Electro-optics of electrically controlled birefringence liquid-crystal displays by 2×2 propagation matrix and analytic expression at oblique angle

A new 2×2 propagation matrix for obliquely propagating light is used to compute the electro-optics of an electrically controlled birefringence liquid-crystal display, with arbitrary viewing angle. The results are the same as those obtained by the generalized geometrical optics approximation and are in good agreement with those computed by the 4×4 propagation matrix. By approximating the liquid-crystal medium as a homogeneous medium with a field-dependent orientation, a simple analytic expression is obtained for describing the optical transmission. The computed electro-optical transmissions at oblique angle show a good agreement between the simple formula and the full computation having the liquid crystal divided into 500 sublayers.