Propagation of an arbitrary incident light in a uniaxially planar slab

Similarly to the Jones calculus, a propagation formulation of an arbitrary incident light in a uniaxially planar slab with any orientation of the optic axis is derived, where both the multi-reflections and multi-refractions and the phase difference between the ordinary and extraordinary waves arising at the interface are considered. Unlike the case of propagation in the stratified isotropic media, the elements of the reflection and transmission matrices not only include the reflection and transmission coefficients, but also comprise phase differences caused by the mutual couples between ordinary (O) and extraordinary (E) waves. At this point, the propagation of an arbitrary light in a stratified uniaxially anisotropic media may be viewed as the multi-reflections and multi-refractions of a compound wave composed of one O wave and one E wave.