Vectorial structure of arbitrary vector vortex beams diffracted by a circular aperture in the far field

In terms of the vector angular spectrum representation and the method of stationary phase, the analytical vectorial structure of the arbitrary vector vortex Laguerre-Gaussian beam on the higher-order Poincaré sphere diffracted by a circular aperture is obtained in the far field. The far-field energy flux distributions of the arbitrary apertured vector vortex beams including cylindrical vector beam, circularly polarized vortex beam, and elliptically polarized vortex beam are numerically demonstrated from the vectorial structure. The analyses show that the topological charge, the truncation parameter, and the ellipticity angle play an important role in the vectorial structure and the evolution properties of the apertured vector vortex beam in the far field. This research is useful for manipulating the vector vortex beams by adjusting states of polarization on the higher-order Poincaré sphere.