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arXiv · 2507.08817

Geometric quantification of photonic 4D spin-orbit states

Liang Fang·Jinman Chen·Jia Cheng·Xuqi Guo·Senlin Huang·Qinjun Chen·Chujun Zhao·Shuangchun Wen·Jian Wang
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Abstract

High-dimensional photonic states have significantly advanced the fundamentals and applications of light. However, it remains huge challenges to quantify arbitrary states in high-dimensional Hilbert spaces with spin and orbital angular momentum bases. Here we introduce a geometric method to quantify arbitrary states in a 4D Hilbert space by interferometrically mapping them to unified centroid ellipses. Specifically, nine Stokes parameters can be deduced from three ellipses to quantify the 4D spin-orbit states described by SU(4) Poincar\'e hypersphere. We verify its feasibility by detecting these spin-orbit states gotten by both free-space wave plates and few-mode fibers. For the first time, we completely quantify and reconstruct higher-order modal group evolution of a weakly guiding few-mode fiber under twist perturbation. This geometric quantification, beyond the classical Stokes polarimetry, may pave the way to multi-dimensional optical metrology, sensing, and high-dimensional classical or quantum communications.

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Liang Fang, Jinman Chen, Jia Cheng, Xuqi Guo, Senlin Huang, Qinjun Chen, Chujun Zhao, Shuangchun Wen, Jian Wang. 2025-06-28. Geometric quantification of photonic 4D spin-orbit states. https://arxiv.org/abs/2507.08817

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