Abstract

Light propagation in liquid crystal devices is described by means of rigorous electromagnetic theory. With the numerical finite-difference time-domain method, the field distribution in inhomogeneous molecule arrangements caused by the finite size of the pixel electrodes can be calculated by a full solution of the Maxwell equations. As an example, a two-dimensional calculation of an inversion layer in a twisted nematic display is presented, and the significance of the new method is shown by comparison of the results with those of a one-dimensional Jones calculation.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Kilian, S. Hess, “Derivation and application of an algorithm for the numerical calculation of the local orientation of nematic liquid crystals,” Z. Naturforsch. 44, 693–703 (1989).
  2. S. Dickmann, “Numerische Berechnung von Feld und Molekülausrichtung in Flüssigkristallanzeigen,” Ph.D. thesis (Universität Karlsruhe, Karlsruhe, Germany, 1994).
  3. P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).
  4. R. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–503 (1941).
    [CrossRef]
  5. J. Nehring, “Light propagation and reflection by absorbing cholesteric layers,” J. Chem. Phys. 75, 4326–4337 (1981).
    [CrossRef]
  6. A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
    [CrossRef]
  7. K. Kunz, R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).
  8. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  9. A. Taflove, The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).
  10. M. Veysoglu, R. Shin, J. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
    [CrossRef]
  11. G. Haas, M. Fritsch, H. Wöhler, D. Mlynski, “Simulation of reverse-tilt disclinations in LCDs,” in SID 90 Digest (Society for Information Display, Santa Ana, Calif., 1990), pp. 102–105 (1990).

1993 (1)

M. Veysoglu, R. Shin, J. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[CrossRef]

1990 (1)

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
[CrossRef]

1989 (1)

A. Kilian, S. Hess, “Derivation and application of an algorithm for the numerical calculation of the local orientation of nematic liquid crystals,” Z. Naturforsch. 44, 693–703 (1989).

1981 (1)

J. Nehring, “Light propagation and reflection by absorbing cholesteric layers,” J. Chem. Phys. 75, 4326–4337 (1981).
[CrossRef]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1941 (1)

de Gennes, P. G.

P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

Dickmann, S.

S. Dickmann, “Numerische Berechnung von Feld und Molekülausrichtung in Flüssigkristallanzeigen,” Ph.D. thesis (Universität Karlsruhe, Karlsruhe, Germany, 1994).

Fritsch, M.

G. Haas, M. Fritsch, H. Wöhler, D. Mlynski, “Simulation of reverse-tilt disclinations in LCDs,” in SID 90 Digest (Society for Information Display, Santa Ana, Calif., 1990), pp. 102–105 (1990).

Haas, G.

G. Haas, M. Fritsch, H. Wöhler, D. Mlynski, “Simulation of reverse-tilt disclinations in LCDs,” in SID 90 Digest (Society for Information Display, Santa Ana, Calif., 1990), pp. 102–105 (1990).

Hess, S.

A. Kilian, S. Hess, “Derivation and application of an algorithm for the numerical calculation of the local orientation of nematic liquid crystals,” Z. Naturforsch. 44, 693–703 (1989).

Jones, R.

Kilian, A.

A. Kilian, S. Hess, “Derivation and application of an algorithm for the numerical calculation of the local orientation of nematic liquid crystals,” Z. Naturforsch. 44, 693–703 (1989).

Kong, J.

M. Veysoglu, R. Shin, J. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[CrossRef]

Kunz, K.

K. Kunz, R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

Lien, A.

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
[CrossRef]

Luebbers, R.

K. Kunz, R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

Mlynski, D.

G. Haas, M. Fritsch, H. Wöhler, D. Mlynski, “Simulation of reverse-tilt disclinations in LCDs,” in SID 90 Digest (Society for Information Display, Santa Ana, Calif., 1990), pp. 102–105 (1990).

Nehring, J.

J. Nehring, “Light propagation and reflection by absorbing cholesteric layers,” J. Chem. Phys. 75, 4326–4337 (1981).
[CrossRef]

Shin, R.

M. Veysoglu, R. Shin, J. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[CrossRef]

Taflove, A.

A. Taflove, The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).

Veysoglu, M.

M. Veysoglu, R. Shin, J. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[CrossRef]

Wöhler, H.

G. Haas, M. Fritsch, H. Wöhler, D. Mlynski, “Simulation of reverse-tilt disclinations in LCDs,” in SID 90 Digest (Society for Information Display, Santa Ana, Calif., 1990), pp. 102–105 (1990).

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Appl. Phys. Lett. (1)

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence,” Appl. Phys. Lett. 57, 2767–2769 (1990).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. Chem. Phys. (1)

J. Nehring, “Light propagation and reflection by absorbing cholesteric layers,” J. Chem. Phys. 75, 4326–4337 (1981).
[CrossRef]

J. Electromagn. Waves Appl. (1)

M. Veysoglu, R. Shin, J. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electromagn. Waves Appl. 7, 1595–1607 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Z. Naturforsch. (1)

A. Kilian, S. Hess, “Derivation and application of an algorithm for the numerical calculation of the local orientation of nematic liquid crystals,” Z. Naturforsch. 44, 693–703 (1989).

Other (5)

S. Dickmann, “Numerische Berechnung von Feld und Molekülausrichtung in Flüssigkristallanzeigen,” Ph.D. thesis (Universität Karlsruhe, Karlsruhe, Germany, 1994).

P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

A. Taflove, The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).

K. Kunz, R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, Boca Raton, Fla., 1993).

G. Haas, M. Fritsch, H. Wöhler, D. Mlynski, “Simulation of reverse-tilt disclinations in LCDs,” in SID 90 Digest (Society for Information Display, Santa Ana, Calif., 1990), pp. 102–105 (1990).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Electric field in a TN pixel in the off state. A plane wave Ez illuminates the LC from the left side. Inside the LC the plane of polarization is turned to Ex, and the wave is absorbed at the output polarizer.

Fig. 2
Fig. 2

Electric field in a TN pixel in the on state. A plane wave Ez illuminates the LC from the left side and passes through the display.

Fig. 3
Fig. 3

Molecule orientation and lines of constant potential for a TN pixel with a pretilt angle of θ=2°.

Fig. 4
Fig. 4

Simulation model of a TN LC pixel. At the top electrode, the voltage is applied. The pixel is illuminated from the bottom side.

Fig. 5
Fig. 5

Poynting vector for the molecule configuration of Fig. 3. The source is a monochromatic plane wave illumination at λ=630 nm from the bottom side. The width of the top electrode is 21 µm.

Fig. 6
Fig. 6

Top: Transmittance for a horizontal cross section of Fig. 5 (solid curve) compared with a 1-D extended Jones calculation (dashed curve). Bottom: difference of the two methods in percent of the maximal transmission. The peaks correspond to the loss of light due to lateral scattering effects in the LC material.

Tables (1)

Tables Icon

Table 1 Overview of Parameters Used in the Simulations

Equations (8)

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

×E=-μ Ht,
×H=εˆ Et+σE,
Ein+1=Ein+Δtaijjkl xkHln+1/2-aijσΔtEjn+1/2,
Hin+1/2=Hin-1/2+Δtμijk xjEkn.
Ejn+1/2=12(Ejn+1+Ejn).
Ein+1=Nij-1E˜j,
Nij=1-13δijaijσΔt+13δij,
E˜j=Ejn 1-σ Δt2ajj1+σ Δt2ajj+Δtajkklm xlHmn+1/2-σ Δt2ajkEkn1-13δjk,

Metrics