4×4 Transfer Matrix T _p for Isotropic Films

Abstract

Isotropic materials can be treated much easier and by simpler equations than through the 4×4 approach. However, the isotropic solution within the 4×4 matrix formalism is necessary in order to include isotropic layers into layer models,which also include layers of anisotropic materials. The Berreman-formalism describes use of 4×4 matrices for calculation of reflection and transmission of electromagnetic plane waves by stratified mediums with plane parallel interfaces. Details of this approach shall not be recalled here, and many excellent reviews exist on this matter. Briefly, a characteristic coefficient matrix,Δ, provides Eigenvalues and self-consistent description of the electromagnetic radiation transport between layer boundaries. At any point z within a homogeneous layer, the x and y components of the electric and magnetic fields in Gaussian units and Cartesian coordinates (see also Sect. 2.7, and [1,2,3,4])