Gouy phase and phase singularities of tightly focused, circularly polarized vortex beams

An investigation is made of the phase properties, especially the Gouy phase of the tightly focused, circularly polarized vortex beams. First two groups of symmetry relations of the focused field are derived, from which the effect of the topological charge on the field can be found easily. By decomposing the electric field into three specific components, the corresponding Gouy phases are defined and their properties are examined in detail. Our result shows that not only the polarization of the incident field or the numerical aperture influence the phase behavior, but also the topological charge gives much contribution to the phase structure near the focus.