Abstract

We study how the propagation of light inside recently developed micro-structured cells, can be actively tuned by polarising the nanoscale defects in the nematic liquid crystals they contain. Our ‘planar-spherical’ cells are formed by assembling a planar and a gold-coated hemispherical micro-mirror. Optical reflection images of the back-reflected polarised light show a remarkable change of symmetry as a function of the voltage applied to the cell. Theoretical models of the alignment of the liquid crystal within the cell indicate that the constraints imposed on the liquid crystal by the cell geometry and by the applied electric field induces the formation of defects. Their motion under the effect of the applied electric field is responsible for the change of symmetry of the back-reflected light. Furthermore, experimental measurements of the relaxation time of the back-reflected intensity indicate that the motion of the defect in our micro-structured cells is much faster than in equivalent planar cells.

© 2005 Optical Society of America

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References

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    [CrossRef]

Appl. Phys. Lett.

T. Yamaguchi, Y. Kawata, and Y. Mori, �??Boundary condition effects on field-induced deformation modes in polymer dispersed liquid crystals,�?? Appl. Phys. Lett. 72, 1170�??2 (1998).
[CrossRef]

C. Schuller, F. Klopf, J. P. Reithmaier, M. Kamp, and A. Forchel, �??Tunable photonic crystals fabricated in III-V semiconductor slab waveguides using infiltrated liquid crystals,�?? Appl. Phys. Lett. 82, 2767�??9 (2003).
[CrossRef]

G. Mertens, T. Rošder, R. Schweins, K. Huber, and H. Kitzerow, �??Shift of the photonic band gap in two photonic crystal liquid crystal composites,�?? Appl. Phys. Lett. 80, 1885�??1887 (2002).
[CrossRef]

S. Coyle, G. V. Prakash, J. J. Baumberg, M. Abdelsalem, and P. N. Bartlett, �??Spherical micromirrors from templated self-assembly: Polarization rotation on the micron scale,�?? Appl. Phys. Lett. 83, 767�??769 (2003).
[CrossRef]

Eur. Phys. J. E

R. Barberi, F. Ciuchi, G. E. Durand, M. Iovane, D. Sikharulidze, A. M. Sonnet, and E. G. Virga, �??Electric field induced order reconstructionin a nematic cell,�?? Eur. Phys. J. E 13, 61�??71 (2004).
[CrossRef] [PubMed]

J. Mat. Sci.

M. Abbate, P. Mormile, E. Martuscelli, P. Musto, L. Petti, G. Ragosta, and P. Villano, �??PDLC based on unsaturated polyester resins: molecular, morphological and thermo-optical analysis,�?? J. Mat. Sci. 35, 999�??1008 (2000).
[CrossRef]

J. Phys. D: Appl. Phys.

V. Yu Reshetnyak, T. J. Sluckin, and S. J. Cox, �??Effective medium theory of polymer dispersed liquid crystal droplet systems: II. Partially oriented bipolar droplets,�?? J. Phys. D: Appl. Phys. 30, 3253�??3266 (1997).
[CrossRef]

Jap. J. Appl. Phys. 1

W. Y. Li and S. H. Chen, �??Simulation of normal anchoring nematic droplets under electrical fields,�?? Jap. J. Appl. Phys. 1 38, 1482�??1487 (1999).
[CrossRef]

Langmuir

T. Pfohl, J. H. Kim, M. Yasa, H. P. Miller, G. C. L. Wong, F. Bringezu, Z. Wen, L. Wilson, M. W. Kim, Y. Li, and C. R. Safinya, �??Controlled Modification of Microstructured Silicon Surfaces for Confinement of Biological Macromolecules and Liquid Crystals,�?? Langmuir 17, 5343�??5351 (2001).
[CrossRef]

Liq. Crys.

O. Lavrentovich, �??Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops,�?? Liq. Crys. 24, 117�??125 (1998).
[CrossRef]

Mol. Crys. Liq. Crys.

C. Rosenblatt, �??Nanostructured surfaces: Scientific and optical device applications,�?? Mol. Crys. Liq. Crys. 412, 1727�??1744 (2004).
[CrossRef]

Nature

M. Ibn-Elhaj and M. Schadt, �??Optical polymer thin films with isotropic and anisotropic nano-corrugated surface topologies,�?? Nature 410, 796�??799 (2001).
[CrossRef] [PubMed]

R. Penterman, S. I. Klink, H. de Koning, G. Nisato, and D. J. Broer, �??Single-substrate liquid-crystal displays by photo-enforced stratification,�?? Nature 417, 55�??58 (2002).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. E

A. Sonnet, A. Kilian, and S. Hess, �??Alignement tensor versus director: Description of defects in nematic liquid crystals,�?? Phys. Rev. E 52, 718�??722 (1995).
[CrossRef]

P. Mach, P. Wiltzius, M. Megens, D. A. Weitz, K. H. Lin, T. C. Lubensky, and A. G. Yodh1, �??Electro-optic response and switchable Bragg diffraction for liquid crystals in colloid-templated materials,�?? Phys. Rev. E 65, 031720(3) (2002).
[CrossRef]

Phys. Rev. Lett.

D. W. Berreman, �??Solid Surface Shape and the Alignment of an Adjacent Nematic Liquid Crystal,�?? Phys. Rev. Lett. 28, 1683�??1686 (1972).
[CrossRef]

A. Fernández-Nieves, D. R. Link, D. Rudhardt, and D. A.Weitz, �??Electro-Optics of Bipolar Nematic Liquid Crystal Droplets,�?? Phys. Rev. Lett. 92, 105503(4) (2004).
[CrossRef]

S. C. Sharma, L. Zhang, A. J. Tapiawala, and P. C. Jain, �??Evidence for droplet riorientation and interfacial charges in a plymer-dispersed liquid-crystal cell,�?? Phys. Rev. Lett. 87, 105501(4) (2001).
[CrossRef]

J. H. Erdmann, S. Žumer, and 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]

T. G. Sokolovska, R. O. Sokolovskii, and G. N. Patey, �??Surface-induced ordering of nematics in an external field: The stong influence of tilted walls,�?? Phys. Rev. Lett. 92, 185508(4) (2004).
[CrossRef]

Other

C. Greenough, �??The finite element library (felib),�?? (2001). URL <a href= "http://www.cse.clrc.ac.uk/msw/felib/felib-top.shtml">http://www.cse.clrc.ac.uk/msw/felib/felib-top.shtml</a>.

Liquicoat PA ZLI-3334 0.2% solution in ethanol (Merck).

G. P. Crawford and S. Žumer, eds., Liquid Crystals in Complex Geometries (Taylor & Francis, London, 1996).

P. G. de Gennes and J. Prost, The physics of liquid crystals, 2nd ed. (Clarendon Press, Oxford, 1993).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic liquid crystal alignment in (a) flat hybrid cell, (b,c) in spherical droplet at low/high electric field. (d) Microcavity cell geometry with contacts. (d–f) Liquid crystal cell geometries evolving between (a) and (b), with molecular alignment at 0V predicted by model (2). The shading indicates the magnitude of the scalar order parameter (darker shading corresponds to lower values).

Fig. 2.
Fig. 2.

(a–d) SEM images for 2.5µ radius of curvature Au surfaces grown to a thickness of 0.8,1.5,2.5,4.5 µm (giving apertures D=3.2,4.2,5,0.8 µm). (e,f) Cross-polarized optical reflection images of Au microdishes with D=4.2,5µm. (h) Multiple bounce ray trajectories and (g) the two-bounce ring, with (i) its predicted cross-polarized reflectivity. The arrows indicate the direction of the polarizer (P) and of the analyzer (A).

Fig. 3.
Fig. 3.

Cross-sections showing simulated molecular director (orientation and order parameter S=1.7 (white) to 0.6 (dark)) inside the microcavity for 0V (a,b) and 10V (c,d). (a,c) Plan views just below the rim, (b,d) side-view through microcavity center in xz and yz planes. The void diameter a is 5µm.

Fig. 4.
Fig. 4.

Cross-polarized optical images of LC filled microdishes at 0V (a,c) and 5V (b,d) for (a,b) 1.5µmm thick and (c,d) 2.5µm thick Au films. The arrow shows the rubbing direction (alignment on upper ITO). (e,f) Cross-polarized reflected intensity as a function of azimuthal angle ϕ around the reflected ring, extracted from (e) experiment and (f) theory.

Fig. 5.
Fig. 5.

(a)Applied-field dependent intensity of two-bounce cross-polarized reflectivity at ϕ=0°,45°,90°, compared to the flat hybrid cell. The two traces for ϕ=45°,90° represent the intensity measured clockwise and counter-clockwise with respect to the rubbing direction. (b) Rise and fall times of the light intensity at 90° in a planar-spherical microcavity and in a flat hybrid cell under square wave modulation. The insert shows the dynamical response of the two types of cavities when an applied 3V potential is switched off.

Equations (2)

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Q ij = 3 2 S ( n i n j 1 3 δ ij ) S n n ¯
= 1 2 ξ 0 2 𝓠 2 + 1 2 ϑ Tr ( 𝓠 2 ) 6 Tr ( 𝓠 3 ) + 1 2 Tr 2 ( 𝓠 2 ) χ a Tr ( 𝓠 𝓔 ) .

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