Abstract: With an equivalent anchoring energy formula for grating surface and elastic theory, a hybrid aligned nematic (HAN) liquid crystal cell proposed by Bryan-Brown et al is studied. Equations and boundary conditions for tilt angle and twist angle of director are obtained with variation theory. Tilt angle and twist angle of director with applied voltage at certain δ/λ are calculated with finite-difference iterative method. Electro-optical effect of liquid crystal cells is investigated with Jones matrix method. It depends on geometrical parameters of the grating surface, pitch λ and amplitude δ.

Key words: grating surface, variation theory, finite-difference iterative method, Jones matrix method, electro-optical effect