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We consider the problem of singular beams in optics as a part of the generalquestions of interactions, shaping and transformations of vortex states withfractional topological charges in physics, in particular, in hydrodynamic andquantum mechanic. Starting from the representation of the fractional-ordervortex states as a superposition of infinite number of integer-order vorticeswith distinctive energy distributions (the vortex spectra) we showed that thesmooth wave front of the fractional vortex beam can either decay into anasymmetric array of integer-order vortices or, vice versa, the array of opticalvortices can be gathered together forming a smooth wave front with ahelicoid-shaped phase distribution under propagation in free space. We revealedthat a simple superposition of a finite number of the fractional-order vortexbeams enables us to shape symmetric singular beams with the integer-ordervortices of the desired topological charges.

The mutual transformations of fractional-order and integer-order optical vortices