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We show that a class of vector vortex beams possesses a topological property that derives both from the spatially varying amplitude of the field and its varying polarization. This property arises as a consequence of the inherent skyrmionic nature of such beams and is quantified by the associated skyrmion number. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the skyrmion number in this context.
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Sijia Gao, Fiona C. Speirits, Francesco Castellucci, Sonja Franke-Arnold, Stephen M. Barnett, Jörg B. Götte, "Paraxial skyrmionic beams," Proc. SPIE 11701, Complex Light and Optical Forces XV, 117010W (5 March 2021); https://doi.org/10.1117/12.2592049