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 proof of their mutual orthogonality. Orthogonality in this sense is an inherent property of optical eigenmodes with different real wave vectors. 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. By using the orthogonality property of optical eigenmodes, projection operators and a transformation matrix are constructed that can facilitate numerical calculations and analytical treatments. The equivalence of Berreman’s 4 × 4 matrix method with scattering matrix and transfer matrix formalisms is shown.