Abstract

Recent studies on the behavior of nematic liquid crystals (LC’s) in two basic configurations are described. The phase rate of change Δϕt is studied for the case of parallel aligned nematic cells. It is shown that Δϕt of approximately 3 rad/msec can be obtained with a 4-μm E-7 LC at λ = 0.63 μm. The optical transmission of a 900 twisted-nematic cell is studied with regard to its dependence on the polarization angle of incidence.

© 1986 Optical Society of America

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  1. U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
    [CrossRef]
  2. M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).
  3. U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
    [CrossRef]
  4. U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
    [CrossRef]
  5. S. T. Wu, U. Efron, L. D. Hess, App. Phys. Lett. 44, 842, 1033 (1984).
    [CrossRef]
  6. J. Grinberg, A. Jacobson, W. P. Bleha, L. Miller, L. Fraas, D. Bosewell, G. Myer, Opt. Eng. 14, 217 (1975).
    [CrossRef]
  7. F. J. Kahn, Appl. Phys. Lett. 20, 199 (1972).
    [CrossRef]
  8. F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 26, 1681 (1972); P. Pieranski, F. Brochard, E. Guyon, J. Phys. (Paris) 34, 35 (1973).
    [CrossRef]
  9. U. Efron, T. D. Bates, “Studies of the LCLV for adaptive optics applications,” Internal Res. Rep. (Hughes Research Laboratories, Malibu, Calif., 1984).
  10. S. T. Wu, U. Efron, L. D. Hess, Appl. Opt. 23, 3911 (1984).
    [CrossRef]
  11. C. H. Gooch, H. A. Tarry, J. Phys. D 8, 1575 (1975).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 695.

1985 (2)

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
[CrossRef]

1984 (2)

S. T. Wu, U. Efron, L. D. Hess, App. Phys. Lett. 44, 842, 1033 (1984).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, Appl. Opt. 23, 3911 (1984).
[CrossRef]

1983 (1)

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

1981 (1)

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

1975 (2)

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

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

1972 (2)

F. J. Kahn, Appl. Phys. Lett. 20, 199 (1972).
[CrossRef]

F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 26, 1681 (1972); P. Pieranski, F. Brochard, E. Guyon, J. Phys. (Paris) 34, 35 (1973).
[CrossRef]

Bates, T. D.

U. Efron, T. D. Bates, “Studies of the LCLV for adaptive optics applications,” Internal Res. Rep. (Hughes Research Laboratories, Malibu, Calif., 1984).

Bleha, W. P.

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 695.

Bosewell, D.

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

Braatz, P. O.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

Brochard, F.

F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 26, 1681 (1972); P. Pieranski, F. Brochard, E. Guyon, J. Phys. (Paris) 34, 35 (1973).
[CrossRef]

Efron, U.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, App. Phys. Lett. 44, 842, 1033 (1984).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, Appl. Opt. 23, 3911 (1984).
[CrossRef]

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

U. Efron, T. D. Bates, “Studies of the LCLV for adaptive optics applications,” Internal Res. Rep. (Hughes Research Laboratories, Malibu, Calif., 1984).

Fraas, L.

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

Gooch, C. H.

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

Goodwin, N. W.

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

Grinberg, J.

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
[CrossRef]

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

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

Guyon, E.

F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 26, 1681 (1972); P. Pieranski, F. Brochard, E. Guyon, J. Phys. (Paris) 34, 35 (1973).
[CrossRef]

Hess, L. D.

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, App. Phys. Lett. 44, 842, 1033 (1984).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, Appl. Opt. 23, 3911 (1984).
[CrossRef]

Jacobson, A.

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

Kahn, F. J.

F. J. Kahn, Appl. Phys. Lett. 20, 199 (1972).
[CrossRef]

Little, M. J.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

Miller, L.

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

Myer, G.

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

Pieranski, P.

F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 26, 1681 (1972); P. Pieranski, F. Brochard, E. Guyon, J. Phys. (Paris) 34, 35 (1973).
[CrossRef]

Reif, P. G.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

Schwartz, R. N.

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

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 (Pergamon, New York, 1980), p. 695.

Wu, S. T.

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, App. Phys. Lett. 44, 842, 1033 (1984).
[CrossRef]

S. T. Wu, U. Efron, L. D. Hess, Appl. Opt. 23, 3911 (1984).
[CrossRef]

App. Phys. Lett. (1)

S. T. Wu, U. Efron, L. D. Hess, App. Phys. Lett. 44, 842, 1033 (1984).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. J. Kahn, Appl. Phys. Lett. 20, 199 (1972).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. J. Little, P. O. Braatz, U. Efron, J. Grinberg, N. W. Goodwin, IEEE J. Quantum Electron. QE-17, 148 (1981).

J. Appl. Phys. (1)

U. Efron, J. Grinberg, P. O. Braatz, M. J. Little, P. G. Reif, R. N. Schwartz, J. Appl. Phys. 57, 1356 (1985).
[CrossRef]

J. Phys. D (1)

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

Opt. Eng. (3)

U. Efron, S. T. Wu, J. Grinberg, L. D. Hess, Opt. Eng. 24, 111 (1985).
[CrossRef]

U. Efron, P. O. Braatz, M. J. Little, R. N. Schwartz, J. Grinberg, Opt. Eng. 22, 682 (1983).
[CrossRef]

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

Phys. Rev. Lett. (1)

F. Brochard, P. Pieranski, E. Guyon, Phys. Rev. Lett. 26, 1681 (1972); P. Pieranski, F. Brochard, E. Guyon, J. Phys. (Paris) 34, 35 (1973).
[CrossRef]

Other (2)

U. Efron, T. D. Bates, “Studies of the LCLV for adaptive optics applications,” Internal Res. Rep. (Hughes Research Laboratories, Malibu, Calif., 1984).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 695.

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Figures (5)

Fig. 1
Fig. 1

Hybrid TN/CB operation of a 90° TN cell. Input polarization (Pin) is at an arbitrary angle ψ to LC alignment (E) at front surface.

Fig. 2
Fig. 2

Decomposition of the input polarization into the ordinary (XO) and the extraordinary (XE) components for the 90° TN cell.

Fig. 3
Fig. 3

Experimental results of the 90° TN cell with a varying polarization incidence angle (ψ). The results of a crossed-analyzed CO2 beam (λ = 10.6 μm) are shown for three E-7 cells (d = 13, 24, and 52 μm).

Fig. 4
Fig. 4

Experimental results of the 90° TN cell using 24-μm E-7 and 1132 LC materials. Conditions are the same as those in Fig. 3.

Fig. 5
Fig. 5

Crossed-analyzed transmission (normalized) versus sin 2(2ψ). The cases of two different experimental points (for the same sin2 2ψ) indicate the differences between left-side and right-side normalization of the curves in Figs. 3 and 4.

Tables (4)

Tables Icon

Table 1 ϕ(V): Experiment and Theory

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Table 2 Response Time—Experimental Results and Validation of τ = τ*dLC2/(V/V0)2 − 1a

Tables Icon

Table 3 Δϕt: Comparison of Experiment and Theory (E-7 BDH, λ = 6328 Å)a

Tables Icon

Table 4 Hybrid Twisted-Nematic–Controlled-Birefringence Effect: Comparison of Experiment and Theory

Equations (15)

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Δ ϕ = α ϕ m ( V / V 0 - 1 )             for             V - V 0 V 0 1 ,
ϕ m = 2 π d Δ n / λ ,
Δ ϕ = ϕ m ( 1 - β V )             for high fields V - V 0 V 0 1.
θ m 2 ( t ) = θ m 2 ( )             ( 1 + [ θ m 2 ( ) δ 2 - 1 ] exp { - [ 2 t / τ ( V , d ) ] } ) ,
τ ( V , d ) = τ * d 2 ( V / V 0 ) 2 - 1 ,
Δ ϕ Δ t Δ V τ × [ Δ ϕ ( V , d ) ] V ,
( Δ ϕ Δ t ) L . F . = α ϕ m × Δ V × [ ( V / V 0 ) 2 - 1 ] V 0 τ * d 2 ,
( Δ ϕ Δ t ) H . F . = β ϕ m V 2 Δ V [ ( V / V 0 ) 2 - 1 ] τ * d 2 .
ϕ * = [ Δ ϕ / Δ t ] expt × d Δ V [ ( V / V 0 ) 2 - 1 ] = const ,
2.03 radians × micrometers milliseconds × volts for λ = 0.63 μ m ,
P R ( TN ) = 1 - sin 2 [ θ ( 1 + U 2 ) 1 / 2 ] 1 + U 2 , U = π d Δ n λ θ = 2 d Δ n λ             for a twist angle θ = π 2 .
A = ( A X E A X O ) = 2 [ P R 1 / 2 cos ψ cos ω t + ( 1 - P R ) 1 / 2 sin ψ cos ( ω t + Δ ϕ 2 ) P R 1 / 2 sin ψ cos ( ω t + Δ ϕ ) 2 - ( 1 - P R ) 1 / 2 cos ψ cos ( ω t + Δ ϕ 2 ) ] ,
A = [ A · e ] = 2 [ P R 1 / 2 cos 2 ψ cos ω t + P R 1 / 2 sin 2 ψ cos ( ω t + Δ ϕ ) ] .
A 2 = P R [ 1 - sin 2 ( 2 ψ ) sin 2 ( Δ ϕ / 2 ) ] .
P R 1 / 2 [ 1 - sin 2 2 ψ sin 2 ( Δ ϕ 2 ) ]

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