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Generalized Jones Calculus for Vortex, Vector, and Vortex-Vector Beam Transformations

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posted on 2023-01-11, 22:22 authored by Wen-Hsuan Kuan, Kuei-Huei Lin, Chang-Wen Wang, Ni-Hsuan Hung
The work defines the general form of the Jones vector and establishes the Jones matrix for polarizers, wave plates, Faraday rotators, Q-plates, and spiral phase plates. We establish the generalized Jones calculus for vortex, vector, and vortex-vector beam transformations. Systematic formalism presents the theoretical arrangements in the manipulation of the phase and polarization of the structured lights. The eigenstates and the time-reversal behaviors of optical components and systems are discussed through matrix algebra. The generalized Jones calculus is then used in the characterization of Sagnac interferometers, and the potential applications are proposed.

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