The geometry of distributions of the polarization of light in conoscopic patterns of planar oriented nematic and cholesteric liquid crystal (LC) cells is described in terms of the polarization singularities including C-points (points of circular polarization) and L lines (lines of linear polarization). Conditions for the formation of polarization singularities (C-points) in an ensemble of conoscopic patterns parametrized by the polarization azimuth and ellipticity of the incident light wave have been studied. A characteristic feature of these conditions is selectivity with respect to the polarization parameters of the incident light wave. The polarization azimuth and ellipticity are determining parameters for nematic and cholesteric LC cells, respectively.
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