Johan Fornier

Viewing angle of liquid-crystal displays: representation on the Poincaré sphere

Using the extended Jones calculus for oblique incidence, we have succeeded in representing light propagation through birefringent media on the Poincaré sphere for arbitrary propagation directions. The situation is far more complicated than for the case of perpendicular transmission. To achieve a simple representation method we had to define appropriate conventions. One can use the method to evaluate the efficiency of existing viewing-angle compensation foils. The Poincaré sphere turns out to be a valid geometrical method for the design of new compensation foils that optimize the contrast ratio. The different parameters of a homogeneous compensation foil that is applied to a liquid-crystal display to improve the viewing-angle properties can be systematically determined.

Analytical Treatment of Grey Levels in Antiferroelectric Liquid Crystal Displays

Abstract Under certain simplifying assumptions, which are believed to be non-essential, it is possible to treat grey levels in antiferroelectric liquid crystal displays analytically. This shows more clearly than simulations which parameters play an essential role.

GRATING DIFFRACTION IN (ANTI-)FERROELECTRIC LIQUID CRYSTAL DISPLAYS

Abstract For many inhomogeneous structures in LCDs, such as antiferro- or ferrielectric LCDs and striped textures in classical or short-pitch ferroelectric LCDs, we present a strong, rigorous algorithm for the calculation of the optical transmission. We illustrate the technique in case of some simple alternating structures. The number of diffraction orders strongly depends on the grating period (Λ) - light wavelength (λ) ratio Λ/λ. For the alternating antiferroelectric state the transmission of visible light can be treated with only the zeroth order of diffraction. In this case, we find that the AFLC can be simulated as a birefringent layer with the principal axes parallel and perpendicular to the layers. In case Λ/λ > 1 higher orders of diffraction come into play. The dimension of the corresponding eigenvalue problem becomes too large for analytical treatment. We give some numerical results.

Homogeneous switching in antiferroelectric liquid crystal displays

Abstract We use a very simple bookshelf model to describe the behaviour of antiferroelectric liquid crystals in an electric field. Starting from the energy expression of the LC, which comprises antiferroelectric coupling, coupling with the electric field and surface anchoring, we can derive the dynamic equations. We carry out numerical simulations in order to solve these equations in different cases. We consider the three different switching modes: switching from the alternating state to one of the uniform states, switching from a uniform state to the alternating state, and switching between the two uniform states.

Grey level control by variation of the surface interaction in AFLCD's.

Abstract We report the influence of the rubbing treatment of the alignment layers on the electro-optic characteristics of AFLCDs. We applied a different rubbing treatment on different regions within a pixel. This variation of rubbing strengths causes domains with different surface interaction, which results in a different threshold voltage for each domain. In-pixel variation of the rubbing treatment and of the surface interaction influences the double hysteresis of the transmission-voltage characteristic, which is made less steep. The difference between the voltages at which the transmission starts to increase and the voltage at which the transmission reaches its maximum increases and so the selection of analogue grey levels is made easier. The results also show that the finite slope of the double hysteresis which is observed in normal AFLCDs, without extra rubbing treatment is probably caused by variations of the surface interaction.

Simulation of Switching in Antiferroelectric Liquid Crystals

Abstract We are simulating the dynamic response of surface stabilised antiferroelectric liquid crystal displays, based on a one-dimensional approach. This leads to more detailed modelling than before1. The evolution of director profiles and the resulting optical transmission under applied voltages are studied. The different switching modes between the alternating state and the two uniform states, observed in antiferroelectric test cells, can be understood fairly well. The model incorporates a chevron geometry. The different terms in the bulk energy function can be rationally interpreted. The alignment layers are modelled by a polar and a non-polar surface energy term. The influence of parameters, such as the antiferroelectric coupling parameter, the polar and non-polar anchoring strength, the elastic constant etc. are discussed.

A Simple Numerical Transmission Model for General LCD-Configurations

Abstract The transmission of a LCD for normal incident light can be simply calculated by a clever use of the Jones calculus. Several cases are treated in different ways. The results for a few examples are compared with the more general simulations according to the 4 × 4 Berreman method, which also takes internal reflections into account. Our fast optical calculations are useful when predicted molecular distributions should be confronted with experimental optical spectra.

Analytical model for thresholdless antiferroelectric liquid crystal displays

A simple model for thresholdless antiferroelectric liquid crystal displays is presented, in which the typical thresholdless characteristic is caused by a negative interaction coefficient between the alignment layer and the liquid crystal. This negative interaction coefficient may be caused by the pairing of transverse dipole moments in adjacent layers. It causes a maximum tilt of the liquid crystal molecules in the zero-field antiferroelectric equilibrium state, which then evolves gradually to the ferroelectric state with increasing electric field.

Geometrical averaging of AFLC dielectric tensors

The optical transmission of antiferroelectric liquid crystal layers is non-trivial. For optical wavelengths we average the dielectric tensors. The aim is to provide a geometrical way for this averaging. By a thorough mathematical analysis, we are able to construct the representation ellipsoid for the final e-tensor in most cases. In this way, we can easily predict the axes and indices of refraction of the structure. Especially the molecular states that occur during the hysteresis switching behaviour are studied.

Viewing-angle improvement based on Poincaré sphere representation

We extended the representation of light propagation through birefringent media on the Poincare sphere to the case of oblique incidence. The developed representation was used to design a wide viewing-angle compensation foil for a bi-level TN-LCD.