Possibility of Forming Perfect Vortices from Bessel–Gaussian Beams.

Expressions are obtained for the position of the maximum Imax of the Fourier transform of a 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. Here, as the cone angle is reduced (and, therefore, the diffraction-free region increases), the distances between the maxima of the intensity distributions in the focal plane of the lens, corresponding to different magnitudes of the topological charge, increase. An expression is found for the position of the energy center of the Fourier transform of the BGB 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 γw0 increases, the shift in the energy center of the BGB relative to the radius R of the annular Fourier spectrum in the approximation of geometric optics decreases. These results reveal the impossibility of forming perfect vortices with a BGB. Here the degree of their "imperfection" is determined by the deviation of the maximum of the intensity distribution in the focal plane of the lens on the parameter R which specifies the radius of the ring of the Fourier image of the Bessel beam, which is greater for beams with a larger diffraction-free region. [ABSTRACT FROM AUTHOR]