Analytical approach to grey levels in ferroelectric liquid crystal displays

Grey levels in ferroelectric liquid crystal displays can be obtained throug h 'continuous director rotation' in monostable modes. Displays can only be actively addressed. A very simple description of this continuous director r otation can be given in the so-called uniform phi theory, where it is assum ed that the azimuthal angle phi of the director does not vary throughout th e 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 para llel to the glass substrates. It is shown that the electrooptic response ca n be given an analytic treatment which reduces to the uniform phi theory wi th the appropriate zero voltage equilibrium state. It accounts entirely for the observed V-shaped switching in high-P materials. In particular an exac t expression for the saturation voltage and its dependence on the P value a nd on the alignment layer thickness is given.