Abstract

On the basis of calculations under the discrete dipole approximation and a proposed extended model of nested ellipsoids for bipolar droplets, the changes in optical properties of a spherical liquid-crystal droplet, caused by a change in director configuration under the influence of an external field, have been considered.

© 1999 Optical Society of America

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References

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  1. P. S. Drzaic, Liquid Crystal Dispersions (World Scientific, Singapore, 1995).
    [CrossRef]
  2. J. M. Zharkova, A. S. Sonin, Liquid-Crystal Composites, (Nauka, Moscow, 1994) (in Russian).
  3. A. V. Kovalchyk, M. V. Kyrik, O. O. Lavrentovich, “Structural transformations in nematic droplets in external electrical field,” Zh. Eksp. Teor. Fiz. 94, 350–364 (1988).
  4. J. H. Erdmann, S. Zumer, J. W. Doane, “Configuration transition in a nematic liquid crystal confined to a small spherical cavity,” Phys. Rev. Lett. 64, 1907–1910 (1990).
    [CrossRef] [PubMed]
  5. R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
    [CrossRef]
  6. J. R. Kelly, W. Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1628–1694 (1993).
    [CrossRef]
  7. V. A. Loiko, V. I. Molochko, “Polymer-dispersed liquid crystal droplets: methods of optical characteristics calculation,” Liq. Cryst. 25, 603–612 (1998).
    [CrossRef]
  8. B.-G. Wu, J. L. West, J. W. Doane, “Angular discrimination of light transmission through polymer-dispersed liquid-crystal films,” J. Appl. Phys. 62, 3925–3931 (1987).
    [CrossRef]
  9. O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
    [CrossRef]
  10. P. S. Drzaic, “Droplet density, droplet size, and wavelength effects in PDLC light scattering,” Mol. Cryst. Liq. Cryst. 261, 383–392 (1995).
    [CrossRef]
  11. J. R. Kelly, P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11–29 (1994).
    [CrossRef]
  12. F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
    [CrossRef]
  13. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A. 11, 1491–1499 (1994).
    [CrossRef]
  14. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys J. 333, 848–872 (1988).
    [CrossRef]
  15. F. Xu, H. S. Kitzerow, P. P. Crooker, “Director configurations of nematic-liquid-crystal droplets—negative dielectric anisotropy and parallel surface anchoring,” Phys. Rev. E 49, 3061–3068 (1994).
    [CrossRef]
  16. J. Ding, Y. Yang, “Birefringence patterns of nematic droplets,” Jpn. J. Appl. Phys. 31, 2837–2845 (1992).
    [CrossRef]

1998

V. A. Loiko, V. I. Molochko, “Polymer-dispersed liquid crystal droplets: methods of optical characteristics calculation,” Liq. Cryst. 25, 603–612 (1998).
[CrossRef]

1995

P. S. Drzaic, “Droplet density, droplet size, and wavelength effects in PDLC light scattering,” Mol. Cryst. Liq. Cryst. 261, 383–392 (1995).
[CrossRef]

F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
[CrossRef]

1994

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A. 11, 1491–1499 (1994).
[CrossRef]

F. Xu, H. S. Kitzerow, P. P. Crooker, “Director configurations of nematic-liquid-crystal droplets—negative dielectric anisotropy and parallel surface anchoring,” Phys. Rev. E 49, 3061–3068 (1994).
[CrossRef]

J. R. Kelly, P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11–29 (1994).
[CrossRef]

1993

J. R. Kelly, W. Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1628–1694 (1993).
[CrossRef]

1992

J. Ding, Y. Yang, “Birefringence patterns of nematic droplets,” Jpn. J. Appl. Phys. 31, 2837–2845 (1992).
[CrossRef]

1991

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

1990

J. H. Erdmann, S. Zumer, J. W. Doane, “Configuration transition in a nematic liquid crystal confined to a small spherical cavity,” Phys. Rev. Lett. 64, 1907–1910 (1990).
[CrossRef] [PubMed]

1988

A. V. Kovalchyk, M. V. Kyrik, O. O. Lavrentovich, “Structural transformations in nematic droplets in external electrical field,” Zh. Eksp. Teor. Fiz. 94, 350–364 (1988).

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys J. 333, 848–872 (1988).
[CrossRef]

1987

B.-G. Wu, J. L. West, J. W. Doane, “Angular discrimination of light transmission through polymer-dispersed liquid-crystal films,” J. Appl. Phys. 62, 3925–3931 (1987).
[CrossRef]

O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
[CrossRef]

Aphonin, O. A.

O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
[CrossRef]

Bloisi, F.

F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
[CrossRef]

Boyko, E. P.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

Crooker, P. P.

F. Xu, H. S. Kitzerow, P. P. Crooker, “Director configurations of nematic-liquid-crystal droplets—negative dielectric anisotropy and parallel surface anchoring,” Phys. Rev. E 49, 3061–3068 (1994).
[CrossRef]

Ding, J.

J. Ding, Y. Yang, “Birefringence patterns of nematic droplets,” Jpn. J. Appl. Phys. 31, 2837–2845 (1992).
[CrossRef]

Doane, J. W.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

J. H. Erdmann, S. Zumer, J. W. Doane, “Configuration transition in a nematic liquid crystal confined to a small spherical cavity,” Phys. Rev. Lett. 64, 1907–1910 (1990).
[CrossRef] [PubMed]

B.-G. Wu, J. L. West, J. W. Doane, “Angular discrimination of light transmission through polymer-dispersed liquid-crystal films,” J. Appl. Phys. 62, 3925–3931 (1987).
[CrossRef]

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A. 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys J. 333, 848–872 (1988).
[CrossRef]

Drzaic, P. S.

P. S. Drzaic, “Droplet density, droplet size, and wavelength effects in PDLC light scattering,” Mol. Cryst. Liq. Cryst. 261, 383–392 (1995).
[CrossRef]

P. S. Drzaic, Liquid Crystal Dispersions (World Scientific, Singapore, 1995).
[CrossRef]

Erdmann, J. H.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

J. H. Erdmann, S. Zumer, J. W. Doane, “Configuration transition in a nematic liquid crystal confined to a small spherical cavity,” Phys. Rev. Lett. 64, 1907–1910 (1990).
[CrossRef] [PubMed]

Flatau, P. J.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A. 11, 1491–1499 (1994).
[CrossRef]

Kelly, J. R.

J. R. Kelly, P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11–29 (1994).
[CrossRef]

J. R. Kelly, W. Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1628–1694 (1993).
[CrossRef]

Kitzerow, H. S.

F. Xu, H. S. Kitzerow, P. P. Crooker, “Director configurations of nematic-liquid-crystal droplets—negative dielectric anisotropy and parallel surface anchoring,” Phys. Rev. E 49, 3061–3068 (1994).
[CrossRef]

Kovalchyk, A. V.

A. V. Kovalchyk, M. V. Kyrik, O. O. Lavrentovich, “Structural transformations in nematic droplets in external electrical field,” Zh. Eksp. Teor. Fiz. 94, 350–364 (1988).

Kyrik, M. V.

A. V. Kovalchyk, M. V. Kyrik, O. O. Lavrentovich, “Structural transformations in nematic droplets in external electrical field,” Zh. Eksp. Teor. Fiz. 94, 350–364 (1988).

Lavrentovich, O. O.

A. V. Kovalchyk, M. V. Kyrik, O. O. Lavrentovich, “Structural transformations in nematic droplets in external electrical field,” Zh. Eksp. Teor. Fiz. 94, 350–364 (1988).

Loiko, V. A.

V. A. Loiko, V. I. Molochko, “Polymer-dispersed liquid crystal droplets: methods of optical characteristics calculation,” Liq. Cryst. 25, 603–612 (1998).
[CrossRef]

Molochko, V. I.

V. A. Loiko, V. I. Molochko, “Polymer-dispersed liquid crystal droplets: methods of optical characteristics calculation,” Liq. Cryst. 25, 603–612 (1998).
[CrossRef]

Ondris-Crawford, R.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

Palffy-Muhoray, P.

J. R. Kelly, P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11–29 (1994).
[CrossRef]

Panina, Yu. V.

O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
[CrossRef]

Pravdin, A. B.

O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
[CrossRef]

Simoni, F.

F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
[CrossRef]

Sonin, A. S.

J. M. Zharkova, A. S. Sonin, Liquid-Crystal Composites, (Nauka, Moscow, 1994) (in Russian).

Terrecuso, P.

F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
[CrossRef]

Vicari, L.

F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
[CrossRef]

Wagner, B. G.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

West, J. L.

B.-G. Wu, J. L. West, J. W. Doane, “Angular discrimination of light transmission through polymer-dispersed liquid-crystal films,” J. Appl. Phys. 62, 3925–3931 (1987).
[CrossRef]

Wu, B.-G.

B.-G. Wu, J. L. West, J. W. Doane, “Angular discrimination of light transmission through polymer-dispersed liquid-crystal films,” J. Appl. Phys. 62, 3925–3931 (1987).
[CrossRef]

Wu, W.

J. R. Kelly, W. Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1628–1694 (1993).
[CrossRef]

Xu, F.

F. Xu, H. S. Kitzerow, P. P. Crooker, “Director configurations of nematic-liquid-crystal droplets—negative dielectric anisotropy and parallel surface anchoring,” Phys. Rev. E 49, 3061–3068 (1994).
[CrossRef]

Yakovlev, D. A.

O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
[CrossRef]

Yang, Y.

J. Ding, Y. Yang, “Birefringence patterns of nematic droplets,” Jpn. J. Appl. Phys. 31, 2837–2845 (1992).
[CrossRef]

Zharkova, J. M.

J. M. Zharkova, A. S. Sonin, Liquid-Crystal Composites, (Nauka, Moscow, 1994) (in Russian).

Zumer, S.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

J. H. Erdmann, S. Zumer, J. W. Doane, “Configuration transition in a nematic liquid crystal confined to a small spherical cavity,” Phys. Rev. Lett. 64, 1907–1910 (1990).
[CrossRef] [PubMed]

Astrophys J.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys J. 333, 848–872 (1988).
[CrossRef]

J. Appl. Phys.

R. Ondris-Crawford, E. P. Boyko, B. G. Wagner, J. H. Erdmann, S. Zumer, J. W. Doane, “Microscope textures of nematic droplets in polymer dispersed liquid crystals,” J. Appl. Phys. 69, 6380–6386 (1991).
[CrossRef]

B.-G. Wu, J. L. West, J. W. Doane, “Angular discrimination of light transmission through polymer-dispersed liquid-crystal films,” J. Appl. Phys. 62, 3925–3931 (1987).
[CrossRef]

J. Opt. Soc. Am. A.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A. 11, 1491–1499 (1994).
[CrossRef]

Jpn. J. Appl. Phys.

J. Ding, Y. Yang, “Birefringence patterns of nematic droplets,” Jpn. J. Appl. Phys. 31, 2837–2845 (1992).
[CrossRef]

Liq. Cryst.

J. R. Kelly, W. Wu, “Multiple scattering effects in polymer dispersed liquid crystals,” Liq. Cryst. 14, 1628–1694 (1993).
[CrossRef]

V. A. Loiko, V. I. Molochko, “Polymer-dispersed liquid crystal droplets: methods of optical characteristics calculation,” Liq. Cryst. 25, 603–612 (1998).
[CrossRef]

O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, D. A. Yakovlev, “Optical properties of stretched polymer dispersed liquid crystal films,” Liq. Cryst. 15, 395–407 (1987).
[CrossRef]

Mol. Cryst. Liq. Cryst.

P. S. Drzaic, “Droplet density, droplet size, and wavelength effects in PDLC light scattering,” Mol. Cryst. Liq. Cryst. 261, 383–392 (1995).
[CrossRef]

J. R. Kelly, P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11–29 (1994).
[CrossRef]

F. Bloisi, P. Terrecuso, L. Vicari, F. Simoni, “Voltage controlled light transmittance in polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 266, 229–239 (1995).
[CrossRef]

Phys. Rev. E

F. Xu, H. S. Kitzerow, P. P. Crooker, “Director configurations of nematic-liquid-crystal droplets—negative dielectric anisotropy and parallel surface anchoring,” Phys. Rev. E 49, 3061–3068 (1994).
[CrossRef]

Phys. Rev. Lett.

J. H. Erdmann, S. Zumer, J. W. Doane, “Configuration transition in a nematic liquid crystal confined to a small spherical cavity,” Phys. Rev. Lett. 64, 1907–1910 (1990).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz.

A. V. Kovalchyk, M. V. Kyrik, O. O. Lavrentovich, “Structural transformations in nematic droplets in external electrical field,” Zh. Eksp. Teor. Fiz. 94, 350–364 (1988).

Other

P. S. Drzaic, Liquid Crystal Dispersions (World Scientific, Singapore, 1995).
[CrossRef]

J. M. Zharkova, A. S. Sonin, Liquid-Crystal Composites, (Nauka, Moscow, 1994) (in Russian).

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Figures (4)

Fig. 1
Fig. 1

Geometry of the model of nested ellipsoids for an LC droplet with a bipolar structure (for notation, see text).

Fig. 2
Fig. 2

Extinction efficiency factor Q of a spherical bipolar droplet versus the LC droplet size for n e = 1.15 and (a) n o = 0.999, u = 0, 0.1, 0.6, 16; (b) n o = 0.99, u = 0, 16. The incident light direction coincides with the droplet director (α = 0). The short-and-long–dashed curves represent the calculation from the Mie formulas. Here and in Figs. 3 and 4, the notation 1E-x indicates 10-x .

Fig. 3
Fig. 3

Angular structure of scattered radiation I = (|S 1|2 + |S 2|2)/2 of a spherical bipolar droplet for n o = 0.999, n e = 1.15; (a) x = 1, (b) x = 4, (c) x = 15 for the parameter values u = 0.0, 0.1, 0.5, 1.0, 2.0, 16.0 under illumination by natural light with the direction coinciding with the droplet director (α = 0).

Fig. 4
Fig. 4

Extinction efficiency factor Q of a spherical bipolar droplet as a function of a LC droplet size x for natural light at n o = 0.999, n e = 1.15 and for the model voltage values u = 0, 16. The incident light direction α = 0°, 10°, 20°, 30°.

Equations (8)

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

EE=expikr-ikrS2S3S4S1EincEinc,
Pj=αˆjEinc+kj AˆjkPk.
αˆj=Mˆj-1αˆMˆj,
Mˆj=RˆxαjRˆyβjRˆzγj,
αj=arctanzj, yj  βj=0, γj=π2-arctanxjyj2+zj2, b1+u2-xj2, ud-bb,  -b/2xjb/2, -a/2yja/2,  -a/2zja/2.
Qsca=4xE02j=1NImk3PjEjinc,
I½|S1|2+|S2|2.
I=dσdΩ k2.

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