Reducing the Berreman 4 × 4 propagation matrix method for layered inhomogeneous anisotropic media to the Abelés 2 × 2 matrix method for isotropic media

Abstract

With the use of the exact expression for the local propagation matrix that was obtained by Wöhler et al. [ J. Opt. Soc. Am. A5, 1554 ( 1988)], we show explicitly that the Berreman 4 × 4 propagation matrix method for layered inhomogeneous anisotropic media reduces to the Abelés 2 × 2 propagation matrix method for layered inhomogeneous isotropic media when the anisotropic medium becomes isotropic. The optical properties of isotropic and anisotropic media have been extensively studied, and a number of schemes for the computation of the optical effects of layered inhomogeneous media have been proposed. Propagation matrix methods have been shown to be particularly useful for studying the reflection and the transmission of electromagnetic waves by layered inhomogeneous isotropic and anisotropic media.1–5 Generally, the Abelés 2 × 2 matrix method is used for layered inhomogeneous isotropic media,1,2,4,5 and the Berreman 4 × 4 matrix method is used for layered inhomogeneous anisotropic media.3 The 4 × 4 matrix method is more general than the 2 × 2 matrix method and is applicable to problems involving media of low optical symmetry.