Light diffraction from volume phase holograms in electrooptic photorefractive crystals,” J. Opt. (Paris) 12, 287–292 (1981).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction from the volume holograms in electrooptic birefringent crystals,” Opt. Commun. 29, 44–48 (1979).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction in photorefractive ferroelectrics,” Ferroelectrics 21, 631–633 (1978).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Image polarization characteristics storage in birefringent crystals,” Opt. Commun. 21, 297–300 (1977).
[Crossref]

Strand, T. C.

Tanguay, A. R.

A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[Crossref]

S. McCahon, S. Kim, and A. R. Tanguay, “Optically modulated linear-array total-internal-reflection spatial light modulator,” J. Opt. Soc. Am. A 1, 1314 (A) (1984).

A. R. Tanguay, P. Chavel, T. C. Strand, C. S. Wu, and B. H. Soffer, “Polarization properties of the variable-grating-mode liquid-crystal device,” Opt. Lett. 9(5), 174–176 (1984).
[Crossref] [PubMed]

A. R. Tanguay, “Polarization properties of birefringent phase gratings,” J. Opt. Soc. Am. 72, (12), 1832 (1982).

A. R. Tanguay, “The Czochralski growth and optical properties of bismuth silicon oxide,” Ph.D. dissertion (Yale University, New Haven, Conn., 1977).

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. (to be published).

Thylen, L.

Vachss, F.

F. Vachss and L. Hesselink, “Holographic beam coupling in generally retarding media,” J. Opt. Soc. Am. A 1, 1221 (1984).

Valentin, T.

Vinetskii, V. L.

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

White, J. O.

J. O. White and A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[Crossref]

Wilkes, J. O.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 6, Sec. 6.5.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 4, Sec. 4.8.

Wu, C. S.

Yamakita, J.

Yariv, A.

A. Yariv and J. Lotspeich, “Coupled-mode analysis of light propagation in optically active crystals,” J. Opt. Soc. Am. 72, 273–277 (1982).
[Crossref]

J. O. White and A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[Crossref]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Sec. 4.9.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Sec. 4.9.

Yevick, D.

Yu, J.

A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[Crossref]

Appl. Opt. (3)

Appl. Phys. (1)

A. Marrakchi, J. P. Huignard, and P. Gunter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

Appl. Phys. A (1)

N. V. Kukhtarev, G. E. Dovgalenko, and V. N. Starkov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[Crossref]

Appl. Phys. Lett. (2)

J. P. Huignard and F. Micheron, “High-sensitivity read–write volume holographic storage in Bi12SiO20and Bi12GeO20crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

J. O. White and A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[Crossref]

Bell Syst. Tech. J. (1)

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

Ferroelectrics (2)

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

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction in photorefractive ferroelectrics,” Ferroelectrics 21, 631–633 (1978).
[Crossref]

J. Appl. Phys. (2)

R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
[Crossref]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

J. Opt. (Paris) (2)

M. P. Petrov, T. G. Pencheva, and S. I. Stepanov, “Light diffraction from volume phase holograms in electrooptic photorefractive crystals,” J. Opt. (Paris) 12, 287–292 (1981).
[Crossref]

J. P. Herriau, A. Delboulbe, B. Loiseaux, and J. P. Huignard, “Commutateur optique bidimensionnel par reseaux holographiques photoinduits,” J. Opt. (Paris) 15, 314–318 (1984).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

F. Vachss and L. Hesselink, “Holographic beam coupling in generally retarding media,” J. Opt. Soc. Am. A 1, 1221 (1984).

S. McCahon, S. Kim, and A. R. Tanguay, “Optically modulated linear-array total-internal-reflection spatial light modulator,” J. Opt. Soc. Am. A 1, 1314 (A) (1984).

Nature (1)

B. Aurivillius and L. G. Sillen, “Polymorphy of bismuth trioxide,” Nature 155, 305–306 (1945).
[Crossref]

Opt. Acta (2)

V. Kondilenko, V. Markov, S. Odulov, and M. Soskin, “Diffraction of coupled waves and determination of phase mismatch between holographic grating and fringe pattern,” Opt. Acta 26, 238–251 (1979).
[Crossref]

S. I. Stepanov and M. P. Petrov, “Photorefractive crystals of the Bi12SiO20type for interferometry, wavefront conjugation, and processing of nonstationary images,” Opt. Acta 31, 1335–1343 (1984).
[Crossref]

Opt. Commun. (4)

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Image polarization characteristics storage in birefringent crystals,” Opt. Commun. 21, 297–300 (1977).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Light diffraction from the volume holograms in electrooptic birefringent crystals,” Opt. Commun. 29, 44–48 (1979).
[Crossref]

T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, “Selective properties of volume phase holograms in photorefractive crystals.” Opt. Commun. 40, 175–178 (1982).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, and V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic Bi12SiO20crystals,” Opt. Commun. 31, 301–305 (1979).
[Crossref]

Opt. Eng. (2)

B. A. Horwitz and F. J. Corbett, “The PROM—theory and applications for the Pockels readout optical modulator,” Opt. Eng. 17, 353–364 (1978).
[Crossref]

A. Marrakchi, A. R. Tanguay, J. Yu, and D. Psaltis, “Physical characterization of the photorefractive incoherent-to-coherent optical converter,” Opt. Eng. 24, 124–131 (1985).
[Crossref]

Opt. Laser Technol. (1)

V. Markov, S. Odulov, and M. Soskin, “Dynamic holography and optical image processing,” Opt. Laser Technol. 11, 95–99 (1979).
[Crossref]

Opt. Lett. (3)

Phys. Rep. (1)

P. St and J. Russell, “Optical volume holography,” Phys. Rep. 71, 209–312 (1981).
[Crossref]

Proc. IEEE (3)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985), Sec. IV.
[Crossref]

J. M. Goodman, F. J. Leonberger, S. -Y. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[Crossref]

Sov. Phys. Solid State (1)

V. N. Astratov, V. A. Ilinskii, and M. B. Melnikov, “Effect of preliminary optical excitation of traps on charge transfer of Bi12GeO20crystals,” Sov. Phys. Solid State 25, 1244–1247 (1983).

Sov. Phys. Tech. Phys. (2)

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

M. P. Petrov, A. V. Khomenko, M. V. Krasin’kova, V. I. Marakhonov, and M. G. Shlyagin, “The PRIZ image converter and its use in optical data processing systems,” Sov. Phys. Tech. Phys. 26, 816–821 (1981).

Other (5)

A. R. Tanguay, “The Czochralski growth and optical properties of bismuth silicon oxide,” Ph.D. dissertion (Yale University, New Haven, Conn., 1977).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Sec. 4.9.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 4, Sec. 4.8.

B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969), Chap. 6, Sec. 6.5.

R. V. Johnson and A. R. Tanguay, “Optical beam propagation method for birefringent phase grating diffraction,” Opt. Eng. (to be published).

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Figures (21)

Fig. 1
Fig. 1

The {KG || 〈001〉} crystal orientation of Bi12SiO20 for volume holography. The dashed line represents a normal to the entrance face. The x, y, and z coordinate system shown to the left of the crystal is assumed in the light-propagation analysis. The xEO, yEO, and zEO axes shown on the crystal face refer to the principal electrooptic axes induced by the applied bias electric field, as discussed in Section 2.

Fig. 2
Fig. 2

The {KG ⊥ 〈001〉} crystal orientation of Bi12SiO20 for volume holography.

Fig. 3
Fig. 3

Top view of the grating readout process showing the angular separation of the probe beam R and the diffracted signal beam S and defining the propagation angles θR and θS.

Fig. 4
Fig. 4

Theoretical dependence of the diffraction efficiency on the polarization angle of a linearly polarized readout (probe) beam aligned at the nominal Bragg angle [defined in Eq. (23)] for the {KG || 〈001〉} configuration in the diffusion limit (no applied bias field). These curves are valid only in the limit of low diffraction efficiencies and will be modified for higher diffraction efficiencies.

Fig. 5
Fig. 5

Theoretical dependence of the diffraction efficiency on the polarization angle of a linearly polarized readout (probe) beam aligned at the nominal Bragg angle for the {KG 〈001〉} configuration. The same behavior occurs with or without an applied bias field and in both the low and the high diffraction efficiency regimes. The particular spacing of the various ρd lines will vary under these conditions but not their insensitivity to the input probe beam polarization direction.

Fig. 6
Fig. 6

Theoretical dependence of the ellipticity of the diffracted signal beam on the applied bias field strength for a 5-mm-thick crystal of Bi12SiO20 in the {KG ⊥ 〈001〉} configuration, comparing the polarization states of the diffracted signal beam with and without optical activity. The input probe beam is linearly polarized and is aligned along the nominal Bragg angle.

Fig. 7
Fig. 7

Momentum-matching condition for an isotropic grating in an off-Bragg alignment. The physical diffracted beam is characterized by a wave-vector kS + Δki, where the ith increment is determined by the boundary conditions as described in Subsection 3.D.

Fig. 8
Fig. 8

Typical polarization states for the readout (probe) and diffracted signal beams for a 5-mm-thick crystal of Bi12SiO20 in the {KG || 〈001〉} orientation. The incident probe beam is linearly polarized, as shown in the left column, with a wavelength of 6328 Å, and is aligned along the nominal Bragg angle. The polarization states of the transmitted beams for the case of no applied bias field and no optical activity and for the case of a 6-kV/cm bias field with 21.4-deg/mm optical rotatory power are compared.

Fig. 9
Fig. 9

Typical polarization states for the readout (probe) and diffracted signal beams for a 5-mm-thick crystal of Bi12SiO20 in the {KG ⊥ 〈001〉} orientation and for the same conditions as those assumed in Fig. 8.

Fig. 10
Fig. 10

Evolution of the polarization states as a function of depth into the crystal for the {KG || 〈001〉} orientation (top sequence) and for the {KG ⊥ 〈001〉} orientation (bottom sequence). A 6328-Å-wavelength input probe beam is assumed, is aligned along the nominal Bragg angle, and is linearly polarized along one particular direction, as shown in the left column. A bias field of 6 kV/cm is applied to the crystal, and an optical rotatory power of 21.4 deg/mm is assumed. Note that the predictions shown here and in Figs. 1114 assume uniform grating strength and phase throughout the bulk of the crystal. In some cases, self-diffraction effects will modify these results.

Fig. 11
Fig. 11

Evolution of the polarization angle for both probe and diffracted signal beams as a function of grating depth for a typical {KG || 〈001〉} configuration. The same conditions as those in Fig. 10 are assumed in this figure and in Figs. 1214.

Fig. 12
Fig. 12

Evolution of the ellipticity for both probe and diffracted signal beams as a function of grating depth for a typical {KG || 〈001〉} configuration.

Fig. 13
Fig. 13

Evolution of the polarization angle for both probe and diffracted signal beams as a function of grating depth for a typical {KG ⊥ 〈001〉} configuration.

Fig. 14
Fig. 14

Evolution of the ellipticity for both probe and diffracted signal beams as a function of grating depth for a typical {KG ⊥ 〈001〉} configuration.

Fig. 15
Fig. 15

Wave-vector-matching diagram for birefringent phase gratings showing the cause of the angular shift of the optimum diffraction efficiency angles for the incident probe and the diffracted signal beams from the nominal isotropic Bragg-diffraction condition. See the discussion in Subsection 4.B.

Fig. 16
Fig. 16

Angular alignment sensitivity of a typical holographic grating written in a Bi12SiO20 crystal in the {KG 〈001〉} orientation, in the diffusion limit (no applied bias electric field) and for linearly polarized incident probe light. These curves were generated in the regime of low diffraction efficiencies, but very similar curves exist for higher diffraction efficiencies. Note that the double-peak structure is not adequately resolved for gratings thinner than ρd = 80°.

Fig. 17
Fig. 17

Angular alignment sensitivity of a typical holographic grating written in a Bi12SiO20 crystal (ρd = 80°) in the {KG ⊥ 〈001〉} orientation with no applied bias electric field comparing the diffraction efficiency for linearly polarized incident probe light with the diffraction efficiency for circularly polarized input light.

Fig. 18
Fig. 18

Comparison of the diffraction efficiency as a function of grating thickness for circularly polarized probe light at the anisotropic Bragg peak and for linearly polarized probe light at the nominal isotropic Bragg peak, for the {KG ⊥ 〈001〉} orientation in the diffusion limit.

Fig. 19
Fig. 19

Dependence of the diffraction efficiency on the polarization angle of a linearly polarized 6328-Å-wavelength readout (probe) beam aligned along the nominal Bragg angle for a 1.27-mm-thick crystal of Bi12SiO20 in the {KG || 〈001〉} configuration and in the diffusion limit (experimental points and theoretical curve).

Fig. 20
Fig. 20

Dependence of the diffraction efficiency on the polarization angle of a linearly polarized readout (probe) beam for a 1.27-mm-thick crystal of Bi12SiO20 in the {KG ⊥ 〈001〉} configuration, with the same conditions as assumed in Fig. 19 (experimental points and theoretical curve).

Fig. 21
Fig. 21

Dependence of the diffraction efficiency on the polarization angle of a linearly polarized readout (probe) beam for a 5.0-mm-thick crystal of Bi12SiO20 in the {KG || 〈001〉} configuration, with the same conditions as assumed in Fig. 19 (experimental points and theoretical curve).

Tables (1)

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Table 1 Values of Material Parameters for Bi12SiO20a

Equations (39)

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2 E + k 0 2 0 D = 0 ,
D i = 0 ( i j + G i j + Δ i j ) E j ,
i j = ( n 0 2 + i α n 0 / k 0 ) δ i j ω δ i j .
G i j E j g [ × E ] i ,
g = 2 ρ / k 0 2 .
Δ ( 1 ) i j = r i j k E k .
T = ( 0 0 1 - 1 / 2 - 1 / 2 0 1 / 2 - 1 / 2 0 ) .
i j = ( ω 0 0 0 ω + Δ 0 0 0 ω - Δ ) .
T = ( 1 / 2 1 / 2 0 0 0 - 1 - 1 / 2 + 1 / 2 0 ) .
i j ( ω - Δ 0 - Δ ω 0 0 0 ω ) .
Δ = n 0 r 4 41 E ( x ) .
E ( x ) = E 0 + E sc cos ( K G x + ϕ ) ,
E sc = m E q [ E 0 2 + E d 2 E 0 2 + ( E d + E q ) 2 ] 1 / 2 ,
tan ϕ = ( E d E 0 ) ( 1 + E d E q + E 0 2 E d E q ) .
E d = K G k B T e ,
E q = e N A 0 K G ,
p = Q / 2 γ ,
Q = K G 2 d n 0 k 0 .
E ( x , y , z ) = R ( z ) exp ( i k R · r ) + S ( z ) exp ( i k S · r ) ,
k R · r = n 0 k 0 ( x sin θ R + z cos θ R ) - 1 / 2 α z .
R = R E y ^ + R M ( x ^ cos θ R - z ^ sin θ R )
S = S E y ^ + S M ( x ^ cos θ S - z ^ sin θ S ) ,
sin θ B = sin θ R = sin θ S = K G 2 n 0 k 0
k S = k R + K G .
( D M D E ) = ( ω i a - i a ω + Δ ) ( E M E E ) ,
( D M D E ) = ( ω - Δ + i a - Δ - i a ω ) ( E M E E ) .
a = n 0 k 0 g = 2 n 0 ρ / k 0 .
d R M d z = - ρ R E ,
d R E d z = ρ R M + i C 0 R E + i e - i ϕ C sc S E ,
d S M d z = - ρ S E - i Δ S M ,
d S E d z = ρ S M + i ( C 0 - Δ ) S E + i e i ϕ C sc R E
d R M d z = - ( ρ + i C 0 ) R E - i e - i ϕ C sc S E ,
d R E d z = ( ρ - i C 0 ) R M - i e - i ϕ C sc S M ,
d S M d z = - i Δ S M - ( ρ + i C 0 ) S E - i e i ϕ C sc R E ,
d S E d z = ( ρ - i C 0 ) S M - i Δ S E - i e i ϕ C sc R M
C 0 = π n 0 r 3 41 E 0 / λ ,
C sc = 1 / 2 π n 0 r 3 41 E sc / λ .
Δ = 1 2 Q d ( 1 - sin θ R sin θ B )
δ θ = 2 ρ / K G .

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