Generation of donut Humbert beam of type-II

A new family of donut beams known as Humbert beam of type-II was developed by converting the Bessel-Gauss beams that were travelling through an ABCD paraxial optical system with a spiral phase plate. The superposition of Whittaker beam can be used to represent the amplitude field of Humbert beam of type-II. The transformation and propagation of the Bessel-Gauss beams using a spiral phase plate after propagating the examined optical system, is shown and deduced in detail. To investigate the comportment of Humbert beams of type-II in free space and through telescope, numerical simulations are performed.