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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 12 — Dec. 1, 2005
  • pp: 2818–2826

Optical properties of electrohydrodynamic convection patterns: rigorous and approximate methods

Christian Bohley, Jana Heuer, and Ralf Stannarius  »View Author Affiliations


JOSA A, Vol. 22, Issue 12, pp. 2818-2826 (2005)
http://dx.doi.org/10.1364/JOSAA.22.002818


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Abstract

We analyze the optical behavior of two-dimensionally periodic structures that occur in electrohydrodynamic convection (EHC) patterns in nematic sandwich cells. These structures are anisotropic, locally uniaxial, and periodic on the scale of micrometers. For the first time, the optics of these structures is investigated with a rigorous method. The method used for the description of the electromagnetic waves interacting with EHC director patterns is a numerical approach that discretizes directly the Maxwell equations. It works as a space-grid-time-domain method and computes electric and magnetic fields in time steps. This so-called finite-difference-time-domain (FDTD) method is able to generate the fields with arbitrary accuracy. We compare this rigorous method with earlier attempts based on ray-tracing and analytical approximations. Results of optical studies of EHC structures made earlier based on ray-tracing methods are confirmed for thin cells, when the spatial periods of the pattern are sufficiently large. For the treatment of small-scale convection structures, the FDTD method is without alternatives.

© 2005 Optical Society of America

OCIS Codes
(230.1950) Optical devices : Diffraction gratings
(260.0260) Physical optics : Physical optics
(260.1180) Physical optics : Crystal optics

ToC Category:
Physical Optics

Citation
Christian Bohley, Jana Heuer, and Ralf Stannarius, "Optical properties of electrohydrodynamic convection patterns: rigorous and approximate methods," J. Opt. Soc. Am. A 22, 2818-2826 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-12-2818


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References

  1. P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, 1993).
  2. C. M. Titus, P. J. Bos, J. R. Kelly, and E. C. Gartland, "Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures," J. Appl. Phys. 38, 1188-1190 (1999).
  3. T. Scharf and C. Bohley, "Light propagation through alignment-patterned liquid crystal gratings," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 375, 491-500 (2002).
  4. C. Bohley, Polarization Optics of Periodic Media (UFO-Verlag, 2004).
  5. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
  6. G. Mur, "Absorbing boundary conditions for the finite-difference approximation of time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
  7. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 184-208 (1994).
  8. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).
  9. B. Witzigmann, P. Regli, and W. Fichtner, "Rigorous electromagnetic simulation of liquid crystal displays," J. Opt. Soc. Am. A 15, 753-757 (1998).
  10. E. Kriezis and S. J. Elston, "Finite-difference time domain method for light wave propagation within liquid crystal devices," Opt. Commun. 165, 99-105 (1999).
  11. E. Kriezis, "A comparative study of light scattering from liquid crystal droplets," Microwave Opt. Technol. Lett. 35, 437-441 (2002).
  12. R. Williams, "Domains in liquid crystals," J. Chem. Phys. 39, 384-388 (1963).
  13. L. Kramer and W. Pesch, "Electrohydrodynamic instabilities," in Pattern Formation in Liquid Crystals, A.Buka and L.Kramer, eds. (Springer, 1996), pp. 221-255.
  14. T. John and R. Stannarius, "Preparation of subharmonic patterns in nematic electroconvection," Phys. Rev. E 70, 025202 (2004). [CrossRef]
  15. T. John, J. Heuer, and R. Stannarius, "Influence of excitation wave forms and frequencies on the fundamental time symmetry of the system dynamics, studied in nematic electroconvection," Phys. Rev. E 71, 056307 (2005). [CrossRef]
  16. S. Rasenat, G. Hartung, B. L. Winkler, and I. Rehberg, "The shadowgraph method in convection experiments," Exp. Fluids 7, 412-420 (1989).
  17. T. O. Carroll, "Liquid crystal diffraction grating," J. Appl. Phys. 43, 767-770 (1972).
  18. H. M. Zenginoglou and J. A. Kosmopoulos, "Geometrical optics approach to the obliquely illuminated nematic liquid crystal diffraction grating," Appl. Opt. 27, 3898-3901 (1988).
  19. H. M. Zenginoglou and 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).
  20. M. Bouvier and T. Scharf, "Analysis of nematic liquid crystal binary gratings with high spatial frequency," Opt. Eng. 39, 2129-2137 (2000).
  21. S. Trainoff and D. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
  22. T. John, U. Behn, and R. Stannarius, "Laser diffraction by periodic dynamic patterns in anisotropic fluids," Eur. Phys. J. B 35, 267-278 (2003).
  23. H. Amm, M. Grigutsch, and R. Stannarius, "Optical characterization of electroconvection in nematics," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 320, 11-27 (1998).
  24. H. Amm, M. Grigutsch, and R. Stannarius, "Spatiotemporal analysis of electroconvection in nematics," Z. Naturforsch., A: Phys. Sci. 53a, 117-126 (1998).
  25. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  26. R. Dändliker, P. Blattner, C. Rockstuhl, and H. P. Herzig, "Phase singularities generated by optical microstructures: Theory and experimental results," in Singular Optics (Optical Vortices) Fundamentals and Applications, M.S.Soskin and M.V.Vastenov, eds., Proc. SPIE 4403, 257-261 (2001).
  27. P. Blattner, "Light fields emerging from periodic optical microstructures," Ph.D. thesis (University of Neuchâtel, 1999).

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