Modelling zenithal bistability at an isolated edge in nematic liquid crystal cells

In recent experiments we observed bistable switching in devices made with long pitch square gratings on one surface. It was also discovered that the switching in these devices was localized mainly at isolated edges of the square grating profile. In this paper we present an initial study of surface-induced director configurations at isolated edges of a square profile in the absence of an applied voltage. Our emphasis is on understanding the effect of edge features such as the edge depth and edge inclination in forming stable high and low pre-tilt states. Models based on a Landau-de Gennes approach were used and solutions were found through numerical simulation using finite element methods; optical response was determined, based on wide angle beam propagation methods. Results from real cells are also presented. Our results show that static defect-stabilized states exist for a range of isolated edge depths and inclination angles. In particular, a combination of deep edge depths and steep edge inclinations produce stable high and low pre-tilt director configurations.