Focus evolution of linearly polarized Lorentz beam with sine-azimuthal variation wavefront induced by one on-axis optical vortex

Focus evolution of linearly polarized Lorentz beam with sine-azimuthal variation wavefront induced by one on-axis optical vortex was investigated theoretically in this article. Calculation results show that the focal pattern can be altered considerably by the charge number of on-axis optical vortex under condition of certain beam parameters and phase parameter that indicates the sine phase change frequency on increasing azimuthal angle. And the focal evolution principle differs remarkably for different beam parameters and the phase parameter. In focus evolution process, some novel focal patterns appear, including annular focal pattern, two-peak focal pattern, intensity lines, hexagon containing two peaks, swallowtail shape, multipede shape, and complex focal pattern. Introduction of optical vortex adds one controllable parameter to alter focal pattern, which may extend application of Lorentz beam in some focusing systems.