Fraunhofer diffraction of Laguerre–Gaussian laser beam by helical axicon

In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre–Gaussian laser beam with “0” radial mode number and “l  ” azimuthal mode number (LG0l) by helical axicon. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the back focal plane of a convergent lens are derived in a form of product of a Gauss-doughnut function and a sum of hypergeometric Kummer functions. Also, the diffracted LG beam by axicon only, as well as by spiral phase plate only, and the diffracted Gaussian beam by helical axicon, are described mathematically in the back focal plane of a convergent lens. Different possibilities for obtaining output vortex beam with reduced or increased topological charge compared to that of the incident beam, or for obtaining chargeless beam are analyzed.