Vortex vector optical fields (VVOFs) refer to a kind of vector optical field with an azimuth-variant polarization and a helical phase, simultaneously. Such a VVOF is defined by the topological index of the polarization singularity and the topological charge of the phase vortex. We present a simple method to measure the topological charge and index of VVOFs by using a space-variant half-wave plate (SV-HWP). The geometric phase grating of the SV-HWP diffracts a VVOF into $\pm 1$ orders with orthogonally left- and right-handed circular polarizations. By inserting a polarizer behind the SV-HWP, the two circular polarization states project into the linear polarization and then interfere with each other to form the interference pattern, which enables the direct measurement of the topological charge and index of VVOFs.

中文翻译：

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用时变半波片测量涡旋矢量光场的拓扑电荷和折射率

涡旋矢量光场（VVOF）是指同时具有方位角变化的偏振和螺旋相位的矢量光场。这样的VVOF由极化奇点的拓扑指数和相涡的拓扑电荷定义。我们提出了一种简单的方法，通过使用空间变半波片（SV-HWP）来测量VVOF的拓扑电荷和指数。SV-HWP的几何相位光栅将VVOF衍射为$\pm \mathrm{1个}$正交的左手和右手圆极化的顺序。通过在SV-HWP后面插入偏振器，两个圆偏振状态会投射到线性偏振中，然后相互干扰形成干涉图样，从而可以直接测量VVOF的拓扑电荷和折射率。