Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems

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 X 4 matrix algorithm is obtained using Berreman's 4 X 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.