Focal shift in spatial-variant polarized vector Bessel-Gauss beams

The three dimensional intensity distribution of focused spatial-variant polarized vector Bessel-Gauss beams is investigated in the vicinity of the focal plane by using the Richards-Wolf vectorial diffraction method. The local polarized states of the incident beams vary between linearity and ellipse, and can be easily controlled in real time by a new parameter, namely the phase delay angle, which is introduced by a liquid crystal variable retarder. Our analysis proves the existence of a focal shift toward the focusing objective for this type of beam. The dependence of the focal shift on the different parameters of the beams is discussed in detail. Numerical results indicate that the magnitude of the focal shift is associated with the mode number, the local polarization, the beam width and the wavelength of the incident beams. The controllability of the focal shift indirectly caused by the phase delay angle will have great potential applications in optical micro-manipulation.