Abstract
We consider the oscillations of the orbital angular momentum in the vortex beams with fractional topological charges, taking into account the vortex influence, beam astigmatism, and the displacement of the center of gravity on the basis of the intensity momenta approach. We revealed also that base contribution gives the optical vortices and displacement of the center of gravity. In addition, we analyze the distribution of the current lines in the erf-G beams with the topological charge p=1/2, revealing that there are two types of the curves: (1) closed C-like lines and (2) the inner closed lines.
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