  We consider the problem of singular beams in optics as a part of the general
questions of interactions, shaping and transformations of vortex states with
fractional topological charges in physics, in particular, in hydrodynamic and
quantum mechanic. Starting from the representation of the fractional-order
vortex states as a superposition of infinite number of integer-order vortices
with distinctive energy distributions (the vortex spectra) we showed that the
smooth wave front of the fractional vortex beam can either decay into an
asymmetric array of integer-order vortices or, vice versa, the array of optical
vortices can be gathered together forming a smooth wave front with a
helicoid-shaped phase distribution under propagation in free space. We revealed
that a simple superposition of a finite number of the fractional-order vortex
beams enables us to shape symmetric singular beams with the integer-order
vortices of the desired topological charges.
