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In this work, an explicit formula is deduced for identifying the orbitalangular moment (OAM) of vectorial vortex with space-variant state ofpolarization (SOP). Different to scalar vortex, the OAM of vectorial vortex canbe attributed to two parts: the azimuthal gradient of Pancharatnam phase andthe product of the azimuthal gradient of orientation angle of SOP and relevantsolid angle on the Poincar\'{e} sphere. With our formula, a geometricaldescription for OAM of light beams can be achieved under the framework of thetraditional Poincar\'{e} sphere. Numerical simulations for two types ofvectorial vortices have been carried on to confirm our presented formula anddemonstrate the geometrical description of OAM. Furthermore, the finding willpave the way for precise characterization of OAM charge of vectorial vortices.

Identifying orbital angular momentum of vectorial vortices with Pancharatnam phase and Stokes parameters