https://doi.org/10.1140/epjd/s10053-025-01110-x
Research - Photons
Research on the focusing characteristics of circularly polarized vortex beams under high-numerical aperture
1
School of Automation and Information Engineering, Xi’an University of Technology, 710048, Xi’an, China
2
Xi’an University, 710048, Xi’an, China
3
Shaanxi Polytechnic University, Xi’an, China
4
Xianyang Key Laboratory of Intelligent Manufacturing Equipment Technology, 712000, Xianyang, China
a
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Received:
3
September
2025
Accepted:
8
December
2025
Published online:
25
February
2026
Abstract
This study is based on the Richards–Wolf vector diffraction integral theory and investigates the field evolution and angular momentum characteristics of circularly polarized vortex beams focused by a high-numerical aperture (NA) lens. By simulating the focusing process of left- and right-handed circularly polarized vortex beams with different topological charges, the intensity, phase, spin angular momentum (SAM), and orbital angular momentum (OAM) density distributions in the focal plane are analyzed in connection with the theoretical formulations. On this basis, the focusing characteristics of fractional-order circularly polarized vortex beams are further examined. Moreover, the effects of different NA values on the focal intensity distribution, angular momentum conversion, and depth of focus are compared. The results indicate that the topological charge l plays a crucial role in modulating the focal field. As the NA increases, SAM is more readily converted into OAM, while the depth of focus decreases. Additionally, fractional topological charges lead to phase singularity splitting and dark-core expansion during focusing. This study provides a theoretical foundation for understanding the spin–orbit angular momentum interaction in high-NA lens systems and offers insights for applications in vector beam control, high-resolution imaging, and optical manipulation.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
