Propagation characteristics of the kurtosis parameters of flat-topped beams passing through fractional Fourier transformation systems with a spherically aberrated lens

Abstract

Based on the Collins diffraction integral formula and irradiance moment definition, the propagation characteristics of the kurtosis parameters of flat-topped beams passing through fractional Fourier transformation systems with spherically aberrated lenses are studied in detail. By introducing an efficient algorithm, numerical calculations are performed and the results show that under certain conditions the evolution characteristics of the kurtosis parameters of a flattened-Gaussian beam passing through the fractional Fourier transformation systems with spherically aberrated lenses are very similar to those of a super-Gaussian beam, but they are different from the propagation characteristics of the kurtosis parameter of a flat-topped beam defined by Yajun. It is also shown that the kurtosis parameters of a flat-topped beam passing through two optical setups are very different. It is implied that the two optical setups for implementing the fractional Fourier transformation are no longer equal in the presence of spherically aberrated lenses. We also find that the kurtosis parameters change with the fractional orders periodically and the fundamental periods for the two optical setups with spherically aberrated lenses are different.