Propagation analysis of Whittaker–Gaussian laser beam in a gradient-index medium

In this paper, the propagation of Whittaker–Gaussian beam passing through a gradient-index (GRIN) medium is studied. Based on the extended Huygens–Fresnel diffraction integral, the analytical expression of the intensity distribution for the resulting beam called Humbert beam is derived and discussed through numerical examples. The obtained results indicate that the diffracted beam evolves periodically versus the propagation distance in GRIN and its behavior depends interestingly on the beam initial parameters and the gradient-index parameter. Our results can be useful for some applications such as in multi-dimensional optical manipulation, remote sensing domain and imaging.