Focal shift in tightly focused hybridly polarized Laguerre-Gaussian vector beams with zero radial index

Hybridly polarized Laguerre-Gaussian vector beams (HPLGVBs) with zero radial index are obtained based on the third type of Laguerre-Gaussian vector beams. Polarization distributions of HPLGVBs are controlled by the phase retardation of a wave plate. The ellipticity angle and polarization orientation angle are used to describe the polarization distributions of the HPLGVBs. The electric field intensity distributions of tightly focused HPLGVBs are analyzed in the focal plane by the Richards-Wolf vectorial diffraction method. It is found that the tightly focused HPLGVBs have a focal shift phenomenon. The dependence of the focal shift of the HPLGVBs on the different parameters is discussed in detail. The simulation results show that the magnitude of the focal shift is related to the polarization distribution, and the focal shift is quite obvious for large azimuthal mode index, long focal length, large numerical aperture, and narrow beam waist. The effective control of the focal shift will have great potential applications in optical micromanipulation.