Propagation of Bessel-Gaussian beams through a Spiral Phase Plate: Generation of Donut Humbert beam of type-II

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