Optimization of single layer and double layer general twisted nematic liquid crystal displays

Abstract

The author derives the Jones matrix representation for a general DTN (double-layer twisted nematic) display with an arbitrary uniform pretilt angle. This representation is used to obtain an analytic closed-form expression for the optical transmission for a DTN display. The optimum design criteria for both single-layer and double-layer TN displays are then obtained. For the single TN display, two design criteria have to be met: one is the optimum cell thickness; the other is optimum polarizer orientation. Design criteria for special cases of single layer TN displays are presented in tabular form. For the DTN display, at the field-off state, the author obtains a completely dark state (for crossed polarizer arrangement) or a completely bright state (for parallel polarizer arrangement); this transmission is independent of the wavelength of the incident light, the magnitude of the twist angle, and other cell and LC (liquid crystal) parameters as long as the entrance LC director of the second layer makes an angle of π/2 with respect to the exit LC director of the first layer, and provided both layers have the same cell thickness, some pretilt angle, same indices of refraction of the LC used, and twist of the same degree but in the opposite sense. Since only one layer is turned on during the field-on state, the optimum cell-thickness design criterion obtained for the single-layer TN display is applicable to both layers of the DTN display, and the optimum polarizer orientation criterion for the single TN displays is also applicable for the DTN display.