Abstract

It is shown that twisted nematic liquid-crystal spatial light modulators behave as phase-only modulators when operated below the conventional optical threshold. Thus such devices, when operated in a reflection mode, behave as spatial amplitude modulators when used between crossed polarizers above the optical threshold; they behave as phase modulators when used between parallel polarizers and operated below that threshold.

© 1988 Optical Society of America

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References

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  1. M. Schadt, W. Helfrich, Appl. Phys. Lett. 18, 27 (1971).
    [CrossRef]
  2. C. H. Gooch, H. A. Tarry, J. Phys. D 8, 1575 (1975).
    [CrossRef]
  3. D. W. Berreman, Appl. Phys. Lett. 25, 12 (1974); J. Appl. Phys. 46, 3746 (1975).
    [CrossRef]
  4. L. M. Blinov, Electro-Optical and Magneto-Optical Effects of Liquid Crystals (Wiley, New York, 1983).
  5. U. Efron, S. T. Wu, T. D. Bates, J. Opt. Soc. Am. B 3, 247 (1986).
    [CrossRef]
  6. S. T. Wu, U. Efron, L. D. Hess, Appl. Phys. Lett. 44, 842 (1984).
    [CrossRef]
  7. S. T. Wu, Opt. Eng. 26, 120 (1987).
  8. M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).
  9. M. Schadt, F. Muller, IEEE Trans. Electron Devices ED-24, 1125 (1978).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 679.
  11. J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).
  12. F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
    [CrossRef]
  13. E. Marom, N. Konforti, Opt. Lett. 12, 539 (1987).
    [CrossRef] [PubMed]

1987

S. T. Wu, Opt. Eng. 26, 120 (1987).

F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
[CrossRef]

E. Marom, N. Konforti, Opt. Lett. 12, 539 (1987).
[CrossRef] [PubMed]

1986

1984

S. T. Wu, U. Efron, L. D. Hess, Appl. Phys. Lett. 44, 842 (1984).
[CrossRef]

1978

M. Schadt, F. Muller, IEEE Trans. Electron Devices ED-24, 1125 (1978).
[CrossRef]

1976

M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).

1975

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

C. H. Gooch, H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

1974

D. W. Berreman, Appl. Phys. Lett. 25, 12 (1974); J. Appl. Phys. 46, 3746 (1975).
[CrossRef]

1971

M. Schadt, W. Helfrich, Appl. Phys. Lett. 18, 27 (1971).
[CrossRef]

Bates, T. D.

Berreman, D. W.

D. W. Berreman, Appl. Phys. Lett. 25, 12 (1974); J. Appl. Phys. 46, 3746 (1975).
[CrossRef]

Bleha, W. P.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Blinov, L. M.

L. M. Blinov, Electro-Optical and Magneto-Optical Effects of Liquid Crystals (Wiley, New York, 1983).

Blinov, L.M.

M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 679.

Boswell, D.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Chigrinov, V. G.

M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).

Efron, U.

U. Efron, S. T. Wu, T. D. Bates, J. Opt. Soc. Am. B 3, 247 (1986).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, Appl. Phys. Lett. 44, 842 (1984).
[CrossRef]

Fraas, L.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Gooch, C. H.

C. H. Gooch, H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

Grebenkin, M. F.

M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).

Grinberg, J.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Helfrich, W.

M. Schadt, W. Helfrich, Appl. Phys. Lett. 18, 27 (1971).
[CrossRef]

Hess, L. D.

S. T. Wu, U. Efron, L. D. Hess, Appl. Phys. Lett. 44, 842 (1984).
[CrossRef]

Huang, X. L.

F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
[CrossRef]

Jacobson, A.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Jutamulia, S.

F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
[CrossRef]

Konforti, N.

Lin, T. W.

F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
[CrossRef]

Marom, E.

Miller, L.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Muller, F.

M. Schadt, F. Muller, IEEE Trans. Electron Devices ED-24, 1125 (1978).
[CrossRef]

Myer, G.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

Schadt, M.

M. Schadt, F. Muller, IEEE Trans. Electron Devices ED-24, 1125 (1978).
[CrossRef]

M. Schadt, W. Helfrich, Appl. Phys. Lett. 18, 27 (1971).
[CrossRef]

Seliverstov, V. A.

M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).

Tarry, H. A.

C. H. Gooch, H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 679.

Wu, S. T.

S. T. Wu, Opt. Eng. 26, 120 (1987).

U. Efron, S. T. Wu, T. D. Bates, J. Opt. Soc. Am. B 3, 247 (1986).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, Appl. Phys. Lett. 44, 842 (1984).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
[CrossRef]

Appl. Phys. Lett.

S. T. Wu, U. Efron, L. D. Hess, Appl. Phys. Lett. 44, 842 (1984).
[CrossRef]

M. Schadt, W. Helfrich, Appl. Phys. Lett. 18, 27 (1971).
[CrossRef]

D. W. Berreman, Appl. Phys. Lett. 25, 12 (1974); J. Appl. Phys. 46, 3746 (1975).
[CrossRef]

IEEE Trans. Electron Devices

M. Schadt, F. Muller, IEEE Trans. Electron Devices ED-24, 1125 (1978).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D

C. H. Gooch, H. A. Tarry, J. Phys. D 8, 1575 (1975).
[CrossRef]

Opt. Eng.

J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, Opt. Eng. 14, 217 (1975).

S. T. Wu, Opt. Eng. 26, 120 (1987).

Opt. Laser Technol.

F. T. S. Yu, S. Jutamulia, T. W. Lin, X. L. Huang, Opt. Laser Technol. 19, 45 (1987).
[CrossRef]

Opt. Lett.

Sov. Phys. Crystallogr.

M. F. Grebenkin, V. A. Seliverstov, L.M. Blinov, V. G. Chigrinov, Sov. Phys. Crystallogr. 20, 604 (1976).

Other

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 679.

L. M. Blinov, Electro-Optical and Magneto-Optical Effects of Liquid Crystals (Wiley, New York, 1983).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup used for investigating the phase modulation of 90° twist cells. (S.F., spatial filter; B/S’s, beam splitters; M’s, mirrors; A, analyzer; L, lens; D, detector.)

Fig. 2
Fig. 2

Phase and amplitude response of a BDH-E-7 LC cell. Note the coincidence of the occurrence of the first two cycles in the phase-response curve with the respective bumps in the amplitude curve. The third cycle is obscured by crossing the optical threshold where nonuniform twisting takes place. The phase change from peak to peak is equal to 2π. Cell thickness 8 μm; λ = 0.63 μm; T ≃ 24°C; electric-field frequency 10 kHz, sine wave.

Fig. 3
Fig. 3

Same as Fig. 2 but for a cell filled with ZLI-1132 nematic LC.

Equations (9)

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T = P R ( 1 sin 2 2 ψ sin 2 Δ ϕ 2 ) ,
T = 1 T .
P R = 1 sin 2 [ θ ( 1 + U 2 ) 1 / 2 ] 1 + U 2 ,
Δ ϕ = { α ϕ m ( V V 0 1 ) V V 0 V 0 1 ,
Δ ϕ = { ϕ m ( 1 β V ) V V 0 V 0 1 ,
γ = A ( V ) sin ( πz / d ) ,
n γ = n e n o ( 1 + tan 2 γ n 0 + n e 2 tan 2 γ ) 1 / 2 ,
ϕ V = 0 d 2 π n γ dz λ 4 π 0 d / 2 n e n o λ [ 1 + A 2 ( V ) sin 2 πz d n 0 + n e A 2 ( V ) sin 2 πz d ] 1 / 2 d z 4 π n e λ 0 d / 2 [ 1 ( n e 2 n 0 2 1 ) A 2 ( V ) sin 2 πz d ] 1 / 2 d z = 4 n e d λ E { sin 1 [ ( n e 2 n 0 2 1 ) 1 / 2 A ( V ) ] } ,
0 V 0 = 4 π 0 d / 2 n e λ d z = 2 π n e d / λ .

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