Abstract

A coupled-mode theory is used to find simple exact expressions for the transmission of light through a twisted nematic liquid-crystal layer. The thickness of the layer for zero transmission is shown to depend on the total twist angle. A previous theoretical model for tuning a liquid-crystal cell is shown to be in error and alternatives are suggested.

© 1978 Optical Society of America

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References

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  1. J. Grinberg and A. D. Jacobson, “Transmission characteristics of a twisted nematic liquid-crystal layer,” J. Opt. Soc. Am. 66, 1003–1009 (1976).
    [CrossRef]
  2. P. D. McIntyre, “Crosstalk between optical waveguides with applications to visual photoreceptors,” Ph.D. Thesis, Australian National University, Canberra (1976).
  3. P. D. McIntyre and A. W. Snyder, “Light propagation in twisted anisotropic media: Application to photoreceptors,” J. Opt. Soc. Am. 68, 149–157 (1978).
    [CrossRef]
  4. H. L. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219 (1951).
    [CrossRef]
  5. A. S. Marathay, “Matrix-operator description of the propagation of polarized light through cholesteric liquid crystals,” J. Opt. Soc. Am. 61, 1363 (1971).
    [CrossRef]
  6. R. M. A. Azzam and N. M. Bashara, “Simplified approach to the propagation of polarized light in anisotropic media–application to liquid crystals,” J. Opt. Soc. Am. 62, 1252 (1972).
    [CrossRef]
  7. D. W. Berreman, “Optics in smoothly varying planar structures: Applications to liquid-crystal twist cells,” J. Opt. Soc. Am. 63, 1374 (1973).
    [CrossRef]
  8. J. E. Bigelow and R. A. Kashnow, G.E. Technical Information Series Report No. 74, CDR 090, June1974 (unpublished).

1978 (1)

1976 (1)

1973 (1)

1972 (1)

1971 (1)

1951 (1)

H. L. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219 (1951).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

Berreman, D. W.

Bigelow, J. E.

J. E. Bigelow and R. A. Kashnow, G.E. Technical Information Series Report No. 74, CDR 090, June1974 (unpublished).

de Vries, H. L.

H. L. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219 (1951).
[CrossRef]

Grinberg, J.

Jacobson, A. D.

Kashnow, R. A.

J. E. Bigelow and R. A. Kashnow, G.E. Technical Information Series Report No. 74, CDR 090, June1974 (unpublished).

Marathay, A. S.

McIntyre, P. D.

P. D. McIntyre and A. W. Snyder, “Light propagation in twisted anisotropic media: Application to photoreceptors,” J. Opt. Soc. Am. 68, 149–157 (1978).
[CrossRef]

P. D. McIntyre, “Crosstalk between optical waveguides with applications to visual photoreceptors,” Ph.D. Thesis, Australian National University, Canberra (1976).

Snyder, A. W.

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Figures (3)

FIG. 1
FIG. 1

Coordinate axes for a twisted medium. The axes x ˆ(z), ŷ(z) are fixed in the medium which twists about the z axis. The axis x ˆ(z) is parallel to the long axes of the aligned liquid-crystal molecules in the x-y plane at position z, Ω(z) = ξz.

FIG. 2
FIG. 2

The angle γm(ϕm = −γm) for Tmin = 0, and the resulting transmission Tmax = cos2 2γm in the on-state. X = 2dΔn/λ and Ω = 90°. The contrast is 100%.

FIG. 3
FIG. 3

The angle γm(ϕ = 0) for minimum transmission in the off-state (and maximum contrast), the resulting Tmax = cos2γm and the maximum contrast Cmax. C0 is the contrast when γ = 0. X = 2dΔn/λ and Ω = 90°.

Equations (20)

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E ( z ) = A x ( z ) x ˆ ( z ) + A y ( z ) ŷ ( z ) ,
A x ( z ) = [ p cos τ + F ( i p X + q ) sin τ ] e i β s z ,
A y ( z ) = [ q cos τ - F ( i q X + p ) sin τ ] e i β s z ,
τ = ξ z ( 1 + X 2 ) 1 / 2 ,
F = 1 / ( 1 + X 2 ) ,
X = β x - β y 2 ξ = π Δ n ξ λ .
T = ( 1 / 2 ) E ( d ) · â 2 ,
T = ( 1 / 2 ) A y ( d ) 2
T = sin 2 τ / ( 1 + X 2 ) ,
τ = Ω ( 1 + X 2 ) 1 / 2 = K π ,             K = 1 , 2 , 3 , .
d Δ n λ = ( K 2 - s 2 ) 1 / 2 .
T = ( 1 / 2 ) { 1 - cos 2 γ { F cos 2 ϕ ( cos 2 τ + X 2 ) + F sin 2 ϕ sin 2 τ ] - sin 2 γ [ sin 2 ϕ cos 2 τ - F cos 2 ϕ sin 2 τ ] } ,
T ( γ ) = [ sin 2 τ / ( 1 + X 2 ) ] ( 1 + X 2 sin 2 2 γ ) ,
C = ( T max - T min ) / ( T max + T min ) .
tan 2 γ m = - tan τ ( 1 + X 2 ) 1 / 2 .
T max = cos 2 2 γ m = 1 / ( 1 + tan 2 τ 1 + X 2 ) .
tan 2 γ m = - ( 1 + X 2 ) 1 / 2 sin 2 τ cos 2 τ + X 2 ,
T min = 1 2 { 1 - [ 1 - ( 2 X sin 2 τ 1 + X 2 ) 2 ] 1 / 2 }
( X sin 2 τ 1 + X 2 ) 2 ,
C max 1 - 2 ( X sin 2 τ ) 2 ( 1 + X 2 ) ( cos 2 τ + X 2 ) .