Propagation of the kurtosis parameter of Hollow higher-order Cosh Gaussian beams through paraxial optical ABCD system

Based on the second-order and fourth-order irradiance moments, the closed-form of the propagation of the kurtosis parameter of non-truncated Hollow higher-order Cosh-Gaussian beam passing through an ABCD optical system was derived. Some numerical examples to illustrate the analytical results were given. The kurtosis parameter of some particular cases such, as fundamental Gaussian, Cosh-Gaussian and higher Cosh-Gaussian beams are also can be deduced from the main formula of this study. The obtained results were consistent with the previous works and constitute a more generalized investigation of kurtosis parameter of laser beams.

Automated summary

In this study, the closed-form of the propagation of the kurtosis parameter of non-truncated Hollow higher-order Cosh-Gaussian beam passing through an ABCD optical system was derived based on the second-order and fourth-order irradiance moments. Numerical examples were provided to illustrate the analytical results. The kurtosis parameter of specific cases such as fundamental Gaussian, Cosh-Gaussian, and higher Cosh-Gaussian beams can also be deduced from the main formula of this study. The obtained results are consistent with previous works and offer a more comprehensive investigation of the kurtosis parameter of laser beams.