Optics of anisotropic layered media: A new 4 × 4 matrix algebra

A new 4 × 4 matrix algebra, which combines and generalizes Abelès' 2 × 2 matrix method and Jones' 2 × 2 matrix method, is introduced to investigate plane-wave propagation in an arbitrarily anisotropic medium. In this new method, each layer of finite thickness is represented by a propagation matrix which is diagonal and consists of the phase excursions of the four partial plane waves. Each side of an interface is represented by a dynamical matrix that depends on the direction of the eigenpolarizations in the anisotropic medium.