  Spatial characteristics of diffracted beams produced by the "fork" holograms
from incident circular Lauerre-Gaussian modes are studied theoretically. The
complex amplitude distribution of a diffracted beam is described by models of
the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most
cases its structure is formed under the influence of the divergent spherical
wave originating from the discontinuity in the beam spatial profile or its
derivatives caused by the hologram's groove bifurcation. Presence of this wave
is manifested by the ripple structure in the near-field diffracted beam
profiles and in the power-law amplitude decay at the beam periphery. Conditions
when the divergent wave is not excited are discussed.
  The diffracted beam carries a screw wavefront dislocation (optical vortex)
whose order equals to algebraic sum of the incident beam azimuthal index and
the topological charge of the singularity imparted by the hologram. The input
beam singularity can be healed when the above sum is zero. In such cases the
diffracted beam can provide better energy concentration in the central
intensity peak than the Gaussian beam whose initial distribution coincides with
the Gaussian envelope of the incident beam. Applications are possible for
generation of optical-vortex beams with prescribed properties and for analyzing
the optical-vortex beams in problems of information processing.
