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.

© 1989 Optical Society of America

4 × 4 Matrix formalisms for optics in stratified anisotropic media

P. J. Lin-Chung and S. Teitler
J. Opt. Soc. Am. A 1(7) 703-705 (1984)

Generalized 4 × 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures

Nikolai Christian Passler and Alexander Paarmann
J. Opt. Soc. Am. B 34(10) 2128-2139 (2017)

Characteristic matrix method for stratified anisotropic media: optical properties of special configurations

H. Wöhler, M. Fritsch, G. Haas, and D. A. Mlynski
J. Opt. Soc. Am. A 8(3) 536-540 (1991)

Optics in Stratified and Anisotropic Media: 4×4-Matrix Formulation

Dwight W. Berreman
J. Opt. Soc. Am. 62(4) 502-510 (1972)

Accurate and efficient calculation of light propagation in one-dimensional inhomogeneous anisotropic media through extrapolation

Zhao Lu
J. Opt. Soc. Am. A 24(1) 236-242 (2007)