Radially polarized Lorentz-Gauss vortex beam with sine-azimuthal variation wavefront

Radially polarized Lorentz-Gauss vortex beam with sine-azimuthal variation wavefront was proposed and its focusing properties were investigated by vector diffraction theory. The effect of phase parameter on focal pattern is very considerable, and some novel intensity pattern comes into being under certain focusing condition, including multiple-peaks, crescent shape, multiple intensity lines, intensity cross. Especially, the symmetry characteristics are systematical on increasing phase parameter. For case of even number of phase parameter, there are two symmetric axes for whole focal pattern, while there is only one symmetric axis for odd number of phase parameter. When topological charge is small, the intensity maximum shifts within small distance range, while intensity maximum may switch for higher topological charge in focal pattern evolution process.