Parametric characterization of Mathieu-Gauss beams

Based on the irradiance moments definitions, the expression of MG2 factor of truncated zeroth-order Mathieu-Gauss beams (MGBs) is derived analytically. Furthermore, the propagation equation of kurtosis parameter of non-truncated MBGs passing through a paraxial ABCD optical system is established. Particularly, the dependence of MG2 factor and kurtosis parameter on the spatial profile of the beam are illustrated numerically and analyzed in details.