Light Propagation in Stratified Anisotropic Media: Orthogonality and Symmetry Properties of the 4×4 Matrix Formalisms

Abstract

For light propagation in stratified media the normal component of the Poynting vector is defined as an indefinite scalar product. The vanishing of this scalar product for two waves is regarded as their mutual orthogonality. Orthogonality in this sense is an inherent property of optical eigenmodes in loss less media. It is shown that the matrices D and P appearing in Berreman's 4×4 matrix formalism are hermitian and unitary, respectively, within this metric. The application of these properties can facilitate numerical calculations and analytical treatments