用Pancharatnam相位和Stokes参数识别矢量涡的轨道angular momentum
Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters
摘要：
本文推导了一个确定矢量涡旋空间变偏振态轨道角动量的显式公式。与标量涡旋不同，矢量涡旋的OAM可以归结为两部分：Pancharatnam相的方位角梯度和SOP的取向角的方位角梯度与Poincaré球上相关立体角的乘积。利用该公式，可以在传统的庞加莱球框架下对光束的OAM进行几何描述。对两种矢量涡进行了数值模拟，验证了所提出的公式，并验证了OAM的几何描述。此外，这一发现将为矢量涡OAM荷的精确表征铺平道路。
英文摘要：
In this work, an explicit formula is deduced for identifying the orbital angular moment (OAM) of vectorial vortex with space-variant state of polarization (SOP). Different to scalar vortex, the OAM of vectorial vortex can be attributed to two parts: the azimuthal gradient of Pancharatnam phase and the product of the azimuthal gradient of orientation angle of SOP and relevant solid angle on the Poincaré sphere. With our formula, a geometrical description for OAM of light beams can be achieved under the framework of the traditional Poincaré sphere. Numerical simulations for two types of vectorial vortices have been carried on to confirm our presented formula and demonstrate the geometrical description of OAM. Furthermore, the finding will pave the way for precise characterization of OAM charge of vectorial vortices.
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