Reducing Berreman’s 4×4 formulation of LCD optics to 2×2 Jones vector equations

Abstract

The propagation of polarized light in inhomogeneous anisotropic media such as twisted nematic liquid crystal displays (LCDs) has been studied by the Berreman's 4×4 formulation and the 2×2 Jones calculus. However, the relationship and equivalence between these two approaches have not been explicitly shown. We derive the 2×2 Jones vector equations from the Berreman's 4×4 equations. We show that the Berreman's formulation can be transformed to a bidirectional Jones vector space described by differential equations that govern the two transmissive waves and the two reflective waves. We use a perturbation expansion to obtain a generalized 2×2 Jones vector description that is equivalent to the Berreman's description. The first-order term can also be directly derived from the conventional Jones calculus approach, and the higher-order terms represent the multiple reflections within the medium. We find that for the LCD the transmissive subspace is almost invariant, i.e., the bulk reflection effects in the LCD are very weak. Therefore, the accuracy of the first-order solution is in general sufficient. This new method significantly increases the speed of computing the overall optical properties of LCD devices under arbitrary conditions.