Abstract

The complex amplitude reflectance of the liquid crystal light valve (LCLV) is determined as a function of the writing intensity and applied voltage using an approximate model. The input and output polarizers are assumed to have arbitrary directions. The theoretical results based on this model match our experimental measurements. This theory allows us to optimize the operation of the LCLV as an intensity or phase-only spatial light modulator. When the polarizers are orthogonal and the input polarizer is at −34° with the front liquid crystal director, the intensity reflectance reaches 100% (compared to 81% for the conventional configuration). Phase-only modulation is realizable by use of appropriate applied voltage bias and configuration of polarizers.

© 1991 Optical Society of America

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References

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  1. J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).
  2. W. P. Bleha, “Progress in Liquid Crystal Light Valves,” Laser Focus/Electro-optics, 111–120 (Oct.1983).
  3. U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).
  4. U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).
  5. W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).
  6. A. Fisher, L. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).
  7. M. Schadt, W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 15, 127–128 (1971).
    [CrossRef]
  8. D. W. Berreman, “Optics in Stratified and Anisotropic Media: 4 × 4-Matrix Formulation,” J. Opt. Soc. Am. 62, 502–510 (1972).
    [CrossRef]
  9. R. M. A. Azzam, N. M. Bashara, “Simplified Approach to the Propagation of Polarized Light in Anisotropic Media—Application to Liquid Crystals,” J. Opt. Soc. Am. 62, 1252–1257 (1972).
    [CrossRef]
  10. D. W. Berreman, “Optics in Smoothly Varying Anisotropic Planar Structures: Application to Liquid-Crystal Twist Cells,” J. Opt. Soc. Am. 63, 1374–1379 (1973).
    [CrossRef]
  11. L. A. Goodman, “Liquid Crystal Displays,” J. Vac. Sci. Technol. 10, 804–823 (1973).
    [CrossRef]
  12. C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Film,” Electron. Lett. 10, 2–4 (1974).
    [CrossRef]
  13. D. W. Berreman, “Dynamics of Liquid-Crystal Twist Cells,” Appl. Phys. Lett. 25, 12–15 (1974).
    [CrossRef]
  14. C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twisted Angle ≤90°,” Appl. Phys. D 8, 1575–1584 (1975).
    [CrossRef]
  15. P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1975), Chap. 3.
  16. J. Grinberg, A. D. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003–1009 (1976).
    [CrossRef]
  17. G. Buar, “Optical Characteristics of Liquid Crystal Displays,” in Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, Ed. (Plenum, New York, 1980), pp. 61–78.
  18. R. J. Gagnon, “Liquid-Crystal Twist-Cell Optics,” J. Opt. Soc. Am. 71, 348–353 (1981).
    [CrossRef]
  19. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.
  20. F. Leenhots, M. Schadt, “Optics of Twisted Nematic and Supertwisted Nematic Liquid-Crystal Displays,” J. Appl. Phys. 60, 3275–3281 (1986).
    [CrossRef]
  21. K. Lu, B. E. A. Saleh, “Theory and Design of the Liquid Crystal TV as an Optical Phase Modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  22. D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).
  23. U. Efron, S. T. Wu, T. D. Bates, “Nematic Liquid Crystals for Spatial Light Modulators: Recent Studies,” J. Opt. Soc. Am. B 3, 247–252 (1986).
    [CrossRef]
  24. N. Konforti, E. Marom, S.-T. Wu, “Phase-Only Modulation with Twisted Nematic Liquid-Crystal Spatial Light Modulators,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  25. K. Lu, B. E. A. Saleh, “Optimal Twist and Polarization Angles for the Reflective Liquid-Crystal Light Modulators,” OSA Annual MeetingTechnical Digest Series, Vol. 15 (Optical Society of America, Washington, DC, 1990), p. 255.
  26. F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199–201 (1971).
    [CrossRef]

1990 (2)

K. Lu, B. E. A. Saleh, “Theory and Design of the Liquid Crystal TV as an Optical Phase Modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

1988 (1)

1986 (3)

F. Leenhots, M. Schadt, “Optics of Twisted Nematic and Supertwisted Nematic Liquid-Crystal Displays,” J. Appl. Phys. 60, 3275–3281 (1986).
[CrossRef]

A. Fisher, L. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

U. Efron, S. T. Wu, T. D. Bates, “Nematic Liquid Crystals for Spatial Light Modulators: Recent Studies,” J. Opt. Soc. Am. B 3, 247–252 (1986).
[CrossRef]

1985 (1)

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).

1983 (2)

W. P. Bleha, “Progress in Liquid Crystal Light Valves,” Laser Focus/Electro-optics, 111–120 (Oct.1983).

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

1981 (1)

1978 (1)

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

1976 (1)

1975 (2)

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twisted Angle ≤90°,” Appl. Phys. D 8, 1575–1584 (1975).
[CrossRef]

1974 (2)

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Film,” Electron. Lett. 10, 2–4 (1974).
[CrossRef]

D. W. Berreman, “Dynamics of Liquid-Crystal Twist Cells,” Appl. Phys. Lett. 25, 12–15 (1974).
[CrossRef]

1973 (2)

1972 (2)

1971 (2)

F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199–201 (1971).
[CrossRef]

M. Schadt, W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 15, 127–128 (1971).
[CrossRef]

Azzam, R. M. A.

Barns, T. H.

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

Bashara, N. M.

Bates, T. D.

Berreman, D. W.

Bleha, W. P.

W. P. Bleha, “Progress in Liquid Crystal Light Valves,” Laser Focus/Electro-optics, 111–120 (Oct.1983).

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Boswell, D.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Braatz, P. O.

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

Brown, H. B.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

Buar, G.

G. Buar, “Optical Characteristics of Liquid Crystal Displays,” in Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, Ed. (Plenum, New York, 1980), pp. 61–78.

Casasent, D. P.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

de Gennes, P. G.

P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1975), Chap. 3.

Efron, U.

U. Efron, S. T. Wu, T. D. Bates, “Nematic Liquid Crystals for Spatial Light Modulators: Recent Studies,” J. Opt. Soc. Am. B 3, 247–252 (1986).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

Fisher, A.

A. Fisher, L. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

Fraas, L.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Gagnon, R. J.

Gooch, C. H.

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twisted Angle ≤90°,” Appl. Phys. D 8, 1575–1584 (1975).
[CrossRef]

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Film,” Electron. Lett. 10, 2–4 (1974).
[CrossRef]

Goodman, L. A.

L. A. Goodman, “Liquid Crystal Displays,” J. Vac. Sci. Technol. 10, 804–823 (1973).
[CrossRef]

Grinberg, J.

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

J. Grinberg, A. D. Jacobson, “Transmission Characteristics of a Twisted Nematic Liquid-Crystal Layer,” J. Opt. Soc. Am. 66, 1003–1009 (1976).
[CrossRef]

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Helfrich, W.

M. Schadt, W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 15, 127–128 (1971).
[CrossRef]

Hess, L. D.

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).

Jacobson, A.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Jacobson, A. D.

Kahn, F. J.

F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199–201 (1971).
[CrossRef]

Konforti, N.

Lee, L.

A. Fisher, L. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

Leenhots, F.

F. Leenhots, M. Schadt, “Optics of Twisted Nematic and Supertwisted Nematic Liquid-Crystal Displays,” J. Appl. Phys. 60, 3275–3281 (1986).
[CrossRef]

Lipton, L. T.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

Little, M. J.

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

Lu, K.

K. Lu, B. E. A. Saleh, “Theory and Design of the Liquid Crystal TV as an Optical Phase Modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

K. Lu, B. E. A. Saleh, “Optimal Twist and Polarization Angles for the Reflective Liquid-Crystal Light Modulators,” OSA Annual MeetingTechnical Digest Series, Vol. 15 (Optical Society of America, Washington, DC, 1990), p. 255.

Markevitch, B. V.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

Marom, E.

Matsumoto, K.

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

Matusda, K.

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

Miller, L.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Myer, G.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

Ooyama, N.

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

Reif, P. G.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

Saleh, B. E. A.

K. Lu, B. E. A. Saleh, “Theory and Design of the Liquid Crystal TV as an Optical Phase Modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

K. Lu, B. E. A. Saleh, “Optimal Twist and Polarization Angles for the Reflective Liquid-Crystal Light Modulators,” OSA Annual MeetingTechnical Digest Series, Vol. 15 (Optical Society of America, Washington, DC, 1990), p. 255.

Schadt, M.

F. Leenhots, M. Schadt, “Optics of Twisted Nematic and Supertwisted Nematic Liquid-Crystal Displays,” J. Appl. Phys. 60, 3275–3281 (1986).
[CrossRef]

M. Schadt, W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 15, 127–128 (1971).
[CrossRef]

Schwartz, R. N.

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

Tarry, H. A.

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twisted Angle ≤90°,” Appl. Phys. D 8, 1575–1584 (1975).
[CrossRef]

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Film,” Electron. Lett. 10, 2–4 (1974).
[CrossRef]

Wiener-Avnear, E.

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

Wu, S. T.

U. Efron, S. T. Wu, T. D. Bates, “Nematic Liquid Crystals for Spatial Light Modulators: Recent Studies,” J. Opt. Soc. Am. B 3, 247–252 (1986).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).

Wu, S.-T.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Yocky, D. A.

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

Appl. Phys. D (1)

C. H. Gooch, H. A. Tarry, “The Optical Properties of Twisted Nematic Liquid Crystal Structures with Twisted Angle ≤90°,” Appl. Phys. D 8, 1575–1584 (1975).
[CrossRef]

Appl. Phys. Lett. (3)

F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199–201 (1971).
[CrossRef]

M. Schadt, W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 15, 127–128 (1971).
[CrossRef]

D. W. Berreman, “Dynamics of Liquid-Crystal Twist Cells,” Appl. Phys. Lett. 25, 12–15 (1974).
[CrossRef]

Electron. Lett. (1)

C. H. Gooch, H. A. Tarry, “Optical Characteristics of Twisted Nematic Liquid-Crystal Film,” Electron. Lett. 10, 2–4 (1974).
[CrossRef]

J. Appl. Phys. (1)

F. Leenhots, M. Schadt, “Optics of Twisted Nematic and Supertwisted Nematic Liquid-Crystal Displays,” J. Appl. Phys. 60, 3275–3281 (1986).
[CrossRef]

J. Opt. Soc. Am. (5)

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

J. Vac. Sci. Technol. (1)

L. A. Goodman, “Liquid Crystal Displays,” J. Vac. Sci. Technol. 10, 804–823 (1973).
[CrossRef]

Laser Focus/Electro-optics (1)

W. P. Bleha, “Progress in Liquid Crystal Light Valves,” Laser Focus/Electro-optics, 111–120 (Oct.1983).

Opt. Eng. (5)

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, “Silicon Liquid Crystal Light Valves: Status and Issues,” Opt. Eng. 22, 682–686 (1983).

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, “Liquid-Crystal-Based Visible-to-Infrared Dynamic Image Converter,” Opt. Eng. 24, 111–118 (1985).

W. P. Bleha, L. T. Lipton, E. Wiener-Avnear, J. Grinberg, P. G. Reif, D. P. Casasent, H. B. Brown, B. V. Markevitch, “Application of Liquid Crystal Light Valve to Real Time Optical Data Processing,” Opt. Eng. 17, 371–384 (1978).

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “New Real Time Noncoherent to Coherent Light Image Converter: Hybrid Field Effect Liquid Crystal Light Valve,” Opt. Eng. 14, 217–225 (1975).

K. Lu, B. E. A. Saleh, “Theory and Design of the Liquid Crystal TV as an Optical Phase Modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Opt. Lett. (1)

Optik (1)

D. A. Yocky, T. H. Barns, K. Matsumoto, N. Ooyama, K. Matusda, “Simple Measurement of the Phase Modulation Capability of Liquid Crystal Phase-Only Light Modulators,” Optik 84, 140–144 (1990).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. Fisher, L. Lee, “The Current Status of Two-Dimensional Spatial Light Modulator Technology,” Proc. Soc. Photo-Opt. Instrum. Eng. 634, 352–371 (1986).

Other (4)

G. Buar, “Optical Characteristics of Liquid Crystal Displays,” in Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, Ed. (Plenum, New York, 1980), pp. 61–78.

K. Lu, B. E. A. Saleh, “Optimal Twist and Polarization Angles for the Reflective Liquid-Crystal Light Modulators,” OSA Annual MeetingTechnical Digest Series, Vol. 15 (Optical Society of America, Washington, DC, 1990), p. 255.

P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1975), Chap. 3.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

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Figures (11)

Fig. 1
Fig. 1

Configuration of the LCLV modulator with normal incident light and arbitrary input and output polarizations.

Fig. 2
Fig. 2

(a) Dependence of intensity reflectance R on β and input polarization angle ψ. The input and output polarizers are orthogonal. (b) A topographic view of the relation in (a); R is a periodic function of ψ with a period of 90°. The first optical threshold occurs when β = 174.3°.

Fig. 3
Fig. 3

Dependence of phase shift δ on β and input polarization angle ψ. The input and output polarizers are parallel.

Fig. 4
Fig. 4

Dependence of the normalized parameter β/βmax on the normalized voltage (VVc)/Vo, where no = 1.5 and ne = 1.7. When ne is changed by ±0.1, this curve is changed only very slightly.

Fig. 5
Fig. 5

Experimental system to measure the dependence of the intensity reflectance R on external voltage Vext and writing intensity I.

Fig. 6
Fig. 6

(a) Measured intensity reflectance R−34,56 vs Vext at a fixed writing intensity I = 500 μW · cm−2. At Vext = 0, β corresponds to βmax = 248° when λ = 633 nm. (b) Theoretical dependence of R−34,56 on β. The peak value of the second lobe from the left is 100%. (c) Measured intensity reflectance R−34,56 vs I when the external voltage bias is Vext = 12.2 V. (d) Theoretical result corresponding to (c). (e) Experimental dependence (left) of R on Vext is compared with the theoretical dependence (right) of R on β for different input polarization angles ψ. Since β is a monotonically decreasing function of Vext, it is plotted in the reverse direction so that experiment and theory can be conveniently compared.

Fig. 7
Fig. 7

Correspondence between the experimental Vext and the theoretical normalized voltage (VVc)/Vo when s(I) = 2.1.

Fig. 8
Fig. 8

(a) Michelson interferometer with an LCLV phase-only modulator replacing the mirror in one arm. A sawtooth grey level pattern is addressed on the CRT. (b) Interference pattern demonstrating phase modulation.

Fig. 9
Fig. 9

Dependence of switching ratio s(I) on writing intensity I. Experimental data are based on Figs. 6(a) and (c). Its best match with Eq. (12) gives the device parameters ssat = 2.4 and k = 1.94% cm2 · μW−1

Fig. 10
Fig. 10

(a) Theoretical dependence of δ0,0 on β. When β > 90°, the relation is approximately linear with a slope of 4. (b) Theoretical dependence of R0,0 in β. The efficiency is high and undergoes relatively small variation when β is large.

Fig. 11
Fig. 11

Operation lines within the shaded area have a dynamic range for phase modulation >360° and associated intensity distortion <10%.

Equations (22)

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J T = j = 1 N J j ,
J T = exp ( - i ϕ ) R ( α ) [ cos ( γ ) - β γ sin ( γ ) - α γ sin ( γ ) α γ sin ( γ ) cos ( γ ) + i β γ sin ( γ ) ] ,
R ( α ) = [ cos ( α ) sin ( α ) - sin ( α ) cos ( α ) ] ,
γ = α 2 + β 2 ,
β = π d λ [ n e - n o ] ,
ϕ = π d λ [ n e + n o ] .
θ = { 0 , V < V c π 2 - 2 tan - 1 [ exp ( - V - V c V o ) ] , V V c
β = π d λ [ n e ( θ ) - n o ] ,
ϕ = π d λ [ n e ( θ ) + n o ] = ϕ o + β ,
1 n e 2 ( θ ) = cos 2 ( θ ) n e 2 + sin 2 ( θ ) n o 2 ,
β max π d λ ( n e - n o ) ;
J = exp ( - i 2 β ) [ ( α γ ) 2 + ( β γ ) 2 cos ( 2 γ ) - i β γ sin ( 2 γ ) i α β γ 2 [ 1 - cos ( 2 γ ) ] i α β γ 2 [ 1 - cos ( 2 γ ) ] ( α γ ) 2 + ( β γ ) 2 cos ( 2 γ ) + i β γ sin ( 2 γ ) ] ,
R = R exp ( - i δ ) ,
R = { [ ( α γ ) 2 + ( β γ ) 2 cos ( 2 γ ) ] cos ( ψ 1 - ψ 2 ) } 2 + { α β γ 2 [ 1 - cos ( 2 γ ) ] sin ( ψ 1 + ψ 2 ) - β γ sin ( 2 γ ) cos ( ψ 1 + ψ 2 ) } 2
δ = 2 β - tan - 1 { α β γ 2 [ 1 - cos ( 2 γ ) ] sin ( ψ 1 + ψ 2 ) - β γ sin ( 2 γ ) cos ( ψ 1 + ψ 2 ) [ ( α γ ) 2 + ( β γ ) 2 cos ( 2 γ ) ] cos ( ψ 1 - ψ 2 ) }
R = { α β γ 2 [ 1 - cos ( 2 γ ) ] cos ( 2 ψ ) + β γ sin ( 2 γ ) sin ( 2 ψ ) } 2 δ = 2 β + n π ,             n = ± 1 , ± 2 , .
β = β n ( n π ) 2 - α 2 ,             n = 1 , 2 , 3 , ,
V = S ( I ) V ext ,
V - V c V o = s ( I ) V ext - V c S ( 0 ) V o S ( 0 ) .
s ( I 1 ) V ext 1 = s ( I 2 ) V ext 2 ,
s ( I ) = V ext 1 I V ext 1 0 .
s ( I ) = k I + 1 k I s sat + 1 ,

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