Analytical approach to grey levels in ferroelectric liquid crystal displays

Grey levels in ferroelectric liquid crystal displays can be obtained through 'continuous director rotation' in monostable modes. Displays can only be actively addressed. A very simple description of this continuous director rotation can be given in the so-called uniform φ theory, where it is assumed that the azimuthal angle φ of the director does not vary throughout the thickness of the liquid crystal. It requires however that the equilibrium state at zero voltage corresponds to the director making a maximum angle, i.e. the cone angle, with the glass substrates, the polarization being parallel to the glass substrates. It is shown that the electrooptic response can be given an analytic treatment which reduces to the uniform φ theory with the appropriate zero voltage equilibrium state. It accounts entirely for the observed V-shaped switching in high-P materials. In particular an exact expression for the saturation voltage and its dependence on the P value and on the alignment layer thickness is given.