Focusing of linearly polarized Lorentz–Gauss beam with one optical vortex

Focusing properties of linearly polarized Lorentz–Gauss beam with one on-axis optical vortex was investigated by vector diffraction theory. Results show that the focal pattern can be altered considerably by charge number of the optical vortex and the beam parameters. Many novel focal patterns may occur, such as dark hollow focus, multiple-peak focal pattern, and dark hollow focus chain. For certain beam parameter, the focal pattern changes more remarkably in the direction perpendicular to the incident polarized direction than that in polarized direction. Especially, there is one clear relation between the intensity distributions along the direction perpendicular to the polarized direction and the charge number of the optical vortex, which may be used as one measurement method of charge number.