Abstract

In the application of a nematic liquid-crystal (LC) spatial light modulator, we derived the formula of retardation dynamic response of the device by solving the Erickson–Leslie equation. Then, the response time of the 2π phase change can be expressed as a function of the LC cell gap. The theoretical and experimental results all indicate that the response time of 2π first decreases and then increases with the LC cell gap increasing, and there is an optimal cell gap to obtain the shortest response time. Therefore, the method of optimizing the cell gap shows potential to improve the switching frequency for all type of nematic LC optical device with specific modulation quantity.

© 2011 Optical Society of America

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References

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2010 (1)

2008 (1)

2006 (1)

H. Y. Wang, X. Y. Nie, T. X. Wu, and S. T. Wu, Mol. Cryst. Liq. Cryst. 454, 285 (2006).
[CrossRef]

2005 (3)

S. Serati and J. Stockley, Proc. SPIE 5894, 58940K (2005).
[CrossRef]

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Z. Cao, L. Xuan, L. Hu, Y. Liu, and Q. Mu, Opt. Express 13, 5186 (2005).
[CrossRef] [PubMed]

2003 (1)

S. Brugioni and R. Meucci, Opt. Commun. 216, 453 (2003).
[CrossRef]

2001 (1)

Q. Wang and S. He, Acta Phys. Sin. 50, 926 (2001).

2000 (1)

1995 (1)

1988 (1)

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

1972 (1)

E. Jakeman and E. P. Raynes, Phys. Lett. 39A, 69 (1972).

1968 (1)

F. M. Leslie, Arch. Ration. Mech. Anal. 28, 265 (1968).
[CrossRef]

1961 (1)

J. L. Erickson, Trans. Soc. Rheol. 5, 23 (1961).
[CrossRef]

Baker, J.

Browne, S.

Brugioni, S.

S. Brugioni and R. Meucci, Opt. Commun. 216, 453 (2003).
[CrossRef]

Cao, Z.

Cheng, K. L.

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Dabrowski, R.

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Dayton, D.

Erickson, J. L.

J. L. Erickson, Trans. Soc. Rheol. 5, 23 (1961).
[CrossRef]

Gallegos, J.

Gauza, S.

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Gonglewski, J.

He, S.

Q. Wang and S. He, Acta Phys. Sin. 50, 926 (2001).

Hu, L.

Jakeman, E.

E. Jakeman and E. P. Raynes, Phys. Lett. 39A, 69 (1972).

Johnson, K. M.

Leslie, F. M.

F. M. Leslie, Arch. Ration. Mech. Anal. 28, 265 (1968).
[CrossRef]

Li, D.

Li, J.

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Liu, Y.

Love, G. D.

G. D. Love, Adaptive Optics Engineering Handbook, R.K.Tyson, ed. (Marcel Dekker, 1999), p. 281.

McDermott, S.

Meucci, R.

S. Brugioni and R. Meucci, Opt. Commun. 216, 453 (2003).
[CrossRef]

Mu, Q.

Nie, X. Y.

H. Y. Wang, X. Y. Nie, T. X. Wu, and S. T. Wu, Mol. Cryst. Liq. Cryst. 454, 285 (2006).
[CrossRef]

Peng, Z.

Raynes, E. P.

E. Jakeman and E. P. Raynes, Phys. Lett. 39A, 69 (1972).

Restaino, S.

Rogers, S.

Serati, S.

S. Serati and J. Stockley, Proc. SPIE 5894, 58940K (2005).
[CrossRef]

Serati, S. A.

Sharp, G. D.

Shilko, M.

Spadlo, A.

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Stockley, J.

S. Serati and J. Stockley, Proc. SPIE 5894, 58940K (2005).
[CrossRef]

Stockley, J. E.

Tzeng, Y. N.

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Wang, H. Y.

H. Y. Wang, X. Y. Nie, T. X. Wu, and S. T. Wu, Mol. Cryst. Liq. Cryst. 454, 285 (2006).
[CrossRef]

Wang, Q.

Q. Wang and S. He, Acta Phys. Sin. 50, 926 (2001).

Wu, C. S.

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

Wu, S. T.

H. Y. Wang, X. Y. Nie, T. X. Wu, and S. T. Wu, Mol. Cryst. Liq. Cryst. 454, 285 (2006).
[CrossRef]

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

Wu, T. X.

H. Y. Wang, X. Y. Nie, T. X. Wu, and S. T. Wu, Mol. Cryst. Liq. Cryst. 454, 285 (2006).
[CrossRef]

Xuan, L.

Acta Phys. Sin. (1)

Q. Wang and S. He, Acta Phys. Sin. 50, 926 (2001).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. T. Wu and C. S. Wu, Appl. Phys. Lett. 53, 1794 (1988).
[CrossRef]

Arch. Ration. Mech. Anal. (1)

F. M. Leslie, Arch. Ration. Mech. Anal. 28, 265 (1968).
[CrossRef]

Liq. Cryst. (1)

S. Gauza, J. Li, S. T. Wu, A. Spadlo, R. Dabrowski, Y. N. Tzeng, and K. L. Cheng, Liq. Cryst. 32, 1077 (2005).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

H. Y. Wang, X. Y. Nie, T. X. Wu, and S. T. Wu, Mol. Cryst. Liq. Cryst. 454, 285 (2006).
[CrossRef]

Opt. Commun. (1)

S. Brugioni and R. Meucci, Opt. Commun. 216, 453 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Lett. (1)

E. Jakeman and E. P. Raynes, Phys. Lett. 39A, 69 (1972).

Proc. SPIE (1)

S. Serati and J. Stockley, Proc. SPIE 5894, 58940K (2005).
[CrossRef]

Trans. Soc. Rheol. (1)

J. L. Erickson, Trans. Soc. Rheol. 5, 23 (1961).
[CrossRef]

Other (1)

G. D. Love, Adaptive Optics Engineering Handbook, R.K.Tyson, ed. (Marcel Dekker, 1999), p. 281.

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Figures (3)

Fig. 1
Fig. 1

Schematics of the parallel-aligned LC cell structure.

Fig. 2
Fig. 2

Response time of the 2 π phase ( λ = 533 nm , 635 nm , 785 nm ) depending on the LC cell gap at θ ¯ t 0 = 1.065 rad . The filled squares with the error bar are the experimental values at λ = 635 nm .

Fig. 3
Fig. 3

Experimental phase change (circles and squares) and response time of 2 π of the two parallel-aligned LC cells in decay response at λ = 635 nm . (a)  d = 2.49 μm , (b)  d = 2.94 μm . The voltage 4.0 V p p was released instantaneously at 0 ms . The solid lines in the figure are theoretical calculated values from Eq. (7).

Equations (9)

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γ 1 θ t = ( K 11 cos 2 θ + K 33 sin 2 θ ) 2 θ z 2 + ( K 33 K 11 ) sin θ cos θ ( θ z ) 2 + ε 0 | Δ ε | E 2 sin θ cos θ ,
γ 1 θ t = K 11 2 θ z 2 .
θ ( z , t ) = θ m sin ( π z / d ) exp ( t / τ d ) ,
Δ n d = 0 d n e n o n e 2 cos 2 θ ( z ) + n o 2 sin 2 θ ( z ) d z n o d .
δ t 0 = Δ n d 2 π λ 2 π d λ [ n e n o n o 2 cos 2 θ ¯ t 0 + n e 2 sin 2 θ ¯ t 0 n o ] .
θ ¯ ( t ) = θ ¯ t 0 exp ( t / τ d ) .
δ ( t ) 2 π d λ { n e n o n o 2 + ( n e 2 n o 2 ) sin 2 [ θ ¯ t 0 exp ( t / τ d ) ] n o } .
t 2 π ( d ) = τ d ln { 1 θ ¯ t 0 arcsin [ 1 n e 2 n o 2 ( 1 n o 2 cos 2 θ ¯ t 0 + n e 2 sin 2 θ ¯ t 0 + λ d n e n o ) 2 n o 2 n e 2 n o 2 ] 1 / 2 } .
t 2 π ( d ) / d = 0.

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