Abstract

Phase retardation of both extraordinary and ordinary polarized rays passing through a liquid crystal (LC) cell with homogeneous and inhomogeneous LC director distribution is calculated as a function of the LC pretilt angle θ0 on the cell substrates in the range 0θ090°. The LC pretilt on both substrates can have the same or opposite direction, thereby forming homogeneous, splay, or bend director configurations. At the same pretilt angle value, the largest phase retardation ΔΦ is observed in splay LC cells, whereas the smallest phase retardation is observed in bend cells. For the θ0 values close to 0, 45°, and 90°, analytical approximations are derived, showing that phase retardation depends on LC birefringence variation.

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References

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  1. K. Hanaoka, Y. Nakanishi, Y. Inoue, S. Tanuma, and Y. Koike, “A New MVA-LCD by Polymer Sustained Alignment Technology”, in SID’04 Digest, (2004), pp.1200–1203.
  2. P. J. Bos, “Passive Optical Phase Retarders for Liquid Crystal Displays”, in 14th IDRC Proc., (1994), p.118.
  3. X.-D. Mi, M. Xu, D.-K. Yang, and P. J. Bos, “Effects of pretilt angle on electro-optical properties of Pi-cell LCDs”, in SID’99 Digest (1999), pp.24–27.
  4. D. K. Yang and S. T. Wu, “Fundamentals of Liquid Crystal Devices” (Wiley, NY, 2006).
  5. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, 1992).
  6. L. M. Blinov and V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer, 1996). p.149.
  7. V. G. Chigrinov, “Orientation effects in nematic liquid crystals in electric and magnetic fields,” Sov. Phys. Crystallogr.27, 245–264 (1982).
  8. A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
    [CrossRef]
  9. A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
    [CrossRef] [PubMed]
  10. Ch. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express9(13), 780–790 (2001).
    [CrossRef] [PubMed]
  11. G. A. Beresnev, V. G. Chigrinov, and M. F. Grebenkin, “New method to determine K33/K11 ratio in nematic liquid crystals,” Crystallogr. Rep.27, 1019–1021 (1982).
  12. C. Dascalu, “Asymmetric electrooptic response in a nematic liquid crystal,” Rev. Mex. Fis.47, 281–285 (2001).
  13. X. Nie, “Anchoring energy and pretilt angle effects on liquid crystal response time”, Ph.D. Thesis, University of Central Florida, 2007.
  14. V. V. Belyaev and V. G. Mazaeva, “Green technologies of LC alignment on the base of organosilicon compunds”, in SID’11 Digest (2011), pp.1412–1415.
  15. V. V. Belyaev, A. S. Solomatin, D. N. Chausov, and A. A. Gorbunov, “Measurement of the LC pretilt angle and polar anchoring in cells with homogeneous and inhomogeneous LC director configuration and weak anchoring on organosilicon aligning films”, in SID’12 Digest, (2012), pp.1422–1425.

2005 (2)

A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
[CrossRef]

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

2001 (2)

1982 (2)

V. G. Chigrinov, “Orientation effects in nematic liquid crystals in electric and magnetic fields,” Sov. Phys. Crystallogr.27, 245–264 (1982).

G. A. Beresnev, V. G. Chigrinov, and M. F. Grebenkin, “New method to determine K33/K11 ratio in nematic liquid crystals,” Crystallogr. Rep.27, 1019–1021 (1982).

Belyaev, V.

A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
[CrossRef]

Beresnev, G. A.

G. A. Beresnev, V. G. Chigrinov, and M. F. Grebenkin, “New method to determine K33/K11 ratio in nematic liquid crystals,” Crystallogr. Rep.27, 1019–1021 (1982).

Chigrinov, V.

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

Chigrinov, V. G.

V. G. Chigrinov, “Orientation effects in nematic liquid crystals in electric and magnetic fields,” Sov. Phys. Crystallogr.27, 245–264 (1982).

G. A. Beresnev, V. G. Chigrinov, and M. F. Grebenkin, “New method to determine K33/K11 ratio in nematic liquid crystals,” Crystallogr. Rep.27, 1019–1021 (1982).

Dascalu, C.

C. Dascalu, “Asymmetric electrooptic response in a nematic liquid crystal,” Rev. Mex. Fis.47, 281–285 (2001).

Fercher, A.

Goetzinger, E.

Grebenkin, M. F.

G. A. Beresnev, V. G. Chigrinov, and M. F. Grebenkin, “New method to determine K33/K11 ratio in nematic liquid crystals,” Crystallogr. Rep.27, 1019–1021 (1982).

Hitzenberger, Ch.

Ho, J.

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

Kwok, H. S.

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

Mazaeva, V.

A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
[CrossRef]

Murauski, A.

A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
[CrossRef]

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

Muravsky, A.

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
[CrossRef]

Pircher, M.

Sticker, M.

Yeung, F. S. Y.

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

Crystallogr. Rep. (1)

G. A. Beresnev, V. G. Chigrinov, and M. F. Grebenkin, “New method to determine K33/K11 ratio in nematic liquid crystals,” Crystallogr. Rep.27, 1019–1021 (1982).

J. Soc. Inf. Disp. (1)

A. Muravsky, A. Murauski, V. Mazaeva, and V. Belyaev, “Parameters on the LC alignment of organosilicon compound films,” J. Soc. Inf. Disp.13(4), 349–354 (2005).
[CrossRef]

Opt. Express (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Murauski, V. Chigrinov, A. Muravsky, F. S. Y. Yeung, J. Ho, and H. S. Kwok, “Determination of liquid-crystal polar anchoring energy by electrical measurements,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(6), 061707 (2005).
[CrossRef] [PubMed]

Rev. Mex. Fis. (1)

C. Dascalu, “Asymmetric electrooptic response in a nematic liquid crystal,” Rev. Mex. Fis.47, 281–285 (2001).

Sov. Phys. Crystallogr. (1)

V. G. Chigrinov, “Orientation effects in nematic liquid crystals in electric and magnetic fields,” Sov. Phys. Crystallogr.27, 245–264 (1982).

Other (9)

K. Hanaoka, Y. Nakanishi, Y. Inoue, S. Tanuma, and Y. Koike, “A New MVA-LCD by Polymer Sustained Alignment Technology”, in SID’04 Digest, (2004), pp.1200–1203.

P. J. Bos, “Passive Optical Phase Retarders for Liquid Crystal Displays”, in 14th IDRC Proc., (1994), p.118.

X.-D. Mi, M. Xu, D.-K. Yang, and P. J. Bos, “Effects of pretilt angle on electro-optical properties of Pi-cell LCDs”, in SID’99 Digest (1999), pp.24–27.

D. K. Yang and S. T. Wu, “Fundamentals of Liquid Crystal Devices” (Wiley, NY, 2006).

S. Chandrasekhar, Liquid Crystals (Cambridge University Press, 1992).

L. M. Blinov and V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (Springer, 1996). p.149.

X. Nie, “Anchoring energy and pretilt angle effects on liquid crystal response time”, Ph.D. Thesis, University of Central Florida, 2007.

V. V. Belyaev and V. G. Mazaeva, “Green technologies of LC alignment on the base of organosilicon compunds”, in SID’11 Digest (2011), pp.1412–1415.

V. V. Belyaev, A. S. Solomatin, D. N. Chausov, and A. A. Gorbunov, “Measurement of the LC pretilt angle and polar anchoring in cells with homogeneous and inhomogeneous LC director configuration and weak anchoring on organosilicon aligning films”, in SID’12 Digest, (2012), pp.1422–1425.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the LC director distribution in LC cells with homogeneous (H), splay (S), and bend (B) configuration: θ is the deviation from the substrate plane, and δ is the deviation from the normal to the substrate.

Fig. 2
Fig. 2

Dependences of the phase retardation parameter Φ on the pretilt angle value θ 0 for three LC director configurations at different n e and n o =1.5 . For every configuration upper dashed line corresponds to n e =1.6 , middle solid line n e =1.7 , lower dot-dashed line n e =1.8 .

Fig. 3
Fig. 3

Dependences of the phase retardation parameter Φ on the pretilt angle value θ 0 at n o =1.5 : (a) the case of a small pretilt angle ( θ 0 <<1 ) for homogeneous (left) and splay (right) configurations, and (b) the case of a large pretilt angle ( δ 0 <<1 ) for homogeneous (left) and bend (right) configurations. 1-n e =1.6 , 2-n e =1.7 , 3-n e =1.8 .

Fig. 4
Fig. 4

Dependences of the phase retardation parameter Φ on the pretilt angle θ 0 at n o =1.5 for the homogeneous configuration in the case of small deviation of θ 0 from π/4~0.785 . 1-n e =1.6 , 2-n e =1.7 , 3-n e =1.8 .

Tables (1)

Tables Icon

Table 1 Analytical approximations of Φ(θ 0 ) and Φ(δ 0 ) dependences at θ 0 <<1 or δ 0 <<1 .

Equations (11)

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ΔΦ=( n e eff n o )L/λ
θ(z)= θ 0 =const(H)
θ(z)= 0 z/L(S)
θ(z)= π 2 +( π 0 )z/L(B)
δ(z)= 0 z/L(B)
ΔΦ= λ [ 0 L n o n e dz (n o 2 cos 2 θ(z)+ n e 2 sin 2 θ(z)) 1/2 n o L ]
ΔΦ= 2π n o L λ ( n e (n o 2 cos 2 θ 0 + n e 2 sin 2 θ 0 ) 1/2 1 )
θ 0 =arccos { n e 2 n e 2 n o 2 [ 1 ( 1+ ΔΦ ΔΦ max Δn n o ) 2 ] } 1/2
Φ( θ 0 )= 1 n e n o [ 2 n e n o (n e 2 + n o 2 ) 1/2 ( 1+ π 4 n e 2 n o 2 n e 2 + n o 2 ) n o θ 0 2 n e n o (n e 2 + n o 2 ) 1/2 n e 2 n o 2 n e 2 + n o 2 ]
Φ( θ 0 )= 1 x1 [ 2 x (x 2 +1) 1/2 ( 1+ π 4 x 2 1 x 2 +1 )1 θ 0 2 x( x 2 1 ) (x 2 +1) 3/2 ]
Φ( θ 0 )= 1 4 [ (2+π 0 )(1 1 2 α) ]

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