Control of electric equi-potential in a liquid crystal film on a grating surface

We report theoretical results for the distortions of electric equi-potential (EEP) planes in a liquid crystal (LC) film in the presence of surface geometrical grating (SGG). A scaled parameter, the ratio of capacitance per unit area of a LC to that of SGG, is introduced into a simple model to predict the distortions of EEP planes. It is found that the distortions of EEP planes are enhanced by increasing the spatial variations of this scaled parameter inside LC cell. These spatial variations naturally induce the spatially periodic deformations of the LC director which can be employed as a voltage-controlled optical grating.