Abstract

Procedures for designing a tunable liquid crystal (LC) electrooptic filter are illustrated. Selective filtering of one of the two mixed laser lines is used as an example for calculation. It is demonstrated that a LC filter can select a desired beam to pass while rejecting the other one, or vice versa, by switching the voltage biased on the LC cell. The switching times are determined by the liquid crystal properties, thickness, and biased voltage. A multilayered structure is proposed to improve the response times and power loading capability.

© 1989 Optical Society of America

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References

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  1. D. A. Pinnow, R. L. Abrams, J. F. Lotspeich, “Electro-optic Tunable Optical Filter,” U.S. Patent4,197,008 (1980).
  2. H. A. Tarry, “Electrically Tunable Narrowband Optical Filter,” Electron. Lett. 11, 471 (1975).
    [CrossRef]
  3. W. I. Kaye, “Liquid Crystal Tuned Birefringent Filter,” U.S. Patent4,394,069 (1983).
  4. S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 33, 1270 (1986).
    [CrossRef] [PubMed]
  5. F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199 (1972).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  7. V. G. Chigrinov, M. F. Grebenkin, “Determination of the Elastic Constants and Coefficient of Viscosity of Nematic Liquid Crystals from Oriented Electro-optical Effects,” Sov. Phys. Crystallogr. 20, 747 (1976).
  8. S. T. Wu, U. Efron, L. D. Hess, “Birefringence Measurements of Liquid Crystals,” Appl. Opt. 23, 3911 (1984).
    [CrossRef] [PubMed]
  9. S. T. Wu, “Infrared Properties of Liquid Crystals: an Overview,” Opt. Eng. 26, 120 (1987).
    [CrossRef]
  10. For example, see L. M. Blinov, Electro-optical and Magneto-optical Effects of Liquid Crystals (Wiley, New York, 1983).
  11. N. V. Tabiryan, A. V. Sukhov, B. Ya. Zel’dovich, “The Orientational Optical Nonlinearity of Liquid Crystals,” Mol. Cryst. Liq. Cryst. 136, 1 (1986).
    [CrossRef]
  12. I. C. Khoo, Y. R. Shen, “Liquid Crystals: Nonlinear Optical Properties and Processes,” Opt. Eng. 24, 579 (1985).
  13. P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).
  14. S. T. Wu, K. C. Lim, “Absorption and Scattering Measurements of Nematic Liquid Crystals,” Appl. Opt. 26, 1722 (1987).
    [CrossRef] [PubMed]

1987 (2)

1986 (2)

N. V. Tabiryan, A. V. Sukhov, B. Ya. Zel’dovich, “The Orientational Optical Nonlinearity of Liquid Crystals,” Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 33, 1270 (1986).
[CrossRef] [PubMed]

1985 (1)

I. C. Khoo, Y. R. Shen, “Liquid Crystals: Nonlinear Optical Properties and Processes,” Opt. Eng. 24, 579 (1985).

1984 (1)

1976 (1)

V. G. Chigrinov, M. F. Grebenkin, “Determination of the Elastic Constants and Coefficient of Viscosity of Nematic Liquid Crystals from Oriented Electro-optical Effects,” Sov. Phys. Crystallogr. 20, 747 (1976).

1975 (1)

H. A. Tarry, “Electrically Tunable Narrowband Optical Filter,” Electron. Lett. 11, 471 (1975).
[CrossRef]

1972 (1)

F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199 (1972).
[CrossRef]

Abrams, R. L.

D. A. Pinnow, R. L. Abrams, J. F. Lotspeich, “Electro-optic Tunable Optical Filter,” U.S. Patent4,197,008 (1980).

Blinov, L. M.

For example, see L. M. Blinov, Electro-optical and Magneto-optical Effects of Liquid Crystals (Wiley, New York, 1983).

Born, M.

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

Chigrinov, V. G.

V. G. Chigrinov, M. F. Grebenkin, “Determination of the Elastic Constants and Coefficient of Viscosity of Nematic Liquid Crystals from Oriented Electro-optical Effects,” Sov. Phys. Crystallogr. 20, 747 (1976).

deGennes, P. G.

P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

Efron, U.

Grebenkin, M. F.

V. G. Chigrinov, M. F. Grebenkin, “Determination of the Elastic Constants and Coefficient of Viscosity of Nematic Liquid Crystals from Oriented Electro-optical Effects,” Sov. Phys. Crystallogr. 20, 747 (1976).

Hess, L. D.

Kahn, F. J.

F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199 (1972).
[CrossRef]

Kaye, W. I.

W. I. Kaye, “Liquid Crystal Tuned Birefringent Filter,” U.S. Patent4,394,069 (1983).

Khoo, I. C.

I. C. Khoo, Y. R. Shen, “Liquid Crystals: Nonlinear Optical Properties and Processes,” Opt. Eng. 24, 579 (1985).

Lim, K. C.

Lotspeich, J. F.

D. A. Pinnow, R. L. Abrams, J. F. Lotspeich, “Electro-optic Tunable Optical Filter,” U.S. Patent4,197,008 (1980).

Pinnow, D. A.

D. A. Pinnow, R. L. Abrams, J. F. Lotspeich, “Electro-optic Tunable Optical Filter,” U.S. Patent4,197,008 (1980).

Shen, Y. R.

I. C. Khoo, Y. R. Shen, “Liquid Crystals: Nonlinear Optical Properties and Processes,” Opt. Eng. 24, 579 (1985).

Sukhov, A. V.

N. V. Tabiryan, A. V. Sukhov, B. Ya. Zel’dovich, “The Orientational Optical Nonlinearity of Liquid Crystals,” Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Tabiryan, N. V.

N. V. Tabiryan, A. V. Sukhov, B. Ya. Zel’dovich, “The Orientational Optical Nonlinearity of Liquid Crystals,” Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Tarry, H. A.

H. A. Tarry, “Electrically Tunable Narrowband Optical Filter,” Electron. Lett. 11, 471 (1975).
[CrossRef]

Wolf, E.

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

Wu, S. T.

Zel’dovich, B. Ya.

N. V. Tabiryan, A. V. Sukhov, B. Ya. Zel’dovich, “The Orientational Optical Nonlinearity of Liquid Crystals,” Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

F. J. Kahn, “Electric-Field-Induced Orientational Deformation of Nematic Liquid Crystals: Tunable Birefringence,” Appl. Phys. Lett. 20, 199 (1972).
[CrossRef]

Electron. Lett. (1)

H. A. Tarry, “Electrically Tunable Narrowband Optical Filter,” Electron. Lett. 11, 471 (1975).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

N. V. Tabiryan, A. V. Sukhov, B. Ya. Zel’dovich, “The Orientational Optical Nonlinearity of Liquid Crystals,” Mol. Cryst. Liq. Cryst. 136, 1 (1986).
[CrossRef]

Opt. Eng. (2)

I. C. Khoo, Y. R. Shen, “Liquid Crystals: Nonlinear Optical Properties and Processes,” Opt. Eng. 24, 579 (1985).

S. T. Wu, “Infrared Properties of Liquid Crystals: an Overview,” Opt. Eng. 26, 120 (1987).
[CrossRef]

Phys. Rev. A (1)

S. T. Wu, “Birefringence Dispersions of Liquid Crystals,” Phys. Rev. A 33, 1270 (1986).
[CrossRef] [PubMed]

Sov. Phys. Crystallogr. (1)

V. G. Chigrinov, M. F. Grebenkin, “Determination of the Elastic Constants and Coefficient of Viscosity of Nematic Liquid Crystals from Oriented Electro-optical Effects,” Sov. Phys. Crystallogr. 20, 747 (1976).

Other (5)

P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

D. A. Pinnow, R. L. Abrams, J. F. Lotspeich, “Electro-optic Tunable Optical Filter,” U.S. Patent4,197,008 (1980).

W. I. Kaye, “Liquid Crystal Tuned Birefringent Filter,” U.S. Patent4,394,069 (1983).

For example, see L. M. Blinov, Electro-optical and Magneto-optical Effects of Liquid Crystals (Wiley, New York, 1983).

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

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Figures (3)

Fig. 1
Fig. 1

Bias voltage dependent director’s decay time τdecay of 5CB LC (4-cyano-4′-n-pentylbiphenyl) under small signal excitations. τ0 = γ1d2/K11π2 is the free relaxation time of the LC. Dots represent experimental results on τ0/τdecay and solid lines theoretical calculations using Eq. (11 b). The threshold voltage determined by the intersection of these two lines is equal to 0.72 Vrms, which agrees well with that measured by the optical transmission method. The temperature used for these measurements was ~24°C. The electric field used for excitation has a frequency of 10 kHz; sine wave.

Fig. 2
Fig. 2

Voltage dependent optical transmission of a 12.6-μm E-7 LC cell under crossed polarizers for two Ar+ laser lines, λ1 = 0.5145 and λ2 = 0.488 μm. The experimental conditions are: excitation frequency = 10 kHz, T ≅ 24°C. V1 and V2 are 1.19 and 1.30 Vrms, respectively.

Fig. 3
Fig. 3

Switching times of the 12.6-μm LC filter. The rise time (from V1 to V2) is measured to be ~275 ms and decay time (from V2 to V1) ~ 300 ms.

Tables (5)

Tables Icon

Table I Calculated T2 as a Function of N Using Eq. (5) for E-7 LC when T1 = 0. The Wavelengths Used for Calculation are λ1 = 0.5145 μm and λ2 = 0.488 μm

Tables Icon

Table II Calculated T1 as a function of M using Eq. (8) for E-7 LC when T2 = 0. The Wavelengths Used for Calculation are λ1 = 0.5145 μm and λ2 = 0.488 μm

Tables Icon

Table III Summary of the Calculated Results Using a 20-μm-thick E-7 LC Filter for λ1 = 0.5145 μm and λ2 = 0.488 μma

Tables Icon

Table IV Same as Table III but for λ1 = 1.3 μm and λ2 = 1.55 μm

Tables Icon

Table V Same as Table III but for λ1 = 1.152 μm and λ2 = 0.633 μm

Equations (16)

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T j = sin 2 ( δ j / 2 ) ,
δ j = 2 π d Δ n j / λ j
Δ n j ( T , λ j , V ) = Δ n 0 ( T , λ j ) f ( V ) ,
Δ n 0 ( T , λ 0 ) = G ( T ) λ j 2 λ * 2 λ j 2 - λ * 2 ,
d Δ n 1 ( V , λ 1 ) = N λ 1 ,
T 2 = sin 2 [ N π ( λ 2 λ 1 ) ( λ 1 2 - λ * 2 λ 2 2 - λ * 2 ) ] .
1 N d Δ n 0 ( λ 1 ) / λ 1 .
d Δ n 2 ( V , λ 2 ) = M λ 2 .
T 1 = sin 2 [ M π ( λ 1 λ 2 ) ( λ 2 2 - λ * 2 λ 1 2 - λ * 2 ) ] .
1 M d Δ n 0 ( λ 2 ) / λ 2 .
K 11 2 ϕ Z 2 + a E 2 sin ϕ cos ϕ = γ 1 ϕ t             ( rise ) ,
K 11 2 ϕ Z 2 + a E b 2 sin ϕ cos ϕ = γ 1 ϕ t             ( decay ) ,
τ rise = γ 1 d 2 / K 11 π 2 ( V V th ) 2 - 1 ,
τ decay = γ 1 d 2 / K 11 π 2 | ( V b V th ) 2 - 1 | .
T 2 sin 2 [ N ( λ 1 λ 2 ) π ] .
T 1 sin 2 [ M ( λ 2 λ 1 ) π ] sin 2 [ ( M / m ) π ] .

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