Conversion of high-order Laguerre–Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre–Gaussian beam of azimuthal index l and radial index n = 0 (LGl,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre–Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.