Numerical modelling of LCD electro-optical performance

• Autorzy: Wohler H. , Becker M. E.
• Języki publikacji: EN

Abstrakty

EN

Realisation of complex high information density LCDs and systematic optimisation of their electro-optical and ergonomic performance would not be possible in the required time-frame without reliable numerical modelling of the electro-optical performance of such display devices. In this paper, we outline the history of numerical LCD modelling starting with Berreman and van Doorn,finally arriving at modern state-of-art LCD-modelling in two and three dimensions. Numerical modelling of LCDs is carried out in two steps : first, the effect of the electrical field on the orientation of the liquid crystalline alignment has to be evaluated before the corresponding optical properties can be computed. Starting from LC-elasticity theory we present suitable numerical methods for computing various states of LC-deformation (stable, metastable, bistable, etc.) in one-dimensional problems. Light propagation in layered anisotropic absorbing media is evaluated with the methods that are based on Maxwell's equations (Berreman 4 x 4 - matrix approach). This approach can be simplifield to yield methods with reduced computing time and sufficient accuracy for many problems (e. g. extended Jones 2 x 2 - matrix formalism). In two- and three- dimensional problems, i. e., in cells with lateral dimensions comparable to the cell thickness, a variety of different director configurations are possible for a given geometry and electrical driving and addressing, making the modelling more complicated. Moreover, local defects can occur, which should be also considered in the simulation. Suitable approaches for the director field calculation, i. e. the vector and the tensor approach, are discussed. The complexity of the problem increases considerably when a third dimension is added, e. g. the geometry of the problem has to be defined in three dimensions together with the respective boundary conditions (anchoring geometry and elasticity) and electrodes. If strong deformations or even distortions are present in the orientation of the LC-layer, the applicability of known one- dimensional approaches for computing the optical properties must be checked and new approaches eventually have to be developed. The third dimension prohibits the use of some standard methods (e. g. FDTD), solely because of the enormous memory requirements and the long calculation times. Other approaches are presented and discussed.

Słowa kluczowe

EN

LC-deformation; LC-optics; one-dimensional solution

• Wydawca: Stowarzyszenie Elektryków Polskich ; Polska Akademia Nauk ; Wojskowa Akademia Techniczna im. Jarosława Dąbrowskiego
• Czasopismo: Opto-Electronics Review
• Rocznik: 2002
• Tom: Vol. 10, No. 1
• Strony: 23--33
• Opis fizyczny: Bibliogr. 61 poz.

Twórcy

autor

Wohler H.

autor

Becker M. E.

• Autronic-Melchers GmbH, 18 Rosweid Str., D-76229 Karlsruhe, Germany

Bibliografia

• 1. C. Z. van Doorn, "Dynamic behavior of twisted nematic liquid-crystal layers in switched fields", J Appl. Phys. 46, 3738-3745 (1975).
• 2. D. W. Berreman, "Liquid-crystal twist cell dynamics with backflow", J. Appl. Phys. 46, 3746-3751 (1975).
• 3. M. E. Becker, "DIMOS - a software tool for optimizing display system with LCDs", Displays 132, 215-228 (1989).
• 4. C. W. Oseen, "Beiträge zur Theorie anisotroper Flüssigkeiten", Ark. Math. Fys. 19A, 1-19 (1925).
• 5. F. C. Frank, "On the theory of liquid crystals" Discuss. Faraday Soc. 25, 19-28 (1958).
• 6. F. M. Leslie, Quart. J. Mech. Anal. 19, 357 (1966).
• 7. J. L. Ericksen and J. L. Arch, Ration. Mech. Analysis 23, 266 (1966) .
• 8. J. E. Anderson et al., "Shortcomings of the Q-tensor method for modeling liquid crystal devices", SID '99 Digest, 198 (1999).
• 9. D. W. Berreman, "Surface orientation and compliance effects on twist-cell performance", in The Physics and Chemistry of Liquid Crystal Devices, pp. 1-11, edited by C. J. Sprokel, Plenum Press, New Yor, 1980.
• 10. A. Rapini and M. Papoular: "Distortion d'une lamelle nematique sous champ magnetique, conditions d'ancrage aux parois", J. Physique 30, C4-54, C4-56 (1969).
• 11. C. Vertogen et al., Themotropic Liquid Crystals. Fundamentals, Springer, Berlin, 1988.
• 12. H. Gruler, T. J. Scheffer, and G. Meier, "Elastic constants of nematic liquid crystals I. Theory of the normal deformation", Z. Natuiforsch. A, 27, 966-976 (1972).
• 13. R. N. Thurston and D. W. Berreman, "Equilibrium and stability of liquid-crystal configurations in an electric field", J. Appl. Phys. 52, 508-509 (1981).
• 14. M. Akatsuka et al., "Film compensated STN-LCDs with wide viewing angle", 9th IDRC, 336-339 (1989).
• 15. T. Miyashita et al., "A wide-viewing angle color STN-LCD with biaxial retardation films", 12th IDRC, 495-498 (1992).
• 16. D. W. Berreman, "Numerical modelling of twisted nematic devices", Phil. Trans. R. Soc. Lond. A, 309, 203-216 (1983).
• 17. W. H. Press et al., Numerical Recipes in FORTRAN: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1992.
• 18. H. Wöhler et al., "A modifed Ritz method for the calculation of deformation profiles in chiral nematic liquid crystal cells", 9th IDRC, 376-379 (1989).
• 19. M. E. Becker, "A new method for computing director profiles", 11th IDRC, 503-506 (1994).
• 20. T. J. Scheffer and J. Nehring, "Twisted nematic and supertwisted nematic mode LCDs", in Liquid Crystals Applications and Uses 1, pp. 231-274, edited by B. Bahadur, World Scientific, Singapore, 1990.
• 21. M. E. Becker et al., "Surface-induced bistability in chiralnematic liquid crystals: effect of liquid crystal and surface parameters", Proc. SID, 26, 109-115 (1985).
• 22. B. N. Thurston, "Stability of nematic liquid crystal configurations", J. Physique 42, 419-425 (1981).
• 23. R. N. Thurston and F. J. Almgren, "Liquid crystal and geodeics", J. Physique 42, 413-417 (1981).
• 24. B. N. Thurston, "Unit sphere description of liquid-crystal configurations", J. Appl. Phys. 52, 3040-3052 (1981).
• 25. B. N. Thurston, "Stability of nematic liquid crystal configurations", J. Physique 42, 419-425 (1981).
• 26. M. Ch. Mauguin, "Sur les cristaux liquide de Lehmann", Bull. Soc. Fran. Min. 34, 6-15 (1911).
• 27. C. W. Oseen, "Beiträge zur Theorie anisotroper FIüssigkeiten", Ark. Math. Astron. Fys. 21A, 14-35 (1928).
• 28. H. de Vries, "Rotary power and other optical properties of certain liquid crystals", Acta Crystallogr. 4, 219-226 (1951).
• 29. R. C. Jones, "A new calculus for the treatment of optical systems I. Description and discussion of the calculs", J. Opt. Soc. Am. 3, 488-493 (1941).
• 30. D. C. Smith, "Magneto-optical scattering from multilayer magnetic and dielectric films", Optica Acta 12, 13-45 (1965).
• 31. O. W. Berreman, "Optic in stratified and anisotropic media: 4x4-matrix formulation", J. Opt. Soc. Am. 62, 502-510 (1972).
• 32. F. Gharadjedaghi and J. Robert, "Comportement electro-optique d'une structure nematique en helice - application a l'affichage", Rev. Phys. Appl. 11, 467-473 (1976).
• 33. P. Yeh, "Extended Jones matrix method", J. Opt. Soc. Am. 72, 507-513 (1982).
• 34. P. Yeh, "Electromagnetic propagation in birefringent layered media", J. Opt. Soc. Am. 69, 742-756 (1979).
• 35. 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, 1863-1866 (1988).
• 36. F. Abeles: "Recherches sur la propagation des ondes electromagnetique sinusoidales dans les milieux stratifies. Application aux couches minces", Anal. Phys. 5, 596-640 (1950).
• 37. S. Teitler and B. W. Henvis, "Refraction in stratified, ani otropic media", J. Opt. Soc. Am. 60, 830-834 (1970).
• 38. D. W. Berreman, "Optics in smoothly varying planar structures: Application to liquid-crystal twist cells", J. Opt. Soc. Am. 63, 1374-1380 (1973).
• 39. R. J. Gagnon, "Liquid-crystal twist-cell optics", J. Opt. Soc. Am. 71, 348-353 (1981).
• 40. H. Wöhler et al., "Faster 4x4 matrix method for uniaxial inhomogeneous media", J. Opt. Soc. Am. A 5, 1554-1557 (1988).
• 41. K. Eidner et al., "Optics in tratified media - the use of optical eigenmodes of uniaxial crystal in the 4x4-matrix formalism", Mol. Cryst. Liq. Cryst. 172, 191-200 (1989).
• 42. A. Lien, "The general and simplfied Jones matrix representations for the high pretilt twisted nematic cell", J. Appl. Phys. 67, 2853-2856 (l990).
• 43. H. L. Ong: "Electro-optics of a twisted nematic liquid crystal display by 2x2 propagation matrix at oblique incidence", Jpn. J. Appl. Phys. 30, L1028-Ll031 (1991).
• 44. C. Gu and P. Yeh: "Extended Jones matrix method. II", J. Opt. Soc. Am. A 10, 966-973 (1993).
• 45. P. Allia et al., "4x4 matrix approach to chiral liquid-crystal optics", Mol. Ctyst. Liq. Cryst. 143, 17-29 (1987).
• 46. K. H. Yang, "Electro-optical properties of dual-frequency cholesteric liquid crystal reflective display and drive scheme", J. Appl. Phys. 68, 1550-1554 (1990).
• 47. D. W. Berreman, "Ultrafast 4x4 matrix optics with averaged interference fringes", SID 1993 Digest, 101-104 (1993).
• 48. D. W. Berreman, "Quick averaging of interference fringes in 4x4 matrix optics", Freiburger Arbeitst. Flüssigkristalle, 25, Freiburg (1996).
• 49. M. Born and E. Wolf, Principles of Optics, Pergamon Press, Oxford, 1980.
• 50. J. E. Bigelow et al., "Poincare sphere analysis of liquid crystal optics", Appl. Opt. 16, 2090-2096 (1977).
• 51. M. Johnson, "Poincare sphere representation of birefringent networks", Appl. Opt. 20, 2075-2080 (1981).
• 52. O. Zienkiewicz et al., The Finite Element Method, Vol.1, McGraw-Hill, New York (1994).
• 53. B. Witzigmann et al., "Rigorous electrornagnetic simulation of liquid crystal displays", J. Opt. Soc. Am. A 15, 753-739 (1998).
• 54. M. E. Becker et al., "Numerical modeling of IPS effects: A new approach and more results", SID 1996 Digest, 15-18 (1996).
• 55. H. De Vleeschouwer et al., "Ion transport simulations and DC leakage current measurements in nematic LCDs", SID 2001 Digest, 128-131 (2001).
• 56. E. E. Kriezis et al., "Finite-difference time domain method for lightwave propagation within liquid crystal devices", Opt. Comm. 165, 99-105 (1999).
• 57. C. M. Titus et al., "Comparison of analytical calculations to finite-difference time-domain simulations of one-dimensional spatially varying anisotropic liquid crystal structures", Jap. J. Appl. Phys. 38, 1488-1494 (1999).
• 58. E. E. Kriezis et al., "A wide angle beam propagation method for the analysis of tilted nematic liquid crystal structures", J. Mod. Opt. 46, 1201-1212 (1999).
• 59. P. Galatola et al., "Symmetry properties of anisotropic dielectric gratings", J. Opt. Soc. Am. A 11, 1332-1341 (1994).
• 60. O. A. Peverini et al., to be published.
• 61. D. K. G. de Boer et al., "Optical simulations and measurements of in-plane switching structures with rapid refractive-index variations", SID 2001 Digest, 818-821 (2001).