Propagation of vectorial Lorentz beam beyond the paraxial approximation

Based on the vectorial Rayleigh–Sommerfeld integrals, the analytical propagation expression of vectorial Lorentz beam beyond paraxial approximation is presented. The far field expression and the scalar paraxial result are obtained as special cases of the general formulae. According to the analytical representation, the light intensity distribution of vectorial Lorentz beam is depicted at the different reference planes. This research provides an approach to further investigate the propagation of Lorentz beam beyond the paraxial approximation.