Abstract

A complete methodology using matrix representations for describing light transmission and reflection at an interface between an isotropic medium with high refractive index and a uniaxial birefringent material where total internal reflection (TIR) could happen is described systematically. A new TIR-based liquid-crystal (LC) switch system is proposed and investigated in detail by using this analyzing method. The criteria of selection of critical parameters such as LC mixture, waveguide, and operation mode of the LC layer, etc., are discussed. Dependence of transmission on incident angle and dynamic characteristics under an electric field are given for different cell gaps. The results give detailed and useful guidance in the fabrication of the LC switch system.

© 2008 Optical Society of America

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References

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  2. V. G. Chigrinov, Liquid Crystal Devices: Physics and Applications (Artech, 1999).
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  4. K. Wu, J. Liu, and Y. Chen, “Optical attenuator using polarization modulation and a feedback controller,” U.S. patent 5,963,291 (October 5, 1999).
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    [CrossRef]
  6. A. Zhang, K. T. Chan, M. S. Demokan, V. W. C. Chan, P. C. H. Chan, H. S. Kwok, and A. H. P. Chan, “Integrated liquid crystal optical switch based on total internal reflection,” Appl. Phys. Lett. 86, 211108 (2005).
    [CrossRef]
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    [CrossRef]
  10. D.-K. Yang, “A simulation study of a liquid crystal optical switch based on total internal reflection,” J. Opt. A, Pure Appl. Opt. 5, 402-408 (2003).
    [CrossRef]
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  12. J. Qi and G. P. Crawford, “Reflective display based on total internal reflection and grating-grating coupling,” in SID Symposium Digest of Technical Papers (Society of Information Display, 2003), Vol. 34, pp. 648-651.
  13. I. Fujieda, “Theoretical considerations for arrayed waveguide displays,” Appl. Opt. 41, 1391-1399 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
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2005 (2)

A. Zhang, K. T. Chan, M. S. Demokan, V. W. C. Chan, P. C. H. Chan, H. S. Kwok, and A. H. P. Chan, “Integrated liquid crystal optical switch based on total internal reflection,” Appl. Phys. Lett. 86, 211108 (2005).
[CrossRef]

K. L. Woon, M. O'Neill, G. J. Richards, M. P. Aldred, and S. M. Kelly, “Stokes-parameter analysis of the polarization of light transmitted through a chiral nematic liquid-crystal cell,” J. Opt. Soc. Am. A 22, 760-766 (2005).
[CrossRef]

2004 (1)

Y. Semenova, Y. Panarin, G. Farrell, and S. Dovgalets, “Liquid crystal based optical switches,” Mol. Cryst. Liq. Cryst. 413, 385-398 (2004).
[CrossRef]

2003 (1)

D.-K. Yang, “A simulation study of a liquid crystal optical switch based on total internal reflection,” J. Opt. A, Pure Appl. Opt. 5, 402-408 (2003).
[CrossRef]

2002 (2)

I. Fujieda, “Theoretical considerations for arrayed waveguide displays,” Appl. Opt. 41, 1391-1399 (2002).
[CrossRef] [PubMed]

K. Hirabayashi and C. Amano, “Liquid-crystal polarization controller arrays on planar waveguide circuits,” IEEE Photonics Technol. Lett. 14, 504-506 (2002).
[CrossRef]

1999 (1)

1996 (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

1995 (1)

G. D. Landry and T. A. Maldonado, “Complete method to determine transmission and reflection characteristics at a planar interface between arbitrarily oriented biaxial media,” J. Opt. Soc. Am. 12, 2048-2063 (1995).
[CrossRef]

1989 (1)

M. R. Meadows, M. A. Handschy, and N. A. Clark, “Electro-optic switching using total internal reflection by a ferroelectric liquid crystal,” Appl. Phys. Lett. 54, 1394-1396 (1989).
[CrossRef]

1988 (1)

1984 (2)

P. J. Lin-Chung and S. Teitler, “4×4 matrix formalisms for optics in stratified anisotropic media,” J. Opt. Soc. Am. A 1, 703-705 (1984).
[CrossRef]

V. G. Chigrinov, T. V. Korkishko, and B. A. Umanskii, “Total internal reflection during a Freedericksz transition in a nematic liquid crystal,” Opt. Spectrosc. 57, 283-287 (1984).

1979 (1)

1973 (2)

1972 (1)

1970 (1)

Appl. Opt. (2)

Appl. Phys. Lett. (2)

A. Zhang, K. T. Chan, M. S. Demokan, V. W. C. Chan, P. C. H. Chan, H. S. Kwok, and A. H. P. Chan, “Integrated liquid crystal optical switch based on total internal reflection,” Appl. Phys. Lett. 86, 211108 (2005).
[CrossRef]

M. R. Meadows, M. A. Handschy, and N. A. Clark, “Electro-optic switching using total internal reflection by a ferroelectric liquid crystal,” Appl. Phys. Lett. 54, 1394-1396 (1989).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

K. Hirabayashi and C. Amano, “Liquid-crystal polarization controller arrays on planar waveguide circuits,” IEEE Photonics Technol. Lett. 14, 504-506 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

D.-K. Yang, “A simulation study of a liquid crystal optical switch based on total internal reflection,” J. Opt. A, Pure Appl. Opt. 5, 402-408 (2003).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (3)

Mol. Cryst. Liq. Cryst. (1)

Y. Semenova, Y. Panarin, G. Farrell, and S. Dovgalets, “Liquid crystal based optical switches,” Mol. Cryst. Liq. Cryst. 413, 385-398 (2004).
[CrossRef]

Opt. Spectrosc. (1)

V. G. Chigrinov, T. V. Korkishko, and B. A. Umanskii, “Total internal reflection during a Freedericksz transition in a nematic liquid crystal,” Opt. Spectrosc. 57, 283-287 (1984).

Phys. Rev. B (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

Other (9)

P. Xu, J. Ho, V. Chigrinov, and H. S. Kwok, “Novel liquid crystal switch array based on total internal reflection,” in SID Symposium Digest of Technical Papers (Society of Information Display; to be published), Vol. 39, session p-182.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, and S. P. Rao, “New reflective color display technique based on total internal reflection and subtractive color filtering,” in SID Symposium Digest of Technical Papers (Society of Information Display, 2001), Vol. 32, pp. 1054-1057.

J. Qi and G. P. Crawford, “Reflective display based on total internal reflection and grating-grating coupling,” in SID Symposium Digest of Technical Papers (Society of Information Display, 2003), Vol. 34, pp. 648-651.

K. Wu, J. Liu, and Y. Chen, “Optical attenuator using polarization modulation and a feedback controller,” U.S. patent 5,963,291 (October 5, 1999).

P. G. Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).

V. G. Chigrinov, Liquid Crystal Devices: Physics and Applications (Artech, 1999).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1989).

E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, 1970).

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Figures (5)

Fig. 1
Fig. 1

Euler angles of the optical dielectric tensor ( x , y , z ) with respect to the laboratory coordinate system (x, y, z) are represented by θ, ϕ, ψ, respectively.

Fig. 2
Fig. 2

Schematic of the TIR-based LC display.

Fig. 3
Fig. 3

Critical angle change under the electric field.

Fig. 4
Fig. 4

Dependence of transmittance on incident angle for different cell gaps: (a) d = 0.5 μ m , (b) d = 1 μ m , (c) d = 2 μ m .

Fig. 5
Fig. 5

Response time of the LC switch for different cell gaps: (a) d = 0.5 μ m , (b) d = 1 μ m , (c) d = 2 μ m .

Tables (1)

Tables Icon

Table 1 Total and 10%–90% Response Time of the LC Switch for Different Cell Gaps a

Equations (43)

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ϵ = R ϵ R 1 ,
R = ( cos ψ cos ϕ cos θ sin ϕ sin ψ sin ψ cos ϕ cos θ sin ϕ cos ψ sin θ sin ϕ cos ψ sin ϕ + cos θ cos ϕ sin ψ sin ψ sin ϕ + cos θ cos ϕ cos ψ sin θ cos ϕ sin θ sin ψ sin θ cos ψ cos θ ) .
ϵ x x = n x 2 + Δ ϵ a 2 ,
ϵ y y = n x 2 + Δ ϵ b 2 ,
ϵ z z = n x 2 + Δ ϵ c 2 ,
ϵ x y = ϵ y x = Δ ϵ a b ,
ϵ x z = ϵ z x = Δ ϵ a c ,
ϵ y z = ϵ z y = Δ ϵ b c ,
Δ ϵ = n z 2 n x 2 ,
a = sin θ cos ϕ ,
b = sin θ sin ϕ ,
c = cos θ .
Ψ z = i k 0 Δ Ψ ,
Ψ = ( E x , H y , E y , H x ) T ,
k 0 = ω c ( c is the velocity of light in vacuum ) ,
Δ = [ ϵ z x ϵ z z X 1 X 2 ϵ z z ϵ z y ϵ z z X 0 ϵ x x ϵ x z ϵ z x ϵ z z ϵ x z ϵ z z X ϵ x y ϵ x z ϵ z y ϵ z z 0 0 0 0 1 ϵ y x ϵ y z ϵ z x ϵ z z ϵ y z ϵ z z X ϵ y y ϵ y z ϵ z y ϵ z z X 2 0 ] ,
X = n 0 sin θ 0 .
Ψ ( z + h ) = P ( z + h ) Ψ ( z ) .
P ( z + h ) = S K ( h ) S 1 ,
K j j = exp ( i k 0 λ j h ) , j = 1 , 2 , 3 , 4 ,
Ψ ( z ) = P ( z + h ) 1 Ψ ( z + h ) = S ( z + h ) K ( h ) S ( z + h ) 1 Ψ ( z + h ) = S ( z + h ) K ( h ) M ( z + h ) ,
M ( z ) = S ( z ) 1 Ψ ( z ) .
M ( z ) = T ( z + h ) M ( z + h ) ,
T ( z + h ) = S ( z ) 1 S ( z + h ) K ( h ) .
Ψ i = ( E x i , H y i , E y i , H x i ) T
= ( E x i , E x i n 0 cos θ 0 , E y i , E y i n 0 cos θ 0 ) T ,
Ψ r = ( E x r , H y r , E y r , H x r ) T
= ( E x r , E x r n 0 cos θ 0 , E y r , E y r n 0 cos θ 0 ) T .
E x i = A i p cos θ 0 , E y i = A i s ,
E x r = A r p cos θ 0 , E y r = A r s .
Ψ ( z = 0 ) = [ cos θ 0 cos θ 0 0 0 n n 0 0 0 0 1 1 0 0 n cos θ 0 n cos θ 0 ] [ A i p A r p A i s A r s ] .
[ a n b 0 ] = S ( n ) [ a 0 b n ] ,
T = A T A ,
A = [ 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 ] .
S 11 ( n + 1 ) = ( T 11 S 12 T 21 ) 1 S 11 ,
S 12 ( n + 1 ) = ( T 11 S 12 T 21 ) 1 ( S 12 T 22 T 12 ) ,
S 21 ( n + 1 ) = S 22 T 21 S 11 ( n + 1 ) + S 21 ,
S 22 ( n + 1 ) = S 22 T 21 S 12 ( n + 1 ) + S 22 T 22 ,
S 11 = ( T p p T s p T p s T s s ) ,
S 21 = ( R p p R s p R p s R s s ) .
s i = E ¯ T B i E ,
B 0 = [ 1 0 0 1 ] , B 1 = [ 1 0 0 1 ] ,
B 2 = [ 0 1 1 0 ] , B 3 = [ 0 i i 0 ] .

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