Pancharatnam-Berry geometric phase has attracted enormous interest in subwavelength optics and electromagnetics during the past several decades. Traditional theory predicts that the geometric phase is equal to twice the rotation angle of anisotropic elements. Here, we show that high-order geometric phases equal to multiple times the rotation angle could be achieved by meta-atoms with highfold rotational symmetries. As a proof of concept, the broadband angular spin Hall effect of light and optical vortices is experimentally demonstrated by using plasmonic metasurfaces consisting of space-variant nanoapertures with C2, C3, and C5 rotational symmetries. The results provide a fundamentally new understanding of the geometric phase as well as light-matter interaction in nanophotonics.

中文翻译：

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旋转对称元原子中的广义Pancharatnam-Berry相

在过去的几十年中，Pancharatnam-Berry几何相位已经引起了人们对亚波长光学和电磁学的极大兴趣。传统理论预测，几何相位等于各向异性元素旋转角的两倍。在这里，我们表明，具有高旋转对称性的亚原子可以实现等于旋转角倍数的高阶几何相位。作为概念的证明，通过使用由具有C2，C3和C5旋转对称性的时变纳米孔径组成的等离子超表面，实验证明了光和光学涡旋的宽带角自旋霍尔效应。结果为纳米光子学中的几何相位以及光-质相互作用提供了全新的认识。