Abstract

A formula has been derived for predicting the intensities of the first-order fringes that result from the illumination of a periodically reoriented nematic liquid-crystal layer that is excited electrohydrodynamically in the dielectric mode. The agreement between the predictions of the derived formula and those of the more rigorous theory is excellent. It turns out that the intensities of the first-order fringes are proportional to the square of the maximum angle formed between the director and its orientation direction in the undistorted state. It also turns out that these intensities are highly sensitive functions of the incidence angle of the monochromatic light beam that is illuminating the nematic layer; they exhibit two pronounced maxima that correspond to two different incidence angles that are determined by the material and distortion parameters as well as by the wavelength of the illuminating beam. The derived formula is an essential tool for monitoring the motion of the nematic director during electrohydrodynamic excitation in the dielectric mode.

© 2001 Optical Society of America

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References

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  1. L. Liebert, ed., Liquid Crystals, Suppl. 14 of Solid State Physics, H. Ehrenreich, F. Seitz, D. Tumbull, eds. (Academic, New York, 1978), pp. 147–208.
  2. L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983), pp. 147–208.
  3. G. Vertogen, W. H. de Jeu, Thermotropic Liquid Crystals, Fundamentals (Springer-Verlag, Berlin, 1988), pp. 147–208.
  4. P. G. De Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, New York, 1993), pp. 230–245.
  5. R. A. Rigopoulos, H. M. Zenginoglou, “Electrohydrodynamic instability limits of nematics,” Mol. Cryst. Liq. Cryst. 35, 307–18 (1976).
    [CrossRef]
  6. H. M. Zenginoglou, R. A. Rigopoulos, J. A. Kosmopoulos, “On the electrohydrodynamic instability limits of nematics under the action of sinusoidal electric fields,” Mol. Cryst. Liq. Cryst. 39, 27–32 (1977).
    [CrossRef]
  7. H. M. Zenginoglou, J. A. Kosmopoulos, “On the ability of homogeneously aligned nematic mesophases with a positive dielectric anisotropy to exhibit Williams domains as a threshold effect,” Mol. Cryst. Liq. Cryst. 43, 265–77 (1977).
    [CrossRef]
  8. H. M. Zenginoglou, J. A. Kosmopoulos, “Linearized wave optical approach to the grating effect of a periodically distorted nematic liquid crystal layer,” J. Opt. Soc. Am. A 14, 669–675 (1997).
    [CrossRef]
  9. H. M. Zenginoglou, J. A. Kosmopoulos, “Geometrical optics approach to the obliquely illuminated nematic liquid crystal diffraction grating,” Appl. Opt. 27, 3898–3901 (1988).
    [CrossRef] [PubMed]
  10. P. L. Papadopoulos, H. M. Zenginoglou, J. A. Kosmopoulos, “Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal,” J. Appl. Phys. 86, 3042–3047 (1999).
    [CrossRef]

1999 (1)

P. L. Papadopoulos, H. M. Zenginoglou, J. A. Kosmopoulos, “Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal,” J. Appl. Phys. 86, 3042–3047 (1999).
[CrossRef]

1997 (1)

1988 (1)

1977 (2)

H. M. Zenginoglou, R. A. Rigopoulos, J. A. Kosmopoulos, “On the electrohydrodynamic instability limits of nematics under the action of sinusoidal electric fields,” Mol. Cryst. Liq. Cryst. 39, 27–32 (1977).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “On the ability of homogeneously aligned nematic mesophases with a positive dielectric anisotropy to exhibit Williams domains as a threshold effect,” Mol. Cryst. Liq. Cryst. 43, 265–77 (1977).
[CrossRef]

1976 (1)

R. A. Rigopoulos, H. M. Zenginoglou, “Electrohydrodynamic instability limits of nematics,” Mol. Cryst. Liq. Cryst. 35, 307–18 (1976).
[CrossRef]

Blinov, L. M.

L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983), pp. 147–208.

De Gennes, P. G.

P. G. De Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, New York, 1993), pp. 230–245.

de Jeu, W. H.

G. Vertogen, W. H. de Jeu, Thermotropic Liquid Crystals, Fundamentals (Springer-Verlag, Berlin, 1988), pp. 147–208.

Kosmopoulos, J. A.

P. L. Papadopoulos, H. M. Zenginoglou, J. A. Kosmopoulos, “Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal,” J. Appl. Phys. 86, 3042–3047 (1999).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “Linearized wave optical approach to the grating effect of a periodically distorted nematic liquid crystal layer,” J. Opt. Soc. Am. A 14, 669–675 (1997).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “Geometrical optics approach to the obliquely illuminated nematic liquid crystal diffraction grating,” Appl. Opt. 27, 3898–3901 (1988).
[CrossRef] [PubMed]

H. M. Zenginoglou, R. A. Rigopoulos, J. A. Kosmopoulos, “On the electrohydrodynamic instability limits of nematics under the action of sinusoidal electric fields,” Mol. Cryst. Liq. Cryst. 39, 27–32 (1977).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “On the ability of homogeneously aligned nematic mesophases with a positive dielectric anisotropy to exhibit Williams domains as a threshold effect,” Mol. Cryst. Liq. Cryst. 43, 265–77 (1977).
[CrossRef]

Papadopoulos, P. L.

P. L. Papadopoulos, H. M. Zenginoglou, J. A. Kosmopoulos, “Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal,” J. Appl. Phys. 86, 3042–3047 (1999).
[CrossRef]

Prost, J.

P. G. De Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, New York, 1993), pp. 230–245.

Rigopoulos, R. A.

H. M. Zenginoglou, R. A. Rigopoulos, J. A. Kosmopoulos, “On the electrohydrodynamic instability limits of nematics under the action of sinusoidal electric fields,” Mol. Cryst. Liq. Cryst. 39, 27–32 (1977).
[CrossRef]

R. A. Rigopoulos, H. M. Zenginoglou, “Electrohydrodynamic instability limits of nematics,” Mol. Cryst. Liq. Cryst. 35, 307–18 (1976).
[CrossRef]

Vertogen, G.

G. Vertogen, W. H. de Jeu, Thermotropic Liquid Crystals, Fundamentals (Springer-Verlag, Berlin, 1988), pp. 147–208.

Zenginoglou, H. M.

P. L. Papadopoulos, H. M. Zenginoglou, J. A. Kosmopoulos, “Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal,” J. Appl. Phys. 86, 3042–3047 (1999).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “Linearized wave optical approach to the grating effect of a periodically distorted nematic liquid crystal layer,” J. Opt. Soc. Am. A 14, 669–675 (1997).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “Geometrical optics approach to the obliquely illuminated nematic liquid crystal diffraction grating,” Appl. Opt. 27, 3898–3901 (1988).
[CrossRef] [PubMed]

H. M. Zenginoglou, R. A. Rigopoulos, J. A. Kosmopoulos, “On the electrohydrodynamic instability limits of nematics under the action of sinusoidal electric fields,” Mol. Cryst. Liq. Cryst. 39, 27–32 (1977).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “On the ability of homogeneously aligned nematic mesophases with a positive dielectric anisotropy to exhibit Williams domains as a threshold effect,” Mol. Cryst. Liq. Cryst. 43, 265–77 (1977).
[CrossRef]

R. A. Rigopoulos, H. M. Zenginoglou, “Electrohydrodynamic instability limits of nematics,” Mol. Cryst. Liq. Cryst. 35, 307–18 (1976).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

P. L. Papadopoulos, H. M. Zenginoglou, J. A. Kosmopoulos, “Optical measurement of the director relaxation time in a periodically reoriented nematic liquid crystal,” J. Appl. Phys. 86, 3042–3047 (1999).
[CrossRef]

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

Mol. Cryst. Liq. Cryst. (3)

R. A. Rigopoulos, H. M. Zenginoglou, “Electrohydrodynamic instability limits of nematics,” Mol. Cryst. Liq. Cryst. 35, 307–18 (1976).
[CrossRef]

H. M. Zenginoglou, R. A. Rigopoulos, J. A. Kosmopoulos, “On the electrohydrodynamic instability limits of nematics under the action of sinusoidal electric fields,” Mol. Cryst. Liq. Cryst. 39, 27–32 (1977).
[CrossRef]

H. M. Zenginoglou, J. A. Kosmopoulos, “On the ability of homogeneously aligned nematic mesophases with a positive dielectric anisotropy to exhibit Williams domains as a threshold effect,” Mol. Cryst. Liq. Cryst. 43, 265–77 (1977).
[CrossRef]

Other (4)

L. Liebert, ed., Liquid Crystals, Suppl. 14 of Solid State Physics, H. Ehrenreich, F. Seitz, D. Tumbull, eds. (Academic, New York, 1978), pp. 147–208.

L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983), pp. 147–208.

G. Vertogen, W. H. de Jeu, Thermotropic Liquid Crystals, Fundamentals (Springer-Verlag, Berlin, 1988), pp. 147–208.

P. G. De Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, New York, 1993), pp. 230–245.

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Figures (3)

Fig. 1
Fig. 1

Layout of the system. The small line segments represent the local director orientation. The x axis defines the direction of the original alignment of the NLC layer, the distortion of which is parallel to the xz plane. Here, period Λ of the distortion is considered much smaller than the thickness L of the layer, θi is the incidence angle of the polarized light beam whose electric field is parallel to the xz plane, and ϑm is the distortion amplitude.

Fig. 2
Fig. 2

Dependence of the first-order fringe intensity on the distortion amplitude of the NLC layer as computed by expression (16) (solid curve) and by the rigorous theory (circles). The layer is assumed illuminated at an incidence angle of 13.5°.

Fig. 3
Fig. 3

Dependence of the first-order fringe intensity on the incidence angle of the illuminating beam as computed by expression (16) (solid curve) and by the rigorous theory (circles). The distortion amplitude was taken equal to 6°.

Equations (27)

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fn=12π02πexp[H1exp(-jx)+H2exp(+jx)-jnx]dx,
Fn=gnJn2(Qϑmsin θiL/λ),
Hl12 βϑmAl[1+exp(jnfPπ)×(cos σl-jClsin σl)],l=1,2,
β(ne/no)2-1,nfne(1-sin2 θi/no2)1/2,
P2L/λ.
S2L/Λ,RΛ/λ=P/S,
μR sin θi,g(Sne/no)2(1+2μ)
A1=P (1+g)sin θi-2nf2PS(1+2μ)(2nfP)2-(1+g)2,
σ1nfPπ(1-g/nf2P2)1/2,
C1nfPπσ1 (1+B1/A1),
B1S 1+g(1+2μ)(2nfP)2-(1+g)2.
C11+181+2μ(no2-sin2 θi)21R4+O(1/R6).
H1βϑmA1cosnfPπ-σ12exp(jψ1),
ξ1ne2no21+2μ2nfSR
A11+2μ21-γ1/R2ξ12-1,
γ1μ2(no2-sin2 θi).
nfPπ-σ1nfPπ(1-1-δ1/R2),
δ1neno21+2μnf2.
nfPπ-σ12ξ1π2.
H1αRnfϑm1-γ1R2ξ1cos(ξ1π/2)ξ12-1exp(jψ1),
α1-(no/ne)2.
G(ξ)ξ cos(ξπ/2)/(ξ2-1)
ξm=1.36724 .
G(±ξm)=±0.857754,
fn12π02πexp(-jnx)[H1exp(-jx)+H2exp(+jx)]dx,
F-1αRnf1-γ1R2ξ1cos(ξ1π/2)ξ12-12ϑm2
sin θi=12R±ξmnfSno2ne2,

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