An alternative derivation of the 4×4 propagation matrix formalism

Abstract

We present an alternative derivation for the Berreman 4×4 propagation matrix by first transforming the 4×1 generalized field vector to a new 4×1 field vector satisfying wave equations with a diagonal differential wave matrix. Thus one is able to obtain the normal independent modes of the medium. Two forms for the propagation matrix for the generalized field vector are then obtained and agree with the results that were obtained with Berreman's method [D.W. Berreman, J. Opt. Soc. Am. 62 (1972) 502].