Generation of doughnut Humbert beam by a gradient-index medium

In this paper, we generate a new doughnut Humbert beam from a Whittaker-Gaussian (WG) beam propagating through a gradient-index medium (GIM). Based on the extended Huygens-Fresnel diffraction integral, the analytical expression of the intensity distribution for doughnut Humbert beam is derived and discussed through numerical examples. The obtained results indicate that the diffracted beam evolves periodically versus the propagation distance in GIM 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.