Investigation of fringing fields in liquid-crystal devices

A model of liquid crystal orientation under the influence of an arbitrary potential pattern; and therefore, the phase exhibited by the liquid crystal device is presented. The model consists of a two-step iterative solution: (1) the potential distribution for a pre-set liquid crystal tilt and orientation is solved, (2) using this solution, a small angle approximation of Frank's equation, with additional electrical energy term is minimized with respect to new angles of tilt and orientation. These new angles are then used as the pre-set angles in the next iteration. Both steps are implemented with finite element methods.