Abstract

By use of a trans-cis photoisomerization process occurring in an azo-benzene side chain, various twisted nematic liquid-crystal (LC) gratings are fabricated in LC cells. Two counterpropagating orthogonally polarized beams produce a polarization modulation, which inscribes the replica polarization modulation inside LC cells holographically, providing twisted nematic LC gratings. Microstructure, diffraction properties, and electro-optic tunability of diffraction efficiency are examined experimentally. From the Fourier transformation of the Jones matrix of twisted nematic LC gratings, Stokes parameters of the zeroth and first diffraction orders are calculated and compared with the optical measurements, resulting in a good agreement.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. W.-Y. Wu, T.-S. Mo, and A. Y. G. Fuh, “Polarization characteristics of diffracted beams from twisted nematic gratings fabricated by the photoalignment effect in dye-doped liquid-crystal films,” J. Opt. Soc. Am. B 23, 1737-1742 (2006).
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    [CrossRef]

2006

2005

C.-J. Yu, D.-W. Kim, J. Kim, and S.-D. Lee, “Polarization invariant grating based on a photoaligned liquid crystal in an oppositely twisted binary configuration,” Opt. Lett. 30, 1995-1997 (2005).
[CrossRef] [PubMed]

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

2004

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

2003

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

2002

1998

1997

C. M. Titus and P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239-2241 (1997).
[CrossRef]

Bastiaansen, C. W. M.

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

Bos, P. J.

C. M. Titus and P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239-2241 (1997).
[CrossRef]

Broer, D. J.

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

Callan-Jones, A.

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Chang, H. J.

H. Choi, H. J. Chang, B. Park, and J. W. Wu, “Holographically generated twisted nematic liquid crystal gratings,” Appl. Phys. Lett. 88, 021905 (2006).
[CrossRef]

Choi, H.

H. Choi, H. J. Chang, B. Park, and J. W. Wu, “Holographically generated twisted nematic liquid crystal gratings,” Appl. Phys. Lett. 88, 021905 (2006).
[CrossRef]

Crawford, G. P.

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

Crawforda, G. P.

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Eakin, J. N.

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Emoto, A.

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

Fuh, A. Y. G.

Fuh, A. Y.-G.

Gu, C.

P. Yeh and C. Gu, Liquid Crystals Display (Wiley, 1999).

Hasegawa, T.

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

He, Z.

Kawatsuki, N.

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

Kim, D.-W.

Kim, J.

Lee, C.-R.

Lee, S.-D.

Mo, T.-S.

Narayanankutty, S.

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

Ono, H.

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

Park, B.

H. Choi, H. J. Chang, B. Park, and J. W. Wu, “Holographically generated twisted nematic liquid crystal gratings,” Appl. Phys. Lett. 88, 021905 (2006).
[CrossRef]

Pelcovits, R. A.

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Radcliffe, M. D.

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Sato, S.

Takahashi, F.

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

Titus, C. M.

C. M. Titus and P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239-2241 (1997).
[CrossRef]

Varghese, S.

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

Wu, J. W.

H. Choi, H. J. Chang, B. Park, and J. W. Wu, “Holographically generated twisted nematic liquid crystal gratings,” Appl. Phys. Lett. 88, 021905 (2006).
[CrossRef]

Wu, W.-Y.

Yeh, P.

P. Yeh and C. Gu, Liquid Crystals Display (Wiley, 1999).

Yu, C.-J.

Adv. Mater.

S. Varghese, S. Narayanankutty, C. W. M. Bastiaansen, G. P. Crawford, and D. J. Broer, “Patterned alignment of liquid crystals by μ-rubbing,” Adv. Mater. 16, 1600-1605 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

C. M. Titus and P. J. Bos, “Efficient, polarization-independent, reflective liquid crystal phase grating,” Appl. Phys. Lett. 71, 2239-2241 (1997).
[CrossRef]

H. Choi, H. J. Chang, B. Park, and J. W. Wu, “Holographically generated twisted nematic liquid crystal gratings,” Appl. Phys. Lett. 88, 021905 (2006).
[CrossRef]

J. Appl. Phys.

G. P. Crawforda, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298-1303 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Other

P. Yeh and C. Gu, Liquid Crystals Display (Wiley, 1999).

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Figures (10)

Fig. 1
Fig. 1

(a) Slanted reflection holographic setup for S P and + 45 ° , 45 ° linear writing beams. (b) Polarization modulation on the alignment layer in accordance with the phase shift between S P and + 45 ° , 45 ° linear writing beams, with amplitude attenuation in the alignment layers and the azo dye doped LC bulk taken into account.

Fig. 2
Fig. 2

Microscopic domain textures taken by a polarized microscope of LC gratings in (a) type I LC cell in S P , (b) type I LC cell in + 45 ° , 45 ° , (c) type II LC cell in S P , and (d) type II LC cell in + 45 ° , 45 ° orthogonal polarization configurations.

Fig. 3
Fig. 3

Schematics of twisted aligned liquid crystal molecules in adjacent domains of LC gratings in the type I LC cell recorded by (a) S- and P-polarized writing beams, corresponding to Fig. 2a; (b) + 45 ° , 45 ° linear polarized writing beams, corresponding to Fig. 2b, and in type II LC cell recorded by (c) S- and P- polarized writing beams, corresponding to Fig. 2c; (d) + 45 ° , 45 ° linear polarized writing beams, corresponding to Fig. 2d.

Fig. 4
Fig. 4

Schematics of twisted aligned liquid crystal molecules in adjacent domains of RTN LC gratings.

Fig. 5
Fig. 5

Polarization dependence of the diffracted orders of RTNLC (a) + 45 ° , 45 ° in the type I cell, and (c) S P and (e) + 45 ° , 45 ° in the type II cell with the corresponding electro-optic tunability measurements (b), (d), and (f), respectively.

Fig. 6
Fig. 6

(a) and (b) and (c) and (d) show the zeroth and the first diffracted order intensities for a fixed cell thickness d = 8 μ m as a function of α and θ ranging from 0 to 2 π for S P and + 45 ° , 45 ° gratings, respectively.

Fig. 7
Fig. 7

Polarization state of diffraction orders of S P and + 45 ° , 45 ° RTNLC in the type I cell, and S P and + 45 ° , 45 ° in the type II cell.

Fig. 8
Fig. 8

Stock parameters of the zeroth and first diffracted beams from (a) the S P , and (b) the + 45 ° , 45 ° RTNLC by the P-polarized incident beam.

Fig. 9
Fig. 9

Stock parameters of the zeroth and first diffracted beams from (a) the S P , and (b) the + 45 ° , 45 ° RTNLC by the + 45 ° linearly polarized incident beam.

Fig. 10
Fig. 10

Stock parameters of the zeroth and first diffracted beams from (a) the S P , and (b) the + 45 ° , 45 ° RTNLC by the circular polarized incident beam.

Equations (27)

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E + o = ξ + cos θ + ( sin ϕ , cos ϕ , 0 ) exp { i k 0 n o z } ,
E + e = ξ + n e 2 n o 2 sin θ + ( cos ϕ , sin ϕ , 0 ) exp { i k 0 n e z } ,
E o = ξ cos θ ( sin ϕ , cos ϕ , 0 ) exp { i k 0 n o ( d z ) } ,
E e = ξ n e 2 n o 2 sin θ ( cos ϕ , sin ϕ , 0 ) exp { i k 0 n e ( d z ) } ,
ϵ ( x , z ) = ϵ 0 + Δ ϵ cos [ K ( x sin θ s + z cos θ s ) ] ,
( A B C D ) = [ R ( α 1 ) ( a * b * b a ) R ( α 1 ) rect ( x Λ 4 Λ 2 ) + R ( α 2 ) ( a * b * b a ) R ( α 2 ) rect ( x + Λ 4 Λ 2 ) ] * 1 Λ comb ( x Λ ) ,
a = 1 ( 1 + u 2 ) 1 2 sin θ sin [ ( 1 + u 2 ) 1 2 θ ] + cos θ cos [ ( 1 + u 2 ) 1 2 θ ] + i u ( 1 + u 2 ) 1 2 cos θ sin [ ( 1 + u 2 ) 1 2 θ ] ,
b = 1 ( 1 + u 2 ) 1 2 cos θ sin [ ( 1 + u 2 ) 1 2 θ ] sin θ cos [ ( 1 + u 2 ) 1 2 θ ] + i u ( 1 + u 2 ) 1 2 sin θ sin [ ( 1 + u 2 ) 1 2 θ ] ,
u = π d λ θ ( n e n o ) ,
( A B C D ) = n = exp ( i 2 n π Λ x ) ( A n B n C n D n ) .
A ( S P ) n = sinc ( n 2 ) cos n π 2 { a * cos 2 α + a sin 2 α + ( b b * ) sin α cos α }
B ( S P ) n = i sinc ( n 2 ) sin n π 2 { b * cos 2 α + b sin 2 α + ( a * a ) sin α cos α }
C ( S P ) n = i sinc ( n 2 ) sin n π 2 { b cos 2 α + b * sin 2 α + ( a a * ) sin α cos α }
D ( S P ) n = sinc ( n 2 ) cos n π 2 { a * sin 2 α + a cos 2 α ( b b * ) sin α cos α } ,
A ( 45 ) n = 1 2 sinc ( n 2 ) { cos n π 2 ( a * + a ) + i sin n π 2 ( ( a a * ) ( cos 2 α sin 2 α ) + 2 ( b b * ) sin α cos α ) } ,
B ( 45 ) n = 1 2 sinc ( n 2 ) { cos n π 2 ( ( b b * ) ( cos 2 α sin 2 α ) + 2 ( a * a ) sin α cos α ) + i sin n π 2 ( b + b * ) } ,
C ( 45 ) n = 1 2 sinc ( n 2 ) { cos n π 2 ( ( b b * ) ( cos 2 α sin 2 α ) + 2 ( a * a ) sin α cos α ) i sin n π 2 ( b + b * ) } ,
D ( 45 ) n = 1 2 sinc ( n 2 ) { cos n π 2 ( a * + a ) i sin n π 2 ( ( a a * ) ( cos 2 α sin 2 α ) + 2 ( b b * ) sin α cos α ) } ,
( E x E y ) = ( A n B n C n D n ) ( E x in E y in ) .
I ± 1 S P = sinc 2 ( 1 2 ) [ ( 1 1 + u 2 cos θ sin ( 1 + u 2 θ ) sin θ cos ( 1 + u 2 θ ) ) 2 + ( u 1 + u 2 sin ( 1 + u 2 θ ) sin ( 2 α + θ ) ) 2 ] I input ,
I ± 1 45 = sinc 2 ( 1 2 ) [ ( u 1 + u 2 cos ( 2 θ + α ) sin ( 1 + u 2 θ ) ) 2 + ( u 1 + u 2 cos θ sin ( 1 + u 2 θ ) sin θ cos ( 1 + u 2 θ ) ) 2 ] I input .
2 α + θ = π 2 , ( 1 + u 2 ) 1 2 θ = k π ,
n eff = n o n e n e 2 sin 2 [ θ ( a ) ] + n o 2 cos 2 [ θ ( a ) ] ,
S 0 = E x E x * + E y E y * ,
S 1 = E x E x * E y E y * ,
S 2 = E x E y * + E y E x * ,
S 3 = i E x E y * E y E x * .

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