Propagation of super-Lorentzian beams through a paraxial ABCD optical system

Based on the Collins integral, analytical propagation formulae of super-Lorentzian (SL) SL01, SL10, and SL11 beams passing through a paraxial ABCD optical system are derived by means of the convolution theorem of the Fourier transform. The propagation properties of the SL01 and SL11 beams in free space are graphically illustrated with numerical examples. The power in the bucket of the SL01 and SL11 beams has been also examined in the far-field plane. This research is useful to the applications of super-Lorentzian beams.