Abstract

The use of electro-optic (EO) crystal-based Fabry-Perot modulators (FPMs) as high-speed spatial light modulators is proposed. The FPMs operate with an extremely low drive voltage and a high extinction ratio. It is revealed by analysis of both the linear EO effect and the inverse piezoelectric effect of various EO crystals that three kinds of crystal configuration are suitable as FPMs. One of these is applicable to isotropic crystals, point groups 23 and 4̅3m, and the others are better suited for uniaxial EO crystals, point groups 4̅2m and 3m. Typical EO crystals suitable as FPMs are ferroelectric crystals such as LiNbO3, LiTaO3, and LiIO3 and sillenite compounds such as Bi12SiO20 and Bi12GeO20 as well as compound semiconductors such as GaAs and GaP.

© 2003 Optical Society of America

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  1. K. Takizawa, M. Okada, H. Kikuchi, T. Aida, “Bistable spatial light modulator using liquid crystal and Bi12SiO20 crystal layers,” Appl. Phys. Lett. 53, 2359–2361 (1988).
    [CrossRef]
  2. D. Armitage, J. I. Thackara, W. D. Eades, “Photoaddressed liquid crystal spatial light modulators,” Appl. Opt. 28, 4763–4771 (1989).
    [CrossRef] [PubMed]
  3. K. Takizawa, H. Kikuchi, T. Aida, M. Okada, “Optical parallel logic gate using a Pockels readout optical modulator and twisted nematic liquid-crystal cells,” Opt. Lett. 14, 208–210 (1989).
    [CrossRef] [PubMed]
  4. H. Fujikake, K. Takizawa, H. Kikuchi, “Bistable spatial light modulator using guest-host liquid crystal and Bi12GeO20 photoconductive crystal,” Jpn. J. Appl. Phys. 32, 842–848 (1993).
    [CrossRef]
  5. T. Aida, K. Takizawa, H. Kikuchi, M. Okada, “Optical parallel logic processor using a liquid crystal light valve and twisted nematic liquid crystal cells,” Jpn. J. Opt. 21, 724–729 (1992).
  6. Y. Kobayashi, T. Takemori, N. Mukohzaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
    [CrossRef] [PubMed]
  7. B. Javidi, G. Zhang, A. H. Fazlollahi, U. Efron, “Application of a wire-grid-mirror liquid-crystal light valve in a nonlinear joint transform correlator,” Appl. Opt. 33, 2834–2841 (1994).
    [CrossRef] [PubMed]
  8. M. Ishikawa, N. Mukohzaka, H. Toyoda, Y. Suzuki, “Optical associatron: a simple model for optical associative memory,” Appl. Opt. 28, 291–301 (1989).
    [CrossRef] [PubMed]
  9. D. R. Collins, J. B. Sampsell, L. J. Hornbeck, J. M. Florence, P. A. Penz, M. T. Gately, “Deformable mirror device spatial light modulators and their applicability to optical neural network,” Appl. Opt. 28, 4900–4907 (1989).
    [CrossRef] [PubMed]
  10. T. T. True, “High-performance video projector using two oil-film light valves,” in Technical Digest of the Society for Information Display International Symposium 18 (Society for Information Display, Santa Ana, Calif., 1987), pp. 68–71.
  11. V. J. Fritz, “Full-color, liquid crystal light valve projector for shipboard use,” in Large Screen and Projection Displays II, W. P. Bleha, ed., Proc. SPIE1255, 59–68 (1990).
    [CrossRef]
  12. R. A. Forber, A. Au. Efron, K. Sayyah, S. T. Wu, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” in Liquid Crystal Materials, Devices, and Application, P. S. Drzaic, U. Efron, eds., Proc. SPIE1665, 259–273 (1992).
    [CrossRef]
  13. K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
    [CrossRef]
  14. K. Takizawa, T. Fujii, M. Kawakita, H. Kikuchi, H. Fujikake, M. Yokozawa, A. Murata, K. Kishi, “Spatial light modulators for projection displays,” Appl. Opt. 36, 5732–5747 (1997).
    [CrossRef] [PubMed]
  15. K. Takizawa, T. Fujii, H. Kikuchi, H. Fujikake, M. Kawakita, Y. Hirano, F. Sato, “Spatial light modulators for high-brightness projection displays,” Appl. Opt. 38, 5646–5655 (1999).
    [CrossRef]
  16. B. A. Horwitz, F. J. Corbett, “The PROM—theory and applications for Pockels readout optical modulator,” Opt. Eng. 17, 353–364 (1978).
    [CrossRef]
  17. T. Minemoto, K. Okamoto, K. Miyamoto, “Optical parallel logic gate using spatial light modulators with the Pockels effect,” Appl. Opt. 24, 2055–2062 (1985).
    [CrossRef] [PubMed]
  18. C. Warde, A. D. Fisher, D. M. Cocco, M. Y. Burmawi, “Microchannel spatial light modulator,” Opt. Lett. 3, 196–198 (1978).
    [CrossRef] [PubMed]
  19. C. Warde, J. I. Thackara, “Oblique-cut LiNbO3 microchannel spatial light modulator,” Opt. Lett. 7, 344–346 (1982).
    [CrossRef] [PubMed]
  20. C. Warde, J. Thackra, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).
    [CrossRef]
  21. A. Schwartz, X.-Y. Wang, C. Warde, “Electron-beam-addressed microchannel spatial light modulator,” Opt. Eng. 24, 119–123 (1985).
    [CrossRef]
  22. T. Hara, K. Shinoda, T. Kato, M. Sugiyama, Y. Suzuki, “Microchannel spatial light modulator having the functions of image zooming, shifting, and rotating,” Appl. Opt. 25, 2306–2310 (1986).
    [CrossRef] [PubMed]
  23. T. Hara, Y. Ooi, Y. Suzuki, M. H. Wu, “Transfer characteristics of the microchannel spatial light modulator,” Appl. Opt. 28, 4781–4786 (1989).
    [CrossRef] [PubMed]
  24. T. Hara, Y. Suzuki, “Microchannel spatial light modulator,” Optoelectron. Devices Technol. 10, 393–420 (1995).
  25. Y. Kocher, G. Lebreton, B. Moreau, “The TITUS light modulator in optical processing,” in Optical Computing ’88, P. H. Charel, J. W. Goodman, G. Roblin, eds., Proc. SPIE963, 66–77 (1988).
    [CrossRef]
  26. Y. Bitou, T. Minemoto, “High-contrast spatial light modulator by use of the electroabsorption and the electro-optic effects in a GaAs single crystal,” Appl. Opt. 37, 4347–4356 (1998).
    [CrossRef]
  27. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Tokyo, 1980), pp. 66–70.
  28. K.-H. Hellwege, A. M. Hellwege, eds., Elastic, Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals, Vol. 11 of Landolt Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, K.-H. Hellwege, editor in chief Springer-Verlag, Berlin, 1979, pp. 287–670.
  29. K. Takizawa, M. Okada, “Simple method for measuring electro-optic coefficients by detecting the interference signal between transmitted and reflected beams,” J. Opt. Soc. Am. 72, 809–811 (1982).
    [CrossRef]
  30. K. Takizawa, M. Okada, “Determination of relative signs of electro-optic and piezoelectric coefficients by measuring optical phase shifts caused by an applied electric field,” J. Opt. Soc. Am. B 2, 289–293 (1985).
    [CrossRef]

1999 (1)

1998 (1)

1997 (1)

1995 (1)

T. Hara, Y. Suzuki, “Microchannel spatial light modulator,” Optoelectron. Devices Technol. 10, 393–420 (1995).

1994 (3)

1993 (1)

H. Fujikake, K. Takizawa, H. Kikuchi, “Bistable spatial light modulator using guest-host liquid crystal and Bi12GeO20 photoconductive crystal,” Jpn. J. Appl. Phys. 32, 842–848 (1993).
[CrossRef]

1992 (1)

T. Aida, K. Takizawa, H. Kikuchi, M. Okada, “Optical parallel logic processor using a liquid crystal light valve and twisted nematic liquid crystal cells,” Jpn. J. Opt. 21, 724–729 (1992).

1989 (5)

1988 (1)

K. Takizawa, M. Okada, H. Kikuchi, T. Aida, “Bistable spatial light modulator using liquid crystal and Bi12SiO20 crystal layers,” Appl. Phys. Lett. 53, 2359–2361 (1988).
[CrossRef]

1986 (1)

1985 (3)

1983 (1)

C. Warde, J. Thackra, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).
[CrossRef]

1982 (2)

1978 (2)

C. Warde, A. D. Fisher, D. M. Cocco, M. Y. Burmawi, “Microchannel spatial light modulator,” Opt. Lett. 3, 196–198 (1978).
[CrossRef] [PubMed]

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

Aida, T.

T. Aida, K. Takizawa, H. Kikuchi, M. Okada, “Optical parallel logic processor using a liquid crystal light valve and twisted nematic liquid crystal cells,” Jpn. J. Opt. 21, 724–729 (1992).

K. Takizawa, H. Kikuchi, T. Aida, M. Okada, “Optical parallel logic gate using a Pockels readout optical modulator and twisted nematic liquid-crystal cells,” Opt. Lett. 14, 208–210 (1989).
[CrossRef] [PubMed]

K. Takizawa, M. Okada, H. Kikuchi, T. Aida, “Bistable spatial light modulator using liquid crystal and Bi12SiO20 crystal layers,” Appl. Phys. Lett. 53, 2359–2361 (1988).
[CrossRef]

Armitage, D.

Au. Efron, A.

R. A. Forber, A. Au. Efron, K. Sayyah, S. T. Wu, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” in Liquid Crystal Materials, Devices, and Application, P. S. Drzaic, U. Efron, eds., Proc. SPIE1665, 259–273 (1992).
[CrossRef]

Bitou, Y.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Tokyo, 1980), pp. 66–70.

Burmawi, M. Y.

Cocco, D. M.

Collins, D. R.

Corbett, F. J.

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

Eades, W. D.

Efron, U.

Fazlollahi, A. H.

Fisher, A. D.

Florence, J. M.

Forber, R. A.

R. A. Forber, A. Au. Efron, K. Sayyah, S. T. Wu, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” in Liquid Crystal Materials, Devices, and Application, P. S. Drzaic, U. Efron, eds., Proc. SPIE1665, 259–273 (1992).
[CrossRef]

Fritz, V. J.

V. J. Fritz, “Full-color, liquid crystal light valve projector for shipboard use,” in Large Screen and Projection Displays II, W. P. Bleha, ed., Proc. SPIE1255, 59–68 (1990).
[CrossRef]

Fujii, T.

Fujikake, H.

K. Takizawa, T. Fujii, H. Kikuchi, H. Fujikake, M. Kawakita, Y. Hirano, F. Sato, “Spatial light modulators for high-brightness projection displays,” Appl. Opt. 38, 5646–5655 (1999).
[CrossRef]

K. Takizawa, T. Fujii, M. Kawakita, H. Kikuchi, H. Fujikake, M. Yokozawa, A. Murata, K. Kishi, “Spatial light modulators for projection displays,” Appl. Opt. 36, 5732–5747 (1997).
[CrossRef] [PubMed]

K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
[CrossRef]

H. Fujikake, K. Takizawa, H. Kikuchi, “Bistable spatial light modulator using guest-host liquid crystal and Bi12GeO20 photoconductive crystal,” Jpn. J. Appl. Phys. 32, 842–848 (1993).
[CrossRef]

Fukushima, S.

Gately, M. T.

Hara, T.

Hirano, Y.

Hornbeck, L. J.

Horwitz, B. A.

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

Ishikawa, M.

Javidi, B.

Kato, T.

Kawakita, M.

Kikuchi, H.

K. Takizawa, T. Fujii, H. Kikuchi, H. Fujikake, M. Kawakita, Y. Hirano, F. Sato, “Spatial light modulators for high-brightness projection displays,” Appl. Opt. 38, 5646–5655 (1999).
[CrossRef]

K. Takizawa, T. Fujii, M. Kawakita, H. Kikuchi, H. Fujikake, M. Yokozawa, A. Murata, K. Kishi, “Spatial light modulators for projection displays,” Appl. Opt. 36, 5732–5747 (1997).
[CrossRef] [PubMed]

K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
[CrossRef]

H. Fujikake, K. Takizawa, H. Kikuchi, “Bistable spatial light modulator using guest-host liquid crystal and Bi12GeO20 photoconductive crystal,” Jpn. J. Appl. Phys. 32, 842–848 (1993).
[CrossRef]

T. Aida, K. Takizawa, H. Kikuchi, M. Okada, “Optical parallel logic processor using a liquid crystal light valve and twisted nematic liquid crystal cells,” Jpn. J. Opt. 21, 724–729 (1992).

K. Takizawa, H. Kikuchi, T. Aida, M. Okada, “Optical parallel logic gate using a Pockels readout optical modulator and twisted nematic liquid-crystal cells,” Opt. Lett. 14, 208–210 (1989).
[CrossRef] [PubMed]

K. Takizawa, M. Okada, H. Kikuchi, T. Aida, “Bistable spatial light modulator using liquid crystal and Bi12SiO20 crystal layers,” Appl. Phys. Lett. 53, 2359–2361 (1988).
[CrossRef]

Kishi, K.

Kobayashi, Y.

Kocher, Y.

Y. Kocher, G. Lebreton, B. Moreau, “The TITUS light modulator in optical processing,” in Optical Computing ’88, P. H. Charel, J. W. Goodman, G. Roblin, eds., Proc. SPIE963, 66–77 (1988).
[CrossRef]

Lebreton, G.

Y. Kocher, G. Lebreton, B. Moreau, “The TITUS light modulator in optical processing,” in Optical Computing ’88, P. H. Charel, J. W. Goodman, G. Roblin, eds., Proc. SPIE963, 66–77 (1988).
[CrossRef]

Minemoto, T.

Miyamoto, K.

Moreau, B.

Y. Kocher, G. Lebreton, B. Moreau, “The TITUS light modulator in optical processing,” in Optical Computing ’88, P. H. Charel, J. W. Goodman, G. Roblin, eds., Proc. SPIE963, 66–77 (1988).
[CrossRef]

Mukohzaka, N.

Murata, A.

Namikawa, Y.

K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
[CrossRef]

Okada, M.

Okamoto, K.

Ooi, Y.

Penz, P. A.

Sampsell, J. B.

Sato, F.

Sayyah, K.

R. A. Forber, A. Au. Efron, K. Sayyah, S. T. Wu, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” in Liquid Crystal Materials, Devices, and Application, P. S. Drzaic, U. Efron, eds., Proc. SPIE1665, 259–273 (1992).
[CrossRef]

Schwartz, A.

A. Schwartz, X.-Y. Wang, C. Warde, “Electron-beam-addressed microchannel spatial light modulator,” Opt. Eng. 24, 119–123 (1985).
[CrossRef]

Shinoda, K.

Sugiyama, M.

Suzuki, Y.

Tada, K.

K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
[CrossRef]

Takemori, T.

Takizawa, K.

K. Takizawa, T. Fujii, H. Kikuchi, H. Fujikake, M. Kawakita, Y. Hirano, F. Sato, “Spatial light modulators for high-brightness projection displays,” Appl. Opt. 38, 5646–5655 (1999).
[CrossRef]

K. Takizawa, T. Fujii, M. Kawakita, H. Kikuchi, H. Fujikake, M. Yokozawa, A. Murata, K. Kishi, “Spatial light modulators for projection displays,” Appl. Opt. 36, 5732–5747 (1997).
[CrossRef] [PubMed]

K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
[CrossRef]

H. Fujikake, K. Takizawa, H. Kikuchi, “Bistable spatial light modulator using guest-host liquid crystal and Bi12GeO20 photoconductive crystal,” Jpn. J. Appl. Phys. 32, 842–848 (1993).
[CrossRef]

T. Aida, K. Takizawa, H. Kikuchi, M. Okada, “Optical parallel logic processor using a liquid crystal light valve and twisted nematic liquid crystal cells,” Jpn. J. Opt. 21, 724–729 (1992).

K. Takizawa, H. Kikuchi, T. Aida, M. Okada, “Optical parallel logic gate using a Pockels readout optical modulator and twisted nematic liquid-crystal cells,” Opt. Lett. 14, 208–210 (1989).
[CrossRef] [PubMed]

K. Takizawa, M. Okada, H. Kikuchi, T. Aida, “Bistable spatial light modulator using liquid crystal and Bi12SiO20 crystal layers,” Appl. Phys. Lett. 53, 2359–2361 (1988).
[CrossRef]

K. Takizawa, M. Okada, “Determination of relative signs of electro-optic and piezoelectric coefficients by measuring optical phase shifts caused by an applied electric field,” J. Opt. Soc. Am. B 2, 289–293 (1985).
[CrossRef]

K. Takizawa, M. Okada, “Simple method for measuring electro-optic coefficients by detecting the interference signal between transmitted and reflected beams,” J. Opt. Soc. Am. 72, 809–811 (1982).
[CrossRef]

Thackara, J. I.

Thackra, J.

C. Warde, J. Thackra, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).
[CrossRef]

Toyoda, H.

True, T. T.

T. T. True, “High-performance video projector using two oil-film light valves,” in Technical Digest of the Society for Information Display International Symposium 18 (Society for Information Display, Santa Ana, Calif., 1987), pp. 68–71.

Wang, X.-Y.

A. Schwartz, X.-Y. Wang, C. Warde, “Electron-beam-addressed microchannel spatial light modulator,” Opt. Eng. 24, 119–123 (1985).
[CrossRef]

Warde, C.

A. Schwartz, X.-Y. Wang, C. Warde, “Electron-beam-addressed microchannel spatial light modulator,” Opt. Eng. 24, 119–123 (1985).
[CrossRef]

C. Warde, J. Thackra, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).
[CrossRef]

C. Warde, J. I. Thackara, “Oblique-cut LiNbO3 microchannel spatial light modulator,” Opt. Lett. 7, 344–346 (1982).
[CrossRef] [PubMed]

C. Warde, A. D. Fisher, D. M. Cocco, M. Y. Burmawi, “Microchannel spatial light modulator,” Opt. Lett. 3, 196–198 (1978).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Tokyo, 1980), pp. 66–70.

Wu, M. H.

Wu, S. T.

R. A. Forber, A. Au. Efron, K. Sayyah, S. T. Wu, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” in Liquid Crystal Materials, Devices, and Application, P. S. Drzaic, U. Efron, eds., Proc. SPIE1665, 259–273 (1992).
[CrossRef]

Yokozawa, M.

Yoshida, N.

Zhang, G.

Appl. Opt. (11)

D. Armitage, J. I. Thackara, W. D. Eades, “Photoaddressed liquid crystal spatial light modulators,” Appl. Opt. 28, 4763–4771 (1989).
[CrossRef] [PubMed]

Y. Kobayashi, T. Takemori, N. Mukohzaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
[CrossRef] [PubMed]

B. Javidi, G. Zhang, A. H. Fazlollahi, U. Efron, “Application of a wire-grid-mirror liquid-crystal light valve in a nonlinear joint transform correlator,” Appl. Opt. 33, 2834–2841 (1994).
[CrossRef] [PubMed]

M. Ishikawa, N. Mukohzaka, H. Toyoda, Y. Suzuki, “Optical associatron: a simple model for optical associative memory,” Appl. Opt. 28, 291–301 (1989).
[CrossRef] [PubMed]

D. R. Collins, J. B. Sampsell, L. J. Hornbeck, J. M. Florence, P. A. Penz, M. T. Gately, “Deformable mirror device spatial light modulators and their applicability to optical neural network,” Appl. Opt. 28, 4900–4907 (1989).
[CrossRef] [PubMed]

K. Takizawa, T. Fujii, M. Kawakita, H. Kikuchi, H. Fujikake, M. Yokozawa, A. Murata, K. Kishi, “Spatial light modulators for projection displays,” Appl. Opt. 36, 5732–5747 (1997).
[CrossRef] [PubMed]

K. Takizawa, T. Fujii, H. Kikuchi, H. Fujikake, M. Kawakita, Y. Hirano, F. Sato, “Spatial light modulators for high-brightness projection displays,” Appl. Opt. 38, 5646–5655 (1999).
[CrossRef]

T. Minemoto, K. Okamoto, K. Miyamoto, “Optical parallel logic gate using spatial light modulators with the Pockels effect,” Appl. Opt. 24, 2055–2062 (1985).
[CrossRef] [PubMed]

T. Hara, K. Shinoda, T. Kato, M. Sugiyama, Y. Suzuki, “Microchannel spatial light modulator having the functions of image zooming, shifting, and rotating,” Appl. Opt. 25, 2306–2310 (1986).
[CrossRef] [PubMed]

T. Hara, Y. Ooi, Y. Suzuki, M. H. Wu, “Transfer characteristics of the microchannel spatial light modulator,” Appl. Opt. 28, 4781–4786 (1989).
[CrossRef] [PubMed]

Y. Bitou, T. Minemoto, “High-contrast spatial light modulator by use of the electroabsorption and the electro-optic effects in a GaAs single crystal,” Appl. Opt. 37, 4347–4356 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

K. Takizawa, M. Okada, H. Kikuchi, T. Aida, “Bistable spatial light modulator using liquid crystal and Bi12SiO20 crystal layers,” Appl. Phys. Lett. 53, 2359–2361 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (2)

K. Takizawa, H. Kikuchi, H. Fujikake, Y. Namikawa, K. Tada, “Reflection mode polymer-dispersed liquid crystal light valve,” Jpn. J. Appl. Phys. 33, 1346–1351 (1994).
[CrossRef]

H. Fujikake, K. Takizawa, H. Kikuchi, “Bistable spatial light modulator using guest-host liquid crystal and Bi12GeO20 photoconductive crystal,” Jpn. J. Appl. Phys. 32, 842–848 (1993).
[CrossRef]

Jpn. J. Opt. (1)

T. Aida, K. Takizawa, H. Kikuchi, M. Okada, “Optical parallel logic processor using a liquid crystal light valve and twisted nematic liquid crystal cells,” Jpn. J. Opt. 21, 724–729 (1992).

Opt. Eng. (3)

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

C. Warde, J. Thackra, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).
[CrossRef]

A. Schwartz, X.-Y. Wang, C. Warde, “Electron-beam-addressed microchannel spatial light modulator,” Opt. Eng. 24, 119–123 (1985).
[CrossRef]

Opt. Lett. (3)

Optoelectron. Devices Technol. (1)

T. Hara, Y. Suzuki, “Microchannel spatial light modulator,” Optoelectron. Devices Technol. 10, 393–420 (1995).

Other (6)

Y. Kocher, G. Lebreton, B. Moreau, “The TITUS light modulator in optical processing,” in Optical Computing ’88, P. H. Charel, J. W. Goodman, G. Roblin, eds., Proc. SPIE963, 66–77 (1988).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Tokyo, 1980), pp. 66–70.

K.-H. Hellwege, A. M. Hellwege, eds., Elastic, Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals, Vol. 11 of Landolt Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, K.-H. Hellwege, editor in chief Springer-Verlag, Berlin, 1979, pp. 287–670.

T. T. True, “High-performance video projector using two oil-film light valves,” in Technical Digest of the Society for Information Display International Symposium 18 (Society for Information Display, Santa Ana, Calif., 1987), pp. 68–71.

V. J. Fritz, “Full-color, liquid crystal light valve projector for shipboard use,” in Large Screen and Projection Displays II, W. P. Bleha, ed., Proc. SPIE1255, 59–68 (1990).
[CrossRef]

R. A. Forber, A. Au. Efron, K. Sayyah, S. T. Wu, “Dynamic IR scene projection using the Hughes liquid crystal light valve,” in Liquid Crystal Materials, Devices, and Application, P. S. Drzaic, U. Efron, eds., Proc. SPIE1665, 259–273 (1992).
[CrossRef]

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Figures (19)

Fig. 1
Fig. 1

Schematic diagram of a FPM. d c is the thickness of the EO crystal, and d p is the thickness of the photoconductor. V 0 is the drive voltage.

Fig. 2
Fig. 2

Equivalent circuit of the FP SLM. R p and C p are the resistance and the capacitance, respectively, of the photoconductor and C c is the capacitance of the EO crystal. V 0 is the voltage applied to the EO crystal.

Fig. 3
Fig. 3

Multiple reflection of light in the FPM consisting of an EO crystal and dielectric multilayer film mirrors at normal incidence. The figure was drawn schematically to show each optical ray. L is the thickness of the EO crystal.

Fig. 4
Fig. 4

Cross-section view of the dielectric multilayer film mirror. High and low refractive-index layers are stacked alternately. n b and n c are the refractive indices of the high and low refractive-index layers. n a and n d are the refractive indices of the external layers.

Fig. 5
Fig. 5

Dependence of the intensity of the output light I R of the FPM on phase difference θ between two successively reflected rays for various values of reflectance R. A is the point at which θ = π rad and I R is maximum. γL is the optical loss of the FPM.

Fig. 6
Fig. 6

Relationship between extinction ratio E R and the reflectance R for various values of γL.

Fig. 7
Fig. 7

Schematic diagram of the optical system that separates incident beam I i and output beam I R . (a) Simple structure with half-mirror HM but a large optical loss. (b) Requires a PBS and a quarter-wave plate QP but has a small optical loss, provided that linearly polarized light is employed for the input.

Fig. 8
Fig. 8

Schematic diagram of the FPM consisting of an isotropic EO crystal. Both the circularly polarized light and the applied electric field propagate along axis X 3. P is the electric vector of the linearly polarized light passing through the PBS shown in Fig. 7.

Fig. 9
Fig. 9

Dependence of the intensity of the output light I R of the FPM shown in Fig. 8 with optical loss γL = 0.001 on the electro-optically induced phase difference δθ for several values of reflectance R.

Fig. 10
Fig. 10

Dependence of the intensity of the output light I R of the FPM shown in Fig. 8 with a reflectance R = 0.9 and an optical loss γL = 0.001 on electro-optically induced phase difference δθ for several values of p. p denotes the deviation from the phase-matching condition.

Fig. 11
Fig. 11

Schematic diagram of the FPM consisting of a uniaxial EO crystal. Both the circularly polarized light and the applied electric field propagate along axis X 3. P is the electric vector of the linearly polarized light passing through the PBS shown in Fig. 7.

Fig. 12
Fig. 12

Dependence of V/ V π of the FPM shown in Fig. 11 with R = 0.9 and γL = 0.001 on intensity I R of the output light.

Fig. 13
Fig. 13

Dependence of V/ V π of the FPM shown in Fig. 11 with I R = 0.8 and γL = 0.001 on reflectance R.

Fig. 14
Fig. 14

Dependence of the intensity I R of the output light of the FPM shown in Fig. 11 with R = 0.9 and γL = 0.001 on electro-optically induced phase difference δθ for several values of p.

Fig. 15
Fig. 15

Schematic diagram of the FPM consisting of a uniaxial EO crystal. Both the circularly polarized light and the applied electric field propagate along axis X 3′. P is the electric vector of the linearly polarized light passing through the PBS shown in Fig. 7.

Fig. 16
Fig. 16

Dependence of electro-optically induced phase differences δθ X 1 and δθX2 of the FPM shown in Fig. 15 consisting of a LiNbO3 crystal on rotation angle ξ.

Fig. 17
Fig. 17

Dependence of the intensity I R of the output light of the FPM shown in Fig. 15 with q = 0.01, R = 0.9, and γL = 0.001 on the electro-optically induced phase difference δθ for several values of p.

Fig. 18
Fig. 18

Dependence of electro-optically induced phase differences δθ X 1 and δθX2 of the FPM consisting of Ba2NaNb5O15 biaxial crystal on rotation angle ξ.

Fig. 19
Fig. 19

Two Cartesian coordinates: X 1, X 2, and X 3 are the coordinate axes before rotation and X 1′, X 2′, and X 3′ are the coordinate axes after rotation.

Tables (4)

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Table 1 Isotropic EO Material Parameters

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Table 2 Uniaxial EO Material Parameters

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Table 3 Biaxial EO Material Parametersa

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Table 4 Half-Wave Voltage of EO Materialsa

Equations (81)

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Cc=ε0εcdc,Cp=ε0εpdp,Rp=ρdp,
Vc|dark=V01+Cc/Cp=V01+εcdp/εpdc).
Vc|photo=V01+ωCcRp21/2=V01+ωε0εcρpdpdc21/2,
Vc|photo  Vc|dark,
Vs=Vc|photo-Vc|dark
R=1-nb/nanb/ndnb/nc2N1+nb/nanb/ndnb/nc2N2.
IR=α+2/πF sinθ/221+2/πF sinθ/22,
θ=4πnLλ,
F=πRβ1-Rβ,
α=R 1-β21-Rβ2,
β=exp-γL,
ER=1αα+2F/π21+2F/π2.
θ1=4πλ noL+δθ,
θ2=4πλ noL-δθ,
δθ=2πλ no3r41V,
Vπ=λ2n03r41,
4π/λnoL=2mπ  m an integer,
AR1=R1-exp-γL+iδθ21-R exp-γL+iδθ,
AR2=R1-exp-γL-iδθ21-R exp-γL-iδθ.
IR=R41-exp-γL+iδθ1-R exp-γL+iδθ+1-exp-γL-iδθ1-R exp-γL-iδθ2 =α+1+R2/πF sinδθ/22/2R1+2/πF sinδθ/222.
IR=R41-exp-γL+i2m+pπ+δθ1-R exp-γL+i2m+pπ+δθ+1-exp-γL+i2m+pπ-δθ1-R exp-γL+i2m+pπ-δθ2,
δθ=2πλ no3r63V,
Vπ=λ2no3r63.
δθX1=δθX2=4πλnX1+ΔnX1L+ΔL-nX1L4πλΔnX1L+nX1ΔL,
nX1=no,
ΔnX1=-½no3r13E,
ΔL=d33L,
δθX1=-2πλ no3Vr13-2no2 d33,
IR=α+2/πF sinδθX1/221+2/πF sinδθX1/22,
Vπ=λ2no3r13-2/no2d33.
IR=α+2/πF sin2m+pπ+δθX1/221+2/πF sin2m+pπ+δθX1/22,
δθX1=4πλnX1+ΔnX1L+ΔL-nX1L4πλΔnX1L+nX1ΔL,
δθX2=4πλnX2+ΔnX2L+ΔL-nX2L4πλΔnX2L+nX2ΔL.
nX2=nocos2 ξ+no/ne2 sin2 ξ1/2,
ΔnX1=-no3E2r22 sin ξ+r13 cos ξ,
ΔnX2=-nX23E2-r22 sin ξ cos2 ξ+r13 cos3 ξ+r33 sin2 ξ cos ξ-2r51 sin2 ξ cos ξ,
ΔL=LE-d22 sin3 ξ+d31 sin2 ξ cos ξ+d33 cos3 ξ+d15 sin2 ξ cos ξ,
δθX1=-2πλ no3Vr22 sin ξ+r13 cos ξ-2no2-d22 sin3 ξ+d31 sin2 ξ cos ξ+d33 cos3 ξ+d15 sin2 ξ cos ξ,
δθX2=-2πλ nX23V-r22 sin ξ cos2ξ+r13 cos3 ξ+r33 sin2 ξ cos ξ-2r51 sin2 ξ cos ξ-2nX22-d22 sin3 ξ+d31 sin2 ξ cos ξ+d33 cos3 ξ+d15 sin2 ξ cos ξ.
θ1=4πλ nX1L=2mπ,
θ2=4πλ nX2L=2mπ,
IR=R41-exp-γL+i2mπ+δθ1-R exp-γL+i2mπ+δθ+1-exp-γL+i2mπ+δθ1-R exp-γL+i2mπ+δθ2,
Vπ=λ2no3-1r22 sin ξ0+r13 cos ξ0-2no2-d22 sin3 ξ0+d31 sin2 ξ0 cos ξ0+d33 cos3 ξ0+d15 sin2 ξ0 cos ξ0-1.
IR=R41-exp-γL+i2m+pπ+δθ1-R exp-γL+i2m+pπ+δθ+1-exp-γL+i2m+qπ+δθ1-R exp-γL+i2m+qπ+δθ2,
nX1=n1,
nX2=n2cos2 ξ+n2/n32 sin2 ξ1/2,
ΔnX1=-½n13Er13 cos ξ,
ΔnX2=-½nX23E cos ξr23 cos2 ξ+r33-2r42sin2 ξ,
ΔL=LEd32+d24sin2 ξ cos ξ+d33 cos3 ξ,
δθX1=-2πλ n13Vr13 cos ξ-2n12d32+d24sin2 ξ cos ξ+d33 cos3 ξ,
δθX2=-2πλ nX23Vcos ξ r23 cos2 ξ+r33-2r42sin2 ξ-2nX22d32+d24sin2 ξ cos ξ+d33 cos3 ξ.
cos ξ=±n1/nX23r13-r33+2r42+d33+d24nX2-n1/nX23r23-r33+2r42+d32+d24-d33nX2-n1/nX231/2.
cos ξ±n1/nX23r13-r33+2r42r23-r33+2r421/2.
δn=2no3r22 sin ξ0+r13 cos ξ0-2no2-d22 sin3 ξ0+d31 sin2 ξ0 cos ξ0+d33 cos3 ξ0+d15 sin2 ξ0 cos ξ0.
1no2+r22E sin ξ+r13E cos ξX12+ 1no2-r22E sin ξ+r13E cos ξX22+ 1ne2+r33E cos ξX32-2r51E×sin ξX2X3=1.
X2=X2 cos ξ-X3 sin ξ,
X3=X2 sin ξ+X3 cos ξ.
1no2+r22E sin ξ+r13E cos ξX12+1no2cos2 ξ+1ne2sin2 ξ-r22E sin ξ cos2 ξ+r13E cos3 ξ+r33E sin2ξ cos ξ-2r51E sin2 ξ cos ξX22=1.
Si=dmiEm m=13, i=16.
0000d15-2d22-d22d220d1500d31d31d33000.
S1=Ed22 sin ξ+d31 cos ξ,
S2=E-d22 sin ξ+d31 cos ξ,
S3=Ed33 cos ξ,
S4=-Ed15 sin ξ,
S5=0,
S6=0.
S1=S11,
S2=S22,
S3=S33,
S4=2S23=S23+S32,
S5=2S31=S31+S13,
S6=2S12=S12+S21,
Shj=ahkajiSki h, i, j, k=13,
S1=S1,
S2=S2 cos2 ξ+S3 sin2 ξ+S4 sin ξ cos ξ,
S3=S2 sin2 ξ+S3 cos2 ξ-S4 sin ξ cos ξ,
S4=2S3-S2sin ξ cos ξ+S4cos2 ξ-sin2 ξ,
S5=S5 cos ξ-S6 sin ξ,
S6=S5 sin ξ+S6 cos ξ.
S3=E-d22 sin3 ξ+d31 sin2 ξ cos ξ+d33 cos3 ξ+d15 sin2 ξ cos ξ
ΔL=S3L.

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