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<p>Light carries both spin (polarization) and orbital angular momentum. Combining these degrees of freedom produces hybrid spin–orbit states that live in a high-dimensional Hilbert space, offering greater information capacity and robustness for optical communication, quantum technologies, and metrology. However, generating arbitrary states in these spaces and characterizing them efficiently has remained difficult. Here we show a compact metasurface that generates arbitrary spin–orbit states in a four-dimensional Hilbert space, visualized on a Poincaré hypersphere, with straightforward scalability to higher dimensions. Using a tetratomic unit cell, the single-layer device precisely controls complex amplitude, phase, and polarization. We further introduce an efficient interferometric scheme that reconstructs the full density matrix of any <i>N</i>-dimensional spin–orbit state using only three interferograms. This approach uncovers an intrinsic spin–orbit parity order that governs the symmetry of projected intensity patterns, independent of the weighting of the eigenmodes, and enables controlled mode transformations through higher-order geometric phases. These advances establish a versatile platform for high-dimensional photonic technologies.</p>

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Generic generation and manipulation of high-dimensional spin-orbit states in Hilbert space

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月24日

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  • Peijin Li,
  • Ruizhe Zhao,
  • Yang Cui,
  • Guangzhou Geng,
  • Junjie Li,
  • Xifeng Ren,
  • Yunkun Wu,
  • Yongtian Wang,
  • Shuang Zhang,
  • Lingling Huang

摘要

Light carries both spin (polarization) and orbital angular momentum. Combining these degrees of freedom produces hybrid spin–orbit states that live in a high-dimensional Hilbert space, offering greater information capacity and robustness for optical communication, quantum technologies, and metrology. However, generating arbitrary states in these spaces and characterizing them efficiently has remained difficult. Here we show a compact metasurface that generates arbitrary spin–orbit states in a four-dimensional Hilbert space, visualized on a Poincaré hypersphere, with straightforward scalability to higher dimensions. Using a tetratomic unit cell, the single-layer device precisely controls complex amplitude, phase, and polarization. We further introduce an efficient interferometric scheme that reconstructs the full density matrix of any N-dimensional spin–orbit state using only three interferograms. This approach uncovers an intrinsic spin–orbit parity order that governs the symmetry of projected intensity patterns, independent of the weighting of the eigenmodes, and enables controlled mode transformations through higher-order geometric phases. These advances establish a versatile platform for high-dimensional photonic technologies.