Influence of Hyperbolic Vertex on Axicon-Focusing Cylindrical Vector Beams

In this study, we investigate the axicon-focusing characteristics of a cylindrical vector beam based on the Rayleigh-Sommerfeld vector diffraction theory and the amplitude transmittance function. The results prove that the vector focus field of a radially polarized beam comprises radial and longitudinal components, whereas that of an azimuthally polarized beam only comprises an azimuthal component. Further, the focus depth of the focus field increases with the increasing waist radius of the beam. When compared with the ideal case, the focal depth of the focus field remains almost unchanged when the axicon apex is hyperbola; however, its intensity oscillates because of the interference effect, which is dependent on the waist radius of the incident beam. This oscillation phenomenon disappears when the waist radius of the radially and azimuthally polarized beams arc 4 mm and 3.5 mm, respectively. The obtained results provide a reference for the practical application of the axicon systems and the improvement of the theory of cylindrical vector beam focusing.