Abstract

Modern thin-film-transistor-driven twisted nematic (TN) products on the market require thin cell gaps below the value to satisfy the condition of the Gooch–Tarry first minimum in transmission for fast response times and wide viewing angles. For the first time to our knowledge, we have developed a simple experimental method based on a new configuration of out-of-plane cell rotation and analyzed our data by extended Jones matrix method to obtain accurate pretilt angles for such thin TN cells where the well-accepted configuration of the out-of-plane cell rotation method analyzed by Birecki and Kahn [The Physics and Chemistry of Liquid Crystal Devices (1980), p. 115] was insufficient to address.

© 2013 Optical Society of America

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References

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  1. A. Lien and R. J. John, “Lateral field effect in twisted nematic cells,” IBM J. Res. Dev. 36, 51–58 (1992).
    [CrossRef]
  2. T. J. Scheffer and J. Nehring, “Accurate determination of liquid crystal tilt bias angles,” J. Appl. Phys. 48, 1783–1792 (1977).
    [CrossRef]
  3. M.-H. Liu, W.-C. Kuo, H.-C. Wei, C.-C. Tsai, C.-J. Yu, B.-J. Liang, and C. Chou, “Cell parameter measurement of a twisted nematic liquid crystal device using interferometric polarimeter under normal incidence,” Opt. Express 18, 8759–8766 (2010).
    [CrossRef]
  4. C.-C. Tsai, C. Chou, C.-Y. Han, C.-H. Hsieh, K.-Y. Liao, and Y.-F. Chao, “Determination of optical parameters of a twisted-nematic liquid crystal by phase-sensitive optical heterodyne interferometric ellipsometry,” Appl. Opt. 44, 7509–7514 (2005).
    [CrossRef]
  5. T.-C. Yu and Y.-L. Lo, “A novel heterodyne polarimeter for the multiple-parameter measurements of twisted nematic liquid crystal cell using a genetic algorithm approach,” J. Lightwave Technol. 25, 946–951 (2007).
    [CrossRef]
  6. M. Kawamura, Y. Goto, and S. Sato, “A Two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43, 709–714 (2004).
    [CrossRef]
  7. T. Nishioka and T. Kurata, “Novel pretilt angle measurement method for twisted-nematic liquid-crystal cells by apparent retardation measurement,” Jpn. J. Appl. Phys. 40, 6017–6023 (2001).
    [CrossRef]
  8. H. Birecki and F.-J. Kahn, “Accurate optical measurement of small tilt angles in thin twisted nematic layers,” in The Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, ed. (Plenum, NY, 1980), p. 115–123.
  9. C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90  degrees,” J. Phys. D 8, 1575–1584(1975).
    [CrossRef]
  10. A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
    [CrossRef]
  11. A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767 (1990).
    [CrossRef]
  12. P. Yeh, “Extended Jones matrix method,” J. Opt. Soc. Am. 72, 507–513 (1982).
    [CrossRef]

2010

2007

2005

2004

M. Kawamura, Y. Goto, and S. Sato, “A Two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43, 709–714 (2004).
[CrossRef]

2001

T. Nishioka and T. Kurata, “Novel pretilt angle measurement method for twisted-nematic liquid-crystal cells by apparent retardation measurement,” Jpn. J. Appl. Phys. 40, 6017–6023 (2001).
[CrossRef]

1997

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[CrossRef]

1992

A. Lien and R. J. John, “Lateral field effect in twisted nematic cells,” IBM J. Res. Dev. 36, 51–58 (1992).
[CrossRef]

1990

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767 (1990).
[CrossRef]

1982

1977

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

1975

C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90  degrees,” J. Phys. D 8, 1575–1584(1975).
[CrossRef]

Birecki, H.

H. Birecki and F.-J. Kahn, “Accurate optical measurement of small tilt angles in thin twisted nematic layers,” in The Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, ed. (Plenum, NY, 1980), p. 115–123.

Chao, Y.-F.

Chou, C.

Gooch, C. H.

C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90  degrees,” J. Phys. D 8, 1575–1584(1975).
[CrossRef]

Goto, Y.

M. Kawamura, Y. Goto, and S. Sato, “A Two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43, 709–714 (2004).
[CrossRef]

Han, C.-Y.

Hsieh, C.-H.

John, R. J.

A. Lien and R. J. John, “Lateral field effect in twisted nematic cells,” IBM J. Res. Dev. 36, 51–58 (1992).
[CrossRef]

Kahn, F.-J.

H. Birecki and F.-J. Kahn, “Accurate optical measurement of small tilt angles in thin twisted nematic layers,” in The Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, ed. (Plenum, NY, 1980), p. 115–123.

Kawamura, M.

M. Kawamura, Y. Goto, and S. Sato, “A Two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43, 709–714 (2004).
[CrossRef]

Kuo, W.-C.

Kurata, T.

T. Nishioka and T. Kurata, “Novel pretilt angle measurement method for twisted-nematic liquid-crystal cells by apparent retardation measurement,” Jpn. J. Appl. Phys. 40, 6017–6023 (2001).
[CrossRef]

Liang, B.-J.

Liao, K.-Y.

Lien, A.

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[CrossRef]

A. Lien and R. J. John, “Lateral field effect in twisted nematic cells,” IBM J. Res. Dev. 36, 51–58 (1992).
[CrossRef]

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767 (1990).
[CrossRef]

Liu, M.-H.

Lo, Y.-L.

Nehring, J.

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

Nishioka, T.

T. Nishioka and T. Kurata, “Novel pretilt angle measurement method for twisted-nematic liquid-crystal cells by apparent retardation measurement,” Jpn. J. Appl. Phys. 40, 6017–6023 (2001).
[CrossRef]

Sato, S.

M. Kawamura, Y. Goto, and S. Sato, “A Two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43, 709–714 (2004).
[CrossRef]

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]

Tarry, H. A.

C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90  degrees,” J. Phys. D 8, 1575–1584(1975).
[CrossRef]

Tsai, C.-C.

Wei, H.-C.

Yeh, P.

Yu, C.-J.

Yu, T.-C.

Appl. Opt.

Appl. Phys. Lett.

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767 (1990).
[CrossRef]

IBM J. Res. Dev.

A. Lien and R. J. John, “Lateral field effect in twisted nematic cells,” IBM J. Res. Dev. 36, 51–58 (1992).
[CrossRef]

J. Appl. Phys.

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

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Phys. D

C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90  degrees,” J. Phys. D 8, 1575–1584(1975).
[CrossRef]

Jpn. J. Appl. Phys.

M. Kawamura, Y. Goto, and S. Sato, “A Two-dimensional pretilt angle distribution measurement of twisted nematic liquid crystal cells using Stokes parameters at plural wavelengths,” Jpn. J. Appl. Phys. 43, 709–714 (2004).
[CrossRef]

T. Nishioka and T. Kurata, “Novel pretilt angle measurement method for twisted-nematic liquid-crystal cells by apparent retardation measurement,” Jpn. J. Appl. Phys. 40, 6017–6023 (2001).
[CrossRef]

Liq. Cryst.

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[CrossRef]

Opt. Express

Other

H. Birecki and F.-J. Kahn, “Accurate optical measurement of small tilt angles in thin twisted nematic layers,” in The Physics and Chemistry of Liquid Crystal Devices, G. J. Sprokel, ed. (Plenum, NY, 1980), p. 115–123.

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Figures (8)

Fig. 1.
Fig. 1.

Coordinate scheme of the TN cell and incident light.

Fig. 2.
Fig. 2.

Configuration of out-of-plane cell rotation for the measurements of TN Tr-IA curves.

Fig. 3.
Fig. 3.

Transmission versus incident angle (Tr-IA) with pretilt angle as a parameter.

Fig. 4.
Fig. 4.

(a) Transmission extremum versus pretilt angle when the cell gap is set at 3.3 μm. (b) Transmission extremum versus cell gap with pretilt angle as a parameter when the wavelength and the twist angle are set at 590 nm and 90°, respectively.

Fig. 5.
Fig. 5.

Transmission extremum versus wavelength with pretilt angle as a parameter when the cell gap and the twist angle are set at 3.3 μm and 90°, respectively.

Fig. 6.
Fig. 6.

Transmission extremum versus twist angle with pretilt angle as a parameter when the cell gap and the wavelength are set at 3.3 μm and 590 nm, respectively.

Fig. 7.
Fig. 7.

Experimental transmission versus incident angle (Tr-IA) curves (a) for sample A with fitting calculated by extended Jones matrix method and (b) for sample C.

Fig. 8.
Fig. 8.

Experimental transmission versus incident angle (Tr-IA) curve measured by using Birecki–Kahn’s experimental method.

Tables (3)

Tables Icon

Table 1. LC Parameters Used in Calculation

Tables Icon

Table 2. Experimental Results: TN Cells Measured by Our and Birecki’s Methods

Tables Icon

Table 3. Experimental Results: Homogeneous Cells Measured by Scheffer and Nehring’s Method

Equations (16)

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

ε=[εxxεxyεxzεyxεyyεyzεzxεzyεzz],
εxx=no2+(ne2no2)cos2θcos2φεxy=εyx=(ne2no2)cos2θsinφcosφεxz=εzx=(ne2no2)sinθcosθcosφεyy=no2+(ne2no2)cos2θsin2φεyz=εzy=(ne2no2)sinθcosθsinφεzz=no2+(ne2no2)sin2θ,
k⃗=k0(sinθk,0,cosθk),
k0=2πλ,
[ExEy]out=JmJm1J2J1[ExEy]in,
Jm=(SGS1)m,
S=[1c2c11];G=[eikz1dm00eikz2dm],
kz1k0=[no2(kx/k0)2],
kz2k0=εxzεzzkxk0+noneεzz[εzz(1ne2no2ne2cos2θsin2φ)(kxko)2]1/2,
c1=[(kx/k0)2εzz]εyx+[(kx/k0)(kz1/k0)+εzx]εyz[(kz1/k0)2+(kx/k0)2εyy][(kx/k0)2εzz]εyzεzy,
c2=[(kx/k0)2εzz]εxy+[(kx/k0)(kz2/k0)+εxz]εzy[(kz2/k0)2εxx][(kx/k0)2εzz][(kx/k0)(kz2/k0)+εzx][(kx/k0)(kz2/k0)+εxz].
[ExEy]out=[1/21/21/21/2]analyzerJglass_exJITO_exJmJm1J2J1JITO_enJglass_en[1/21/2]in,
Jglass_en=[2cosθkcosθg+ngcosθk002cosθkcosθk+ngcosθg];Jglass_ex=[2ngcosθkcosθg+ngcosθk002ngcosθgcosθk+ngcosθg],
JITO_en=[2ngcosθgngcosθITO+nITOcosθg002ngcosθgngcosθg+nITOcosθITO];JITO_ex=[2nITOcosθITOnITOcosθg+ngcosθITO002nITOcosθITOnITOcosθITO+ngcosθg],
θg=sin1(sinθkng);θITO=sin1(ngsinθgnITO),
sinθp=π2nenone+no+14nesin(π/4)sinθextremum.

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