Abstract

We report on the determination of liquid crystal pre-tilt inside cells fabricated using single crystal birefringent and dichroic windows of cerium doped strontium barium niobate. We show that the average pre-tilt is significantly affected by the crystalline windows, leading to much larger values than those obtained with glass windows using identical fabrication methods. The same technique can be used to determine pre-tilts as large as 40 degrees, which is significantly larger than normally measurable using the cell rotation method.

©2006 Optical Society of America

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References

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  1. I. C. Khoo, B. D. Guenther, M. V. Wood, P. Chen, and M.-Y. Shih, “Coherent beam amplification with a photorefractive liquid crystal,” Opt. Lett. 22, 1229–1231 (1997).
    [Crossref] [PubMed]
  2. F. Kajzar, S. Bartkiewicz, and A. Miniewicz, “Optical amplification with high gain in hybrid-polymerliquid-crystal structures,” Appl. Phys. Lett. 74, 2924–2926 (1999).
    [Crossref]
  3. S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
    [Crossref]
  4. G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
    [Crossref]
  5. G. Cook, J. L. Carns, M. A. Saleh, and D. R. Evans, “Substrate induced pre-tilt in hybrid liquid crystal/inorganic photorefractives,” Mol. Cryst. Liq. Cryst. (in press).
  6. G. Baur, V. Wittmer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56, 142–144 (1976).
    [Crossref]
  7. T. J. Scheffer and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
    [Crossref]
  8. K. Han, T. Miyashita, and T. Uchida, “Accurate determination and measurement error of pretilt angle in liquid crystal cell,” Jpn. J. Appl. Phys.,  32, L277–L279 (1993).
    [Crossref]
  9. P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
    [Crossref]
  10. C. Gu and P. Yeh, “Extended Jones matrix method. II,” J. Opt. Soc. Am. A 10, 966–973 (1993).
    [Crossref]
  11. M. Born and E. Wolf, Principles of Optics, Fifth Ed. (Pergamon Press, New York, 1975).
  12. K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).
  13. J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
    [Crossref]
  14. P. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, “Ferroelectric tungsten bronze-type crystal structures. I. Barium strontium niobate Ba0.27Sr0.75Nb2O5.78,” J. Chem. Phys. 48, 5048–5057 (1968).
    [Crossref]
  15. J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
    [Crossref]

2003 (1)

G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
[Crossref]

2001 (1)

S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
[Crossref]

2000 (1)

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

1999 (1)

F. Kajzar, S. Bartkiewicz, and A. Miniewicz, “Optical amplification with high gain in hybrid-polymerliquid-crystal structures,” Appl. Phys. Lett. 74, 2924–2926 (1999).
[Crossref]

1997 (1)

1993 (2)

K. Han, T. Miyashita, and T. Uchida, “Accurate determination and measurement error of pretilt angle in liquid crystal cell,” Jpn. J. Appl. Phys.,  32, L277–L279 (1993).
[Crossref]

C. Gu and P. Yeh, “Extended Jones matrix method. II,” J. Opt. Soc. Am. A 10, 966–973 (1993).
[Crossref]

1987 (1)

J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
[Crossref]

1982 (1)

1977 (1)

T. J. Scheffer and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[Crossref]

1976 (1)

G. Baur, V. Wittmer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56, 142–144 (1976).
[Crossref]

1968 (1)

P. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, “Ferroelectric tungsten bronze-type crystal structures. I. Barium strontium niobate Ba0.27Sr0.75Nb2O5.78,” J. Chem. Phys. 48, 5048–5057 (1968).
[Crossref]

Abrahams, S. C.

P. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, “Ferroelectric tungsten bronze-type crystal structures. I. Barium strontium niobate Ba0.27Sr0.75Nb2O5.78,” J. Chem. Phys. 48, 5048–5057 (1968).
[Crossref]

Bartkiewicz, S.

S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
[Crossref]

F. Kajzar, S. Bartkiewicz, and A. Miniewicz, “Optical amplification with high gain in hybrid-polymerliquid-crystal structures,” Appl. Phys. Lett. 74, 2924–2926 (1999).
[Crossref]

Baur, G.

G. Baur, V. Wittmer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56, 142–144 (1976).
[Crossref]

Bernstein, J. L.

P. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, “Ferroelectric tungsten bronze-type crystal structures. I. Barium strontium niobate Ba0.27Sr0.75Nb2O5.78,” J. Chem. Phys. 48, 5048–5057 (1968).
[Crossref]

Berreman, D. W.

G. Baur, V. Wittmer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56, 142–144 (1976).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, Fifth Ed. (Pergamon Press, New York, 1975).

Carns, J. L.

G. Cook, J. L. Carns, M. A. Saleh, and D. R. Evans, “Substrate induced pre-tilt in hybrid liquid crystal/inorganic photorefractives,” Mol. Cryst. Liq. Cryst. (in press).

Chen, P.

Cook, G.

G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
[Crossref]

G. Cook, J. L. Carns, M. A. Saleh, and D. R. Evans, “Substrate induced pre-tilt in hybrid liquid crystal/inorganic photorefractives,” Mol. Cryst. Liq. Cryst. (in press).

Deer, M. J.

G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
[Crossref]

Evans, D. R.

G. Cook, J. L. Carns, M. A. Saleh, and D. R. Evans, “Substrate induced pre-tilt in hybrid liquid crystal/inorganic photorefractives,” Mol. Cryst. Liq. Cryst. (in press).

Geary, J. M.

J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
[Crossref]

Goodby, J. W.

J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
[Crossref]

Gu, C.

Guenther, B. D.

Han, K.

K. Han, T. Miyashita, and T. Uchida, “Accurate determination and measurement error of pretilt angle in liquid crystal cell,” Jpn. J. Appl. Phys.,  32, L277–L279 (1993).
[Crossref]

Hasegawa, M.

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

Hasegawa, R.

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

Itoh, N.

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

Jamieson, P. B.

P. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, “Ferroelectric tungsten bronze-type crystal structures. I. Barium strontium niobate Ba0.27Sr0.75Nb2O5.78,” J. Chem. Phys. 48, 5048–5057 (1968).
[Crossref]

Jones, D. C.

G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
[Crossref]

Kajzar, F.

S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
[Crossref]

F. Kajzar, S. Bartkiewicz, and A. Miniewicz, “Optical amplification with high gain in hybrid-polymerliquid-crystal structures,” Appl. Phys. Lett. 74, 2924–2926 (1999).
[Crossref]

Khoo, I. C.

Kmetz, A. R.

J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
[Crossref]

Koden, M.

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

Kremer, R. K.

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

Matczyszyn, K.

S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
[Crossref]

Meyer, M.

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

Miniewicz, A.

S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
[Crossref]

F. Kajzar, S. Bartkiewicz, and A. Miniewicz, “Optical amplification with high gain in hybrid-polymerliquid-crystal structures,” Appl. Phys. Lett. 74, 2924–2926 (1999).
[Crossref]

Miyashita, T.

K. Han, T. Miyashita, and T. Uchida, “Accurate determination and measurement error of pretilt angle in liquid crystal cell,” Jpn. J. Appl. Phys.,  32, L277–L279 (1993).
[Crossref]

Nehring, J.

T. J. Scheffer and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[Crossref]

Pankrath, R.

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

Patel, J. S.

J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
[Crossref]

Sakamoto, M.

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

Saleh, M. A.

G. Cook, J. L. Carns, M. A. Saleh, and D. R. Evans, “Substrate induced pre-tilt in hybrid liquid crystal/inorganic photorefractives,” Mol. Cryst. Liq. Cryst. (in press).

Scheffer, T. J.

T. J. Scheffer and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[Crossref]

Schirmer, O. F.

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

Shih, M.-Y.

Takatoh, K.

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

Uchida, T.

K. Han, T. Miyashita, and T. Uchida, “Accurate determination and measurement error of pretilt angle in liquid crystal cell,” Jpn. J. Appl. Phys.,  32, L277–L279 (1993).
[Crossref]

Wingbermüle, J.

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

Wittmer, V.

G. Baur, V. Wittmer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56, 142–144 (1976).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, Fifth Ed. (Pergamon Press, New York, 1975).

Wood, M. V.

Wyres, C. A.

G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
[Crossref]

Yeh, P.

Appl. Phys. Lett. (1)

F. Kajzar, S. Bartkiewicz, and A. Miniewicz, “Optical amplification with high gain in hybrid-polymerliquid-crystal structures,” Appl. Phys. Lett. 74, 2924–2926 (1999).
[Crossref]

J. Appl. Phys. (2)

T. J. Scheffer and J. Nehring, “Accurate determination of liquid-crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
[Crossref]

J. M. Geary, J. W. Goodby, A. R. Kmetz, and J. S. Patel, “The mechanism of polymer alignment of liquidcrystal materials,” J. Appl. Phys. 62, 4100–4108 (1987).
[Crossref]

J. Chem. Phys. (1)

P. B. Jamieson, S. C. Abrahams, and J. L. Bernstein, “Ferroelectric tungsten bronze-type crystal structures. I. Barium strontium niobate Ba0.27Sr0.75Nb2O5.78,” J. Chem. Phys. 48, 5048–5057 (1968).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys.: Condens. Matter (1)

J. Wingbermüle, M. Meyer, O. F. Schirmer, R. Pankrath, and R. K. Kremer, “Electron paramagnetic resonance of Ce3+in strontium-barium niobate,” J. Phys.: Condens. Matter 12, 4277–4284 (2000).
[Crossref]

Jpn. J. Appl. Phys. (1)

K. Han, T. Miyashita, and T. Uchida, “Accurate determination and measurement error of pretilt angle in liquid crystal cell,” Jpn. J. Appl. Phys.,  32, L277–L279 (1993).
[Crossref]

Opt. Commun. (1)

S. Bartkiewicz, K. Matczyszyn, A. Miniewicz, and F. Kajzar, “High gain of light in photoconducting polymer-nematic liquid crystal hybrid structures,” Opt. Commun. 187, 257–261 (2001).
[Crossref]

Opt. Lett. (1)

Phys. Lett. (1)

G. Baur, V. Wittmer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56, 142–144 (1976).
[Crossref]

Proc. SPIE (1)

G. Cook, C. A. Wyres, M. J. Deer, and D. C. Jones, “Hybrid organic-inorganic photorefractives,” Proc. SPIE 5213, 63–77 (2003).
[Crossref]

Other (3)

G. Cook, J. L. Carns, M. A. Saleh, and D. R. Evans, “Substrate induced pre-tilt in hybrid liquid crystal/inorganic photorefractives,” Mol. Cryst. Liq. Cryst. (in press).

M. Born and E. Wolf, Principles of Optics, Fifth Ed. (Pergamon Press, New York, 1975).

K. Takatoh, M. Hasegawa, M. Koden, N. Itoh, R. Hasegawa, and M. Sakamoto, Alignment Technologies and Applications of Liquid Crystal Devices (Taylor & Francis, New York, 2005).

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Figures (6)

Fig. 1.
Fig. 1. Experimental arrangement for measuring pre-tilt angles by the cell rotation method.
Fig. 2.
Fig. 2. Schematic diagram of experiment and coordinate system used to describe light propagation through the cell.
Fig. 3.
Fig. 3. Example of theoretical fit to data (transmission vs. cell rotation angle).
Fig. 4.
Fig. 4. Pre-tilt angle θc as a function of extremum angle θex for a liquid crystal cell with glass windows (ne =1.744, no =1.527).
Fig. 5.
Fig. 5. Pre-tilt angle θc as a function of extremum angle θex for a liquid crystal cell with Ce:SBN windows (ne =1.744, no =1.527, d=8 µm, nwo =2.33, Δnw =-0.03, dw =1.31 mm).
Fig. 6.
Fig. 6. Theoretical plot of transmittance vs. θ for a Ce:SBN-TL205 8-µm hybrid cell. Solid curve is for θc =7°and dashed curve is for θc =0°.

Tables (1)

Tables Icon

Table 1. Fit Parameters θc and d for Six Data Sets

Equations (23)

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

( A s A p ) = D out P D in ( A s A p ) .
D in = ( s ̂ · o ̂ t s p ̂ o · o ̂ t p s ̂ · e ̂ t s p ̂ o · e ̂ t p ) ,
D out = ( o ̂ · s ̂ t s e ̂ · s ̂ t s o ̂ · p ̂ o t p e ̂ · p ̂ o t p ) ,
o ̂ = c ̂ × k o c ̂ × k o , e ̂ k o × o ̂ k o × o ̂ , p ̂ o = k o × s ̂ k o × s ̂ ,
P = ( exp ( i q o · Δ r ) 0 0 exp ( i q e · Δ r ) ) ,
q · Δ r k z d + i ( α d 2 cos θ o ) ,
k j o z = 2 π λ n j o ( 1 sin 2 θ n j o 2 ) 1 2 ,
k j e z = 2 π λ v j + ( v j 2 4 u j w j ) 1 2 2 u j 2 π λ F j ( θ , θ j , ϕ j ) ,
u j = sin 2 θ j n j e 2 + cos 2 θ j n j o 2 ,
v j = sin θ sin 2 θ j sin ϕ j ( 1 n j e 2 1 n j o 2 ) ,
w j = sin 2 θ cos 2 θ j sin 2 ϕ j + sin 2 θ cos 2 ϕ j n j e 2 + sin 2 θ sin 2 θ j sin 2 ϕ j n j o 2 1 .
( A s A p ) = P A j = 1 3 ( D out P D in ) j ( A s A p ) ,
P A = ( cos 2 ψ sin ψ cos ψ sin ψ cos ψ sin 2 ψ ) .
T = A s 2 + A p 2 A s 2 + A p 2 .
T = 1 4 { τ s 2 + τ p 2 2 τ s τ p cos ( 2 Δ φ w + Δ φ L C ) } ,
Δ φ w = 2 π λ ( n w e n w o ) ( 1 sin 2 θ n w o 2 ) 1 2 d w ,
Δ φ L C = 2 π λ { f ( θ , θ c ) n o ( 1 sin 2 θ n o 2 ) 1 2 } d ,
τ s = ( t s ) a i r , w ( t s ) w , L C ( t s ) L C , w ( t s ) w , a i r exp ( α w o d w cos θ w ) ,
τ p = ( t p ) a i r , w ( t p ) w , L C ( t p ) L C , w ( t p ) w , a i r exp ( α w o ( θ w ) d w cos θ w ) .
α w e ( θ w ) = ( α w o sin 2 θ w n w o 3 + α w e cos 2 θ w n w e 3 ) ( sin 2 θ w n w o 2 + cos 2 θ w n w e 2 ) 3 2 .
1 2 c 2 ( θ c ) ( a 2 b 2 ) sin 2 θ c a 2 b 2 c 3 ( θ c ) ( 1 a 2 b 2 c 2 ( θ c ) sin 2 θ e x ) 1 2 sin θ e x
+ b ( 1 b 2 sin 2 θ e x ) 1 2 sin θ e x = 0
g ( θ c , θ e x ) = g 0 ( θ c , θ e x ) + b w 2 Δ n w ( 2 d w d ) ( 1 b w 2 sin 2 θ e x ) 1 2 sin θ e x = 0 ,

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