Focal shift of radial varying polarized Bessel-Gauss beam with radial phase modulation

Focusing shift of Bessel-Gauss (BG) beam with radial varying polarization is investigated by vector diffraction theory in this article. The radial phase modulation is given by a function of radial direction angle θ and m. It was found that the focal shift only can be altered considerably by the phase modulation parameter m, and the focus region intensity shape is variable with the change of the others parameters except m, turning into different shapes such as multiple intensity rings, dark hollow focus without the focus shift. There is an interesting phenomenon that the focus shifts along with the horizontal axis when the phase modulation parameter m is changing, and the shifts distance is linearity to the variation of the phase modulation parameter m.