Tunable birefringence and elliptical polarization eigenmodes in a biplate of two quarter-wave plates

Birefringence of elliptical polarization eigenmodes can be conceptualized as a composite system comprising two distinct media: one with linear polarization eigenmodes and the other with circular polarization eigenmodes. However, the practical realization of such a system often involves the combination of two birefringent quarter-wave plates (QWPs). In this study, our objective is to characterize the variable retardation and variable elliptical polarization eigenmodes exhibited by a biplate consisting of two quarter-wave plates. Additionally, we aim to analyze the geometric properties of the transformation of one state of polarization on the Poincaré sphere, employing the emerging state's curve. This curve corresponds to the intersection between the Poincaré sphere and a cone. The outcomes of our study are presented as a function of the angle between the fast axes of the two QWPs. The findings have the potential to contribute to the configuration of q-plates and facilitate the development of quantum communication protocols.