4 × 4 and 2 × 2 matrix formulations for the optics in stratified and biaxial media

Exact matrix representations for refraction and reflection at an interface between arbitrarily oriented biaxial media and for the wave propagation within a biaxial homogeneous medium are derived. Based on the understanding of the optics in the bulk and at the interface, the relations among the exact 4×4 matrix method and the simplified 2×2 matrix methods with different assumptions for calculating the optical transmission of a stack of stratified and biaxial media are clarified. A simple Fabry–Perot etalon model is proposed to verify the accuracy of the 2×2 matrix methods in terms of the coherency and the polarization of the incident wave. The optical transmission curves obtained from the different 2×2 matrix methods are compared with those obtained from the 4×4 matrix method with the spectrum average for an optically compensated bend mode liquid-crystal display.