Effect of a surface polarized layer on the optical properties of a nematic cell

The optical properties of a cell of nematic liquid crystal presenting a tilted surface polarization submitted to an electric field are theoretically investigated. The origin of the surface polarization is assumed to be related to the interaction of the nematic molecules with the substrate and to the polar order due to the cell filling procedure. The analysis shows that the coupling of the surface polarization with the external field has different effects on the two surfaces limiting the sample. On one of them, the coupling gives rise, in an unbounded sample, to a continuous variation of the easy angle, whereas on the other one it is responsible for a first-order like transition of the easy axis orientation. For a sample of finite thickness our analysis shows that in the presence of a coupling between the two surfaces, operated by the elastic properties of the liquid crystal, the abrupt variation of the easy axis on one of the surfaces induces also on the other surface a discontinuity on the nematic surface orientation. The optical transmission of the cell versus the amplitude of the applied voltage, for an impinging monochromatic linearly polarized light, presents a discontinuity for the critical voltage at which the first-order transition of the surface tilt angles appears.