of An L C cell with (a) the isotropic blue phase when the field is off and (b) the anisotropic phase when the field is on.."/>
Figure 3.28 An LC cell with (a) the isotropic blue phase when the field is off and (b) the anisotropic phase when the field is on. This figure was reproduced from Yang, Y. C. et al., SID 09, p. 586 with permission by The Society for Information Display
Figure 3.29 Phase diagram of chiral nematic LCs with blue phases BP I and BP II. This figure was reproduced from Kikuchi, H. et al., SID 09, p. 580 with permission by The Society for Information Display
Figure 3.30 Response time of the PSI-mode. This figure was reproduced from Yang, Y. C. et al., SID 09, p. 589 with permission by The Society for Information Display
Figure 3.31 Transmittance versus voltage of the PSI-mode. This figure was reproduced from Yang, Y. C. et al., SID 09, p. 588 with permission by The Society for Information Display
Figure 3.30 (Yang et al., 2009) shows the response time of the PSI-mode for a cell with a cell gap of 4 μm and a distance between the cell electrodes of 10 μm. The on/off times are 259 μs/ 258 μs, so the cell is able to handle a 240 Hz frame rate with a frame time of 4.167 ms.
Finally, Figure 3.31 depicts the transmittance of the cell versus the in-plane addressing voltage V; it exhibits a hysteresis. The weight fractions of the mixture as a percentage is LC: monomer: chiral = 68.6 : 11.6 : 19.8. The transmittance does not saturate. For useful values of a 6-17 percent transmittance, rather large voltages from 25 V to 65 V are required. Therefore a goal for further development is to lower the addressing voltage.
References
1 Born, M. and Wolf, E. (1980) Principles of Optics, 6th ed., Pergamon Press, Oxford.
2 Bos, P. J. and Koehler, K. R. (1984) The pi-cell: A fast liquid crystal optical switching device. Mol. Cryst. Liq. Cryst., 113.
3 Degen, W. H. (1980) Physical Properties of Liquid Crystalline Materials. Gordon and Breach, London.
4 Freedericksz, V. and Zolina, V. (1933) Forces causing the orientation of an anisotropic liquid. Trans. Faraday Soc., 29, 919.
5 Glueck, J. (1995) Mit a-Si:H-Dunnschichttransistoren angesteuerte flache Fluessigkristall-Bildschirme fur Direktsicht und Projektion. PhD-Thesis, University of Stuttgart.
6 Jones, R. C. (1941) New calculus for the treatment of optical systems, J. Opt. Soc. Am., 31, 488.
7 Kikuchi, H. et al. (2007) Fast electro-optical switching in polymer-stabilized liquid crystalline blue phases for display application. SID 07, p. 1737.
8 Kikuchi, H. et al. (2009) Optically isotropic nano-structured liquid crystal composites for display applications. SID 09, p. 578.
9 Labrunie, G. and Robert, J. (1973) J. ofAppl. Phys., 44, 487.
10 Lu, K. and Saleh, B. E. A. (1990) Theory and design of the Liquid Crystal TV as an optical spatial phase modulator. Opt. Eng., 29.
11 Lueder, E. (1998) Passive and active matrix liquid crystal displays with plastic substrates. El.-Chem. Soc. Proc., 98-22.
12 Lueder, E. (1998a) Fundamentals of Passive and Active Matrix Liquid Crystal Displays. Short Course S-1, SID, May.
13 Priestley, E. B., Wojtowicz, P. J. and Sheng, P. (1979) Introduction to Liquid Crystals. Plenum Press, New York, London.
14 Saito, S. and Yamamoto, H. (1978) Transient behaviors of field-induced reorientation in variously oriented nematic liquid crystals. Jap. J. ofAppl. Phys., 17(2).
15 Uchida, T. (1999) High performance reflective color LCDs. Proc. Eurodisplay 99, Berlin.
16 Vithana, H. K. M. and Faris, S. M. (1997) Polymer stabilized Pi-cells as switchable phase retarders. SID 1997 Digest.
17 Yang, Y. C. etal. (2009) Sub-millisecond liquid crystal mode utilizing electro-optic Kerr effect comprising polymer-stabilized isotropic liquid crystals. SID 09, p. 586.
18 Yeh, P. (1988) Optical Waves in Layered Media. John Wiley & Sons, Chichester.
19 Yeh, P. and Gu, C. (1999) Optics of Liquid Crystal Displays. John Wiley & Sons, Chichester.
4
Electro-optic Effects in Twisted Nematic Liquid Crystals
4.1 The Propagation of Polarized Light in Twisted Nematic Liquid Crystal Cells
The Twisted Nematic cell (TN cell) is the most widely commercially used LC cell. It was proposed by Schadt and Helfrich (1971), and is therefore also termed the Schadt–Helfrich cell. The theoretical investigation is based on Jones vectors. Solutions for the light exiting a TN cell were given by Yeh (1998), Yeh and Gu (1999), Grinberg and Jacobson (1976) and Rosenbluth et al. (1998). The derivation relies on rotating back the coordinate system to the original coordinates in twisted media and on the Chebychev identity of matrices (Bodewig, 1959). On the other hand, the derivation of the results presented here rotates the coordinates with the twist of the layers. The further calculation is based on Specht (2000).
The planar wave with wave vector
Figure 4.1 The general twisted nematic LCD with twist angle β
in the x–y coordinates. The LC molecules in the x–y plane are all anchored in the rubbing grooves parallel
