Abstract

We present a method that determines the actual surface azimuthal anchoring strength based on the torque balance. It is found by an optical technique of measuring simultaneously the cell thicknesses and twist angles at two regions of a wedge-type liquid crystal cell whose cell thickness varies continuously between different positions in the cell.

© 2010 Optical Society of America

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  1. H. Yokoyama and H. A. van Sprang, J. Appl. Phys. 57, 4520 (1985).
    [CrossRef]
  2. S. Faetti and P. Marianelli, Phys. Rev. E 72, 051708 (2005).
    [CrossRef]
  3. D. W. Berreman, Phys. Rev. Lett. 28, 1683 (1972).
    [CrossRef]
  4. R. Barberi and G. Durand, Appl. Phys. Lett. 58, 2907 (1991).
    [CrossRef]
  5. J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
    [CrossRef]
  6. J. H. Kim, M. Yoneya, and H. Yokoyama, Nature 420, 159 (2002).
    [CrossRef] [PubMed]
  7. J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
    [CrossRef]
  8. J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
    [CrossRef]
  9. V. P. Vorflusev, H.-S. Kitzerow, and V. G. Chigrinov, Jpn. J. Appl. Phys. 34, L1137 (1995).
    [CrossRef]
  10. Y. Saitoh and A. Lien, Jpn. J. Appl. Phys. 39, 1743 (2000).
    [CrossRef]
  11. Y. Iimura, N. Kobayashi, and S. Kobayashi, Jpn. J. Appl. Phys. 33, L434 (1994).
    [CrossRef]
  12. M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
    [CrossRef]
  13. Y. Zhou, Z. He, and S. Sato, Jpn. J. Appl. Phys. 36, 2760 (1997).
    [CrossRef]
  14. T. Akahane, H. Kaneko, and M. Kimura, Jpn. J. Appl. Phys. 35, 4434 (1996).
    [CrossRef]
  15. J. S. Gwag, S. J. Kim, J. G. You, J. Y. Lee, J. C. Kim, and T.-H. Yoon, Opt. Lett. 30, 1387 (2005).
    [CrossRef] [PubMed]
  16. S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
    [CrossRef]
  17. H. S. Kwok, J. Appl. Phys. 80, 3687 (1996).
    [CrossRef]

2009

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

2008

J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
[CrossRef]

2007

J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
[CrossRef]

2005

2002

J. H. Kim, M. Yoneya, and H. Yokoyama, Nature 420, 159 (2002).
[CrossRef] [PubMed]

2001

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

2000

Y. Saitoh and A. Lien, Jpn. J. Appl. Phys. 39, 1743 (2000).
[CrossRef]

1997

Y. Zhou, Z. He, and S. Sato, Jpn. J. Appl. Phys. 36, 2760 (1997).
[CrossRef]

1996

T. Akahane, H. Kaneko, and M. Kimura, Jpn. J. Appl. Phys. 35, 4434 (1996).
[CrossRef]

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

1995

V. P. Vorflusev, H.-S. Kitzerow, and V. G. Chigrinov, Jpn. J. Appl. Phys. 34, L1137 (1995).
[CrossRef]

1994

Y. Iimura, N. Kobayashi, and S. Kobayashi, Jpn. J. Appl. Phys. 33, L434 (1994).
[CrossRef]

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

1991

R. Barberi and G. Durand, Appl. Phys. Lett. 58, 2907 (1991).
[CrossRef]

1985

H. Yokoyama and H. A. van Sprang, J. Appl. Phys. 57, 4520 (1985).
[CrossRef]

1972

D. W. Berreman, Phys. Rev. Lett. 28, 1683 (1972).
[CrossRef]

Akahane, T.

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

T. Akahane, H. Kaneko, and M. Kimura, Jpn. J. Appl. Phys. 35, 4434 (1996).
[CrossRef]

Akao, K.

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

Barberi, R.

R. Barberi and G. Durand, Appl. Phys. Lett. 58, 2907 (1991).
[CrossRef]

Berreman, D. W.

D. W. Berreman, Phys. Rev. Lett. 28, 1683 (1972).
[CrossRef]

Chigrinov, V. G.

V. P. Vorflusev, H.-S. Kitzerow, and V. G. Chigrinov, Jpn. J. Appl. Phys. 34, L1137 (1995).
[CrossRef]

Durand, G.

R. Barberi and G. Durand, Appl. Phys. Lett. 58, 2907 (1991).
[CrossRef]

Faetti, S.

S. Faetti and P. Marianelli, Phys. Rev. E 72, 051708 (2005).
[CrossRef]

Fukuda, J.

J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
[CrossRef]

Gwag, J. S.

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
[CrossRef]

J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
[CrossRef]

J. S. Gwag, S. J. Kim, J. G. You, J. Y. Lee, J. C. Kim, and T.-H. Yoon, Opt. Lett. 30, 1387 (2005).
[CrossRef] [PubMed]

He, Z.

Y. Zhou, Z. He, and S. Sato, Jpn. J. Appl. Phys. 36, 2760 (1997).
[CrossRef]

Huang, X.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Iimura, Y.

Y. Iimura, N. Kobayashi, and S. Kobayashi, Jpn. J. Appl. Phys. 33, L434 (1994).
[CrossRef]

Jiang, M.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Kaneko, H.

T. Akahane, H. Kaneko, and M. Kimura, Jpn. J. Appl. Phys. 35, 4434 (1996).
[CrossRef]

Kim, J. C.

Kim, J. H.

J. H. Kim, M. Yoneya, and H. Yokoyama, Nature 420, 159 (2002).
[CrossRef] [PubMed]

Kim, J. -H.

J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
[CrossRef]

Kim, S. J.

Kimura, M.

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

T. Akahane, H. Kaneko, and M. Kimura, Jpn. J. Appl. Phys. 35, 4434 (1996).
[CrossRef]

Kitzerow, H. -S.

V. P. Vorflusev, H.-S. Kitzerow, and V. G. Chigrinov, Jpn. J. Appl. Phys. 34, L1137 (1995).
[CrossRef]

Kobayashi, N.

Y. Iimura, N. Kobayashi, and S. Kobayashi, Jpn. J. Appl. Phys. 33, L434 (1994).
[CrossRef]

Kobayashi, S.

Y. Iimura, N. Kobayashi, and S. Kobayashi, Jpn. J. Appl. Phys. 33, L434 (1994).
[CrossRef]

Kwok, H. S.

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

Kwon, J. H.

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

Lee, J. Y.

Lien, A.

Y. Saitoh and A. Lien, Jpn. J. Appl. Phys. 39, 1743 (2000).
[CrossRef]

Ma, K.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Ma, R.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Marianelli, P.

S. Faetti and P. Marianelli, Phys. Rev. E 72, 051708 (2005).
[CrossRef]

Niitsuma, J.

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

Oh-e, M.

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

Okutani, S.

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

Saitoh, Y.

Y. Saitoh and A. Lien, Jpn. J. Appl. Phys. 39, 1743 (2000).
[CrossRef]

Sato, S.

Y. Zhou, Z. He, and S. Sato, Jpn. J. Appl. Phys. 36, 2760 (1997).
[CrossRef]

Sun, R.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Tadokoro, T.

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

Toriumi, H.

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

van Sprang, H. A.

H. Yokoyama and H. A. van Sprang, J. Appl. Phys. 57, 4520 (1985).
[CrossRef]

Vorflusev, V. P.

V. P. Vorflusev, H.-S. Kitzerow, and V. G. Chigrinov, Jpn. J. Appl. Phys. 34, L1137 (1995).
[CrossRef]

Wang, Z.

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Yokoyama, H.

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
[CrossRef]

J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
[CrossRef]

J. H. Kim, M. Yoneya, and H. Yokoyama, Nature 420, 159 (2002).
[CrossRef] [PubMed]

H. Yokoyama and H. A. van Sprang, J. Appl. Phys. 57, 4520 (1985).
[CrossRef]

Yoneya, M.

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
[CrossRef]

J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
[CrossRef]

J. H. Kim, M. Yoneya, and H. Yokoyama, Nature 420, 159 (2002).
[CrossRef] [PubMed]

Yoon, T. -H.

You, J. G.

Zhou, Y.

Y. Zhou, Z. He, and S. Sato, Jpn. J. Appl. Phys. 36, 2760 (1997).
[CrossRef]

Appl. Phys. Lett.

J. S. Gwag, J.-H. Kim, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 92, 153110 (2008).
[CrossRef]

J. S. Gwag, J. H. Kwon, M. Oh-e, J. Niitsuma, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 95, 103101 (2009).
[CrossRef]

R. Barberi and G. Durand, Appl. Phys. Lett. 58, 2907 (1991).
[CrossRef]

J. S. Gwag, J. Fukuda, M. Yoneya, and H. Yokoyama, Appl. Phys. Lett. 91, 073504 (2007).
[CrossRef]

J. Appl. Phys.

H. Yokoyama and H. A. van Sprang, J. Appl. Phys. 57, 4520 (1985).
[CrossRef]

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

Jpn. J. Appl. Phys.

V. P. Vorflusev, H.-S. Kitzerow, and V. G. Chigrinov, Jpn. J. Appl. Phys. 34, L1137 (1995).
[CrossRef]

Y. Saitoh and A. Lien, Jpn. J. Appl. Phys. 39, 1743 (2000).
[CrossRef]

Y. Iimura, N. Kobayashi, and S. Kobayashi, Jpn. J. Appl. Phys. 33, L434 (1994).
[CrossRef]

M. Jiang, Z. Wang, R. Sun, K. Ma, R. Ma, and X. Huang, Jpn. J. Appl. Phys. 33, L1242 (1994).
[CrossRef]

Y. Zhou, Z. He, and S. Sato, Jpn. J. Appl. Phys. 36, 2760 (1997).
[CrossRef]

T. Akahane, H. Kaneko, and M. Kimura, Jpn. J. Appl. Phys. 35, 4434 (1996).
[CrossRef]

S. Okutani, M. Kimura, H. Toriumi, K. Akao, T. Tadokoro, and T. Akahane, Jpn. J. Appl. Phys. 40, 244 (2001).
[CrossRef]

Nature

J. H. Kim, M. Yoneya, and H. Yokoyama, Nature 420, 159 (2002).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. E

S. Faetti and P. Marianelli, Phys. Rev. E 72, 051708 (2005).
[CrossRef]

Phys. Rev. Lett.

D. W. Berreman, Phys. Rev. Lett. 28, 1683 (1972).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Coordinate system of optical components at a general TNLC cell.

Fig. 2
Fig. 2

Setup for twisted angle and cell thickness measurement at several positions of TNLC cell.

Fig. 3
Fig. 3

Transmittance measured at each position of the wedge-type TNLC cell.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

F t = F b + F s ,
F b = K 22 2 d ( ϕ r 2 π d p ) 2 , F s = 1 2 W a sin 2 Δ ϕ .
Δ ϕ = ϕ e ϕ r 2 ,
2 K 22 d ( ϕ r 2 π d p ) W a   sin ( 2 Δ ϕ ) = 0.
W a = 2 K 22 sin ( 2 Δ ϕ ) ( ϕ r d 2 π p ) = 2 K 22 sin ( ϕ e ϕ r ) ( ϕ r d 2 π p ) .
W a = 2 K 22 sin ( ϕ e ϕ r 1 ) ( ϕ r 1 d 1 2 π p ) = 2 K 22 sin ( ϕ e ϕ r 2 ) ( ϕ r 2 d 2 2 π p ) = = 2 K 22 sin ( ϕ e ϕ r n ) ( ϕ r n d n 2 π p ) .
T = [ cos   η   cos ( ϕ r φ p ) + ϕ r η sin   η   sin ( ϕ r φ p ) ] 2 + μ 2 η 2 sin 2 η cos 2 ( ϕ r + 2 φ 0 φ p ) ,
η = ( ϕ r 2 + μ 2 ) 1 / 2 ,     μ = π d Δ n / λ ,
Δ n = n e 1 + z sin 2 θ n o ,
z = ( n e / n o ) 2 1.
T = cos 2 ( ϕ r φ p ) = 0 ,   namely , ϕ r φ p = π 2 ± n π .
cos 2 ( ϕ r + 2 φ 0 φ p ) = 0 ,
cos   η   cos ( ϕ r φ p ) + ϕ r η sin   η   sin ( ϕ r φ p ) = 0.

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