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

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Abstract
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.

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