M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon

The effects of axicons on the M-2 factor and kurtosis parameter of,super Gaussian beams(SGBs) are studied in detail. The closed-form expression for the M-2 factor of SGBs after passing, through an axicon, is derived, and the reason why the convergent and divergent axicons, give rise to the same increase of the M-2 factor is explained physically from the similarity of the resulting irradiance distributions. The analytical propagation equation of the K parameter of SGBs passing through an axicon followed by a paraxial optical ABCD system is given, some interesting special cases are discussed. In particular, it,is found. that even for the Gaussian special case the K parameter is no longer a constant due to the effect of the axicon. Numerical examples are also given to illustrate our analytical results.