About Possibility of Formating Perfect Vortices from Bessel-Gaussian Beams

Abstract

In this paper, we received equations determining the position of maximum I_max of the Fourier transformation of the Bessel–Gaussian beam (BGB), and its dependence on the topological charge is substantiated. It is found that Imax depends on the angle of the cone and the parameters of the Gaussian beam. Meanwhile, with a decrease in the cone angle (hence, an increase in the diffraction-free region), the distance between the maxima of the intensity distributions in the focal plane of the lens, corresponding to different values of the topological charge, increases. An expression for the position of the gravity center of the BGB Fourier image is found and it is shown that it also depends on the cone angle γ and the size of the Gaussian beam waist w₀. As the product γ w₀ increases, the displacement of the BGB gravity center with respect to the radius R of the annular Fourier spectrum decreases. The results obtained show the impossibility of forming perfect vortexes with the help of BGB. In this case, the degree of their “imperfection”, determined by the deviation of the maximum intensity distribution in the focal plane of the lens from the parameter R, which specifies the radius of the ring of the Fourier image of the Bessel beam, turns out to be greater for beams with a larger diffraction-free region.