Singularities in polarization resolved angular patterns: transmittance of nematic liquid crystal cells

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analysing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the 4 × 4 matrix formalism and the orthogonality relations are used to derive the exact expressions for the transmission and reflection matrices. The polarization resolved angular patterns in the two-dimensional projection plane are characterized in terms of the polarization singularities such as C-points (points of circular polarization) and L-lines (lines of linear polarization). For linearly polarized plane waves incident on the homeotropically aligned cell, we present the results of detailed theoretical analysis describing the structure of the polarization singularities. We apply the theory to compute the polarization patterns for various orientational structures in the NLC cell and discuss the effects induced by director orientation and biaxiality.