Transformation of a circularly obstructed Bessel beam by a fork-shaped grating

We theoretically investigate the transformation of a nondiverging Bessel beam with phase singularity n, which is transversally obstructed by a circular aperture, in the process of its diffraction by a fork-shaped grating with integer topological charge (TC) p. Analytical expressions describing the diffracted wave field amplitude and intensity distributions are derived and analyzed. The diffracted beams are nondiverging in a defined propagation interval, which is calculated. The zeroth-diffraction-order beam has TC same as that of the incident beam. However, the TC of the higher-diffraction-order beams can be increased or reduced compared to that of the incident beam, or it can be equal to zero. Also, the expressions for the radii of the central bright spot (if the beam is without TC) and of the vortex core (if the beam is with phase singularity) are derived.