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  • Open Access

Quantitative relationship between in-plane and out-of-plane photonic spin Hall effects in vortex beams

Linguo Xie1,*, Qingsong Liu1, Hu Dou1, Zhaoxue Li2, and Xinxing Zhou3,†

  • 1Key Laboratory of Photonic and Optical Detection in Civil Aviation and Atmospheric Lidar Institute, Civil Aviation Flight University of China, Guanghan 618300, China
  • 2Xinjiang Key Laboratory for Luminescence Minerals and Optical Functional Materials, School of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi, Xinjiang 830054, China
  • 3Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, School of Physics and Electronics, Hunan Normal University, Changsha 410081, China

  • *Contact author: xielinguo05@163.com
  • †Contact author: xinxingzhou@hunnu.edu.cn
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Phys. Rev. B 112, 075402 – Published 1 August, 2025

DOI: https://doi.org/10.1103/k3vg-pgpd

Abstract

Over the years, the in-plane and out-of-plane photonic spin Hall effects (PSHEs) have been treated as two independent phenomena. In this work, we establish a unified framework that reveals the interrelationship between the in-plane and out-of-plane PSHEs for arbitrarily polarized vortex beams undergoing reflection and transmission. We quantitatively demonstrate how the vortex-induced in-plane spin spatial shift relates to the out-of-plane spin angular shift of the fundamental Gaussian beam (FGB). Similarly, we show that the vortex-dependent out-of-plane spin spatial shift is quantitatively connected to the in-plane spin angular shift of the FGB. Moreover, we find that the vortex-related in-plane and out-of-plane spin angular shifts remain unaffected by the FGB's in-plane and out-of-plane spin spatial shifts. Additionally, we confirm that all of our theoretical results adhere to the principles of linear and angular momentum conservation.

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Phys. Rev. B 112, 075402– Published 1 August, 2025
  • Received 16 March 2025
  • Revised 4 June 2025
  • Accepted 15 July 2025
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