Abstract

The dielectric anisotropy of a highly dispersive dual-frequency nematic liquid crystal (MDA-00-3969 (Merck KGa)) has been determined using the optical fully-leaky guided-mode technique. A 4Vrms sinusoidal voltage was applied across a 5µm hybrid aligned nematic (HAN) cell at various frequencies in both the positive and negative dielectric anisotropy regime. Optical data was collected at each frequency enabling the director profile in each case to be determined using a multi-layer optics model in combination with a liquid crystal free-energy minimization routine. The thresholdless response of the HAN cell combined with the extreme sensitivity of the optical characterization technique has allowed subtle changes in dielectric permittivity with frequency to be observed. The resulting measured dispersion shows excellent agreement with a single Debye-type relaxation model.

© 2005 Optical Society of America

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References

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  1. G.P. Bryan-Brown, C.V. Brown, I.C. Sage, V.C. Hui, �??Voltage-dependent anchoring of a nematic liquid crystal on a grating surface�??�?? Nature 392, (6674) 365 (1998)
    [CrossRef]
  2. S. Kitson and A. Geisow, �??Controllable alignment of nematic liquid crystals around microscopic posts: Stabilization of multiple states�?? Appl. Phys. Lett. 80, (19) (2002)
    [CrossRef]
  3. E.P. Raynes and I. Shanks, �??Fast switching twisted nematic electro-optical shutter and colour filter,�?? Electron. Lett. 10, 114 (1974)
    [CrossRef]
  4. M. Schadt, �??Liquid crystal materials and liquid crystal displays,�?? Annu. Rev. Mater. Sci. 27, 305 (1997)
    [CrossRef]
  5. S.A. Jewell and J.R. Sambles, �??Fully leaky guided mode study of the flexoelectric effect and surface polarization in hybrid aligned nematic cells,�?? J. Appl. Phys. 92, (1) 19 (2002)
    [CrossRef]
  6. Y.Q. Lu, X. Liang, Y.H. Wu et. al, �??Dual-frequency addressed hybrid-aligned nematic liquid crystal,�?? Appl. Phys. Lett. 85, (16) 3354 (2004)
    [CrossRef]
  7. S.A. Jewell and J.R. Sambles, �??Observation of backflow in the switch-on dynamics of a hybrid aligned nematic,�?? Appl. Phys. Lett. 84, (1) 46 (2004).
    [CrossRef]
  8. P.G. De Gennes, �??The Physics Of Liquid Crystals,�?? Clarendon, Oxford (1974)
  9. S.A. Jewell and J.R. Sambles, �??Fully-leaky guided-mode measurement of the flexoelectric constant (e11+e33) of a nematic liquid crystal,�?? Mol. Cryst. Liq. Cryst. 401, 181
  10. F. Yang, L. Ruan and J.R. Sambles, �??Homeotropic polar anchoring energy of a nematic liquid crystal using the fully leaky waveguide technique,�?? J Appl Phys 88, (11) 6175 (2000)
    [CrossRef]
  11. F. Yang, J.R. Sambles, Y.M. Dong and H. Gao, �??Fully leaky guided wave determination of the polar anchoring energy of a homogeneously aligned nematic liquid crystal,�?? J Appl Phys 87, 2726 (2000)
    [CrossRef]
  12. D.Y.K. Ko and J.R. Sambles, �??Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals,�?? J. Opt. Soc. Am. A. 5, 1863 (1988)
    [CrossRef]
  13. M. Schadt,�?? Kerr effect and orientation relaxation of pretransitional domains and individual molecules in positive dielectric liquid crystals,�?? J. Chem. Phys. 67, 210 (1977)
    [CrossRef]

Annu. Rev. Mater. Sci. (1)

M. Schadt, �??Liquid crystal materials and liquid crystal displays,�?? Annu. Rev. Mater. Sci. 27, 305 (1997)
[CrossRef]

Appl. Phys. Lett. (3)

S. Kitson and A. Geisow, �??Controllable alignment of nematic liquid crystals around microscopic posts: Stabilization of multiple states�?? Appl. Phys. Lett. 80, (19) (2002)
[CrossRef]

Y.Q. Lu, X. Liang, Y.H. Wu et. al, �??Dual-frequency addressed hybrid-aligned nematic liquid crystal,�?? Appl. Phys. Lett. 85, (16) 3354 (2004)
[CrossRef]

S.A. Jewell and J.R. Sambles, �??Observation of backflow in the switch-on dynamics of a hybrid aligned nematic,�?? Appl. Phys. Lett. 84, (1) 46 (2004).
[CrossRef]

Electron. Lett. (1)

E.P. Raynes and I. Shanks, �??Fast switching twisted nematic electro-optical shutter and colour filter,�?? Electron. Lett. 10, 114 (1974)
[CrossRef]

J Appl Phys (2)

F. Yang, L. Ruan and J.R. Sambles, �??Homeotropic polar anchoring energy of a nematic liquid crystal using the fully leaky waveguide technique,�?? J Appl Phys 88, (11) 6175 (2000)
[CrossRef]

F. Yang, J.R. Sambles, Y.M. Dong and H. Gao, �??Fully leaky guided wave determination of the polar anchoring energy of a homogeneously aligned nematic liquid crystal,�?? J Appl Phys 87, 2726 (2000)
[CrossRef]

J. Appl. Phys. (1)

S.A. Jewell and J.R. Sambles, �??Fully leaky guided mode study of the flexoelectric effect and surface polarization in hybrid aligned nematic cells,�?? J. Appl. Phys. 92, (1) 19 (2002)
[CrossRef]

J. Chem. Phys. (1)

M. Schadt,�?? Kerr effect and orientation relaxation of pretransitional domains and individual molecules in positive dielectric liquid crystals,�?? J. Chem. Phys. 67, 210 (1977)
[CrossRef]

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

D.Y.K. Ko and J.R. Sambles, �??Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals,�?? J. Opt. Soc. Am. A. 5, 1863 (1988)
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

S.A. Jewell and J.R. Sambles, �??Fully-leaky guided-mode measurement of the flexoelectric constant (e11+e33) of a nematic liquid crystal,�?? Mol. Cryst. Liq. Cryst. 401, 181

Nature (1)

G.P. Bryan-Brown, C.V. Brown, I.C. Sage, V.C. Hui, �??Voltage-dependent anchoring of a nematic liquid crystal on a grating surface�??�?? Nature 392, (6674) 365 (1998)
[CrossRef]

Other (1)

P.G. De Gennes, �??The Physics Of Liquid Crystals,�?? Clarendon, Oxford (1974)

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the layout of the apparatus used in the fully-leaky guided-mode optical characterization technique.

Fig. 2.
Fig. 2.

Some of the optical fully-leaky guided mode data collected at the frequencies indicated (symbols) and the theoretical data generated using a multi-layer optics model and least-squares fitting procedure (lines) for p- to s-polarization converting transmitted light.

Fig. 3.
Fig. 3.

Measured director profiles at a selection of applied frequencies (shown in kHz) for the variation in the tilt angle of the director (measured from the normal to the substrate) with distance through the cell.

Fig. 4.
Fig. 4.

The variation of the measured dielectric anisotropies (symbols) with frequency determined by fitting to the optical data and the fit to a single Debye-type relaxation (line).

Equations (7)

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G = 0 d [ 1 2 ( K 11 ( n ( · n ) ) 2 + K 22 ( n · ( × n ) ) 2 + K 33 ( n × × n ) 2 ) + 1 2 D · E ] dz
D z = ε 0 ( Δ ε ( f ) sin 2 θ + ε ) E z ( z )
G = 1 2 0 d [ ( K 11 sin 2 θ + K 33 cos 2 θ ) ( d θ dz ) 2 + D z 2 ε 0 ( ε ( f ) cos 2 θ + ε sin 2 θ ) ] dz
ε ( f ) = ε ( ) + ε ( 0 ) ε ( ) 1 + f 2 τ o 2
Δ ε ( f ) = Δ ε ( ) + Δ ε ( 0 ) Δ ε ( ) 1 + f 2 τ o 2
f co = 1 τ o ( Δ ε ( 0 ) Δ ε ( ) ) 1 2
ε ( f ) = ε ( 0 ) ε ( ) f τ o ( 1 + f 2 τ o 2 )

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