V.L. Ginzburg’s elliptic screw polarization modes in an optical medium with linear birefringence and twist: Determination of their parameters by the method of Jones matrices

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Using the method of Jones matrices, we have calculated parameters of elliptic screw polarization modes (ESPMs). ESPM formalism has been proposed by V.L. Ginzburg for an optical medium with unperturbed linear birefringence and circular birefringence induced by twisting of the medium. The evolution of the polarization state of radiation (PSR) in relation to the length of the examined optical medium has been considered, which is important for twisted single-mode optical fibers and cholesteric liquid crystals. We have shown that the problem can be substantially simplified if the evolution of ESPMs is considered in a screw coordinate system comoving with the twist of the optical medium. In particular, we have shown that a curve on the Poincaré sphere mapping the evolution of the PSR for natural (normal) waves of the examined optical medium in the screw coordinate system degenerates into a point. For comparison, we have found natural waves of this medium in a fixed (laboratory) coordinate system and considered the evolution of their PSR, which is represented by a complex curve on the Poincaré sphere. Also, the evolution of the PSR of improper waves passed through the examined optical medium has been studied in both the fixed and the screw coordinate systems.