Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems

TLDR

The authors develop a unified theoretical framework for analyzing electromagnetic plane wave reflection and transmission in arbitrarily anisotropic homogeneous layered systems. They employ Berreman’s 4×4 differential matrix formalism to derive a complete analytical 4×4 transfer matrix algorithm for such systems. The resulting algorithm yields explicit analytic expressions for eigenvalues, transfer matrices, and transition matrices, enabling immediate application to ellipsometric analysis of anisotropic layered media. © 1996 The American Physical Society; Berreman, J.

Abstract

We present a unified theoretical approach to electromagnetic plane waves reflected or transmitted at arbitrarily anisotropic and homogeneous layered systems. Analytic expressions for the eigenvalues for the four-wave components inside a randomly oriented anisotropic medium are reported explicitly. As well, the partial transfer matrix for a slab of a continuously twisted biaxial material at normal incidence is described. Transition matrices for the incident and exit media are presented. Hence, a complete analytical 4\ifmmode\times\else\texttimes\fi{}4 matrix algorithm is obtained using Berreman's 4\ifmmode\times\else\texttimes\fi{}4 differential matrices [D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972)]. The algorithm has a general approach for materials with linear optical response behavior and can be used immediately, for example, to analyze ellipsometric investigations. \textcopyright{} 1996 The American Physical Society.