Diffraction of Laguerre-Gaussian Beam by a Helical Axicon

In this article the transformation of the Laguerre-Gaussian beam with radial mode number n and azimuthal mode number l, into a vortex, diverging or nondiverging Bessel beam with increased, decreased or zeroth phase singularity order has been investigated theoretically. We deduce and study analytical expressions for the amplitude and intensity distribution of the diffracted wave field in the process of Fresnel diffraction, using the stationary phase method, and also, for the vortex radius and the propagation distance of the output field.