LAUSR

Abstract Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.