Abstract

Although reflective bistable twisted nematic (RBTN) displays have potential in low-power-consumption applications, to achieve the optimum conditions for both bistable states simultaneously remains a challenge. We use a geometrical method based on the Poincaré sphere representation to obtain the optimum conditions that can simultaneously satisfy both bistable states for a RBTN structure. With this method, the optimum conditions can be obtained analytically and the operation modes can be clearly visualized and better understood.

© 1999 Optical Society of America

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  1. D. W. Berreman and W. R. Heffner, Appl. Phys. Lett. 37, 1 (1980).
    [CrossRef]
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  4. Z. L. Xie and H. S. Kwok, Jpn. J. Appl. Phys. 37, 2572 (1998).
    [CrossRef]
  5. Y. J. Kim, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’99 (Society for Information Display, San Jose, Calif., 1999), p. 866.
  6. H. S. Kwok, J. Appl. Phys. 80, 3687 (1996).
    [CrossRef]
  7. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  8. N. Vansteenkiste, P. Vignolo, and A. Aspect, J. Opt. Soc. Am. A 10, 2240 (1993).
    [CrossRef]
  9. S. W. Suh, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’98 (Society for Information Display, San Jose, Calif., 1998).
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    [CrossRef] [PubMed]

1998 (1)

Z. L. Xie and H. S. Kwok, Jpn. J. Appl. Phys. 37, 2572 (1998).
[CrossRef]

1996 (1)

H. S. Kwok, J. Appl. Phys. 80, 3687 (1996).
[CrossRef]

1993 (1)

1981 (1)

D. W. Berreman and W. R. Heffner, J. Appl. Phys. 52, 3032 (1981).
[CrossRef]

1980 (1)

D. W. Berreman and W. R. Heffner, Appl. Phys. Lett. 37, 1 (1980).
[CrossRef]

1977 (1)

1941 (1)

Aspect, A.

Berreman, D. W.

D. W. Berreman and W. R. Heffner, J. Appl. Phys. 52, 3032 (1981).
[CrossRef]

D. W. Berreman and W. R. Heffner, Appl. Phys. Lett. 37, 1 (1980).
[CrossRef]

Bigelow, J. E.

Heffner, W. R.

D. W. Berreman and W. R. Heffner, J. Appl. Phys. 52, 3032 (1981).
[CrossRef]

D. W. Berreman and W. R. Heffner, Appl. Phys. Lett. 37, 1 (1980).
[CrossRef]

Iino, S.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

Inoue, A.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

Jones, R. C.

Kashnow, R. A.

Kim, Y. J.

Y. J. Kim, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’99 (Society for Information Display, San Jose, Calif., 1999), p. 866.

Kwok, H. S.

Z. L. Xie and H. S. Kwok, Jpn. J. Appl. Phys. 37, 2572 (1998).
[CrossRef]

H. S. Kwok, J. Appl. Phys. 80, 3687 (1996).
[CrossRef]

Momose, Y.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

Nomura, H.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

Patel, J. S.

Y. J. Kim, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’99 (Society for Information Display, San Jose, Calif., 1999), p. 866.

S. W. Suh, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’98 (Society for Information Display, San Jose, Calif., 1998).

Poincaré, H.

H. Poincaré, in Theorie Mathematique de la Lumiere II, G. Carre, ed. (Gauthier-Villars, Paris, 1892), pp. 275–306.

Sato, Y.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

Suh, S. W.

S. W. Suh, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’98 (Society for Information Display, San Jose, Calif., 1998).

Tanaka, T.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

Vansteenkiste, N.

Vignolo, P.

Xie, Z. L.

Z. L. Xie and H. S. Kwok, Jpn. J. Appl. Phys. 37, 2572 (1998).
[CrossRef]

Zhuang, Z.

S. W. Suh, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’98 (Society for Information Display, San Jose, Calif., 1998).

Y. J. Kim, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’99 (Society for Information Display, San Jose, Calif., 1999), p. 866.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. W. Berreman and W. R. Heffner, Appl. Phys. Lett. 37, 1 (1980).
[CrossRef]

J. Appl. Phys. (2)

D. W. Berreman and W. R. Heffner, J. Appl. Phys. 52, 3032 (1981).
[CrossRef]

H. S. Kwok, J. Appl. Phys. 80, 3687 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

Z. L. Xie and H. S. Kwok, Jpn. J. Appl. Phys. 37, 2572 (1998).
[CrossRef]

Other (4)

Y. J. Kim, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’99 (Society for Information Display, San Jose, Calif., 1999), p. 866.

T. Tanaka, Y. Sato, A. Inoue, Y. Momose, H. Nomura, and S. Iino, in Proceedings of Asia Display ’95 (Society for Information Display, San Jose, Calif., 1995), p. 259.

S. W. Suh, Z. Zhuang, and J. S. Patel, in Proceedings of SID ’98 (Society for Information Display, San Jose, Calif., 1998).

H. Poincaré, in Theorie Mathematique de la Lumiere II, G. Carre, ed. (Gauthier-Villars, Paris, 1892), pp. 275–306.

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Figures (3)

Fig. 1
Fig. 1

(a) Circular SOP output conditions. A is the incident SOP. ON is the cone’s axis, and r is the radius of the cone’s base. (b) S1S3 projection plane, (c) S1S2 projection plane. (d) Total rotation angle required for circular SOP output. The solid line represents the equator of the PS.

Fig. 2
Fig. 2

Linear SOP output conditions: (a) Total rotation angle 2mπ; (b) total rotation angle 2mπ+2χ.

Fig. 3
Fig. 3

Optimum conditions for the RBTN structure. The solid circles are the optimum conditions for perpendicular SOP output. The squares are the optimum conditions for both of the bistable states. The open squares indicate that the other state has a twisted angle φ+2π; the filled squares indicate that the other state has a twisted angle φ-2π.

Tables (1)

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Table 1 Optimum Conditions for the RBTN Structure

Equations (6)

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tan ω=λφ/πdΔn,
Φ=2πdΔn/λ2+2φ21/2.
φ=n+1π-cos-1-cos2 α/2cos α/1+cos2 α1/2, dΔn=λφ/π cos α,
φ=nπ+cos-1-cos2 α/2cos α/1+cos2 α1/2, dΔn=λφ/π cos α,
π2d2Δn2/λ2+φ21/2=mπ
π2d2 Δn2/λ2+φ21/2=mπ+χ,

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