  Special features of the optical-vortex (OV) beams generated by thick
holographic elements (HE) with embedded phase singularity are considered
theoretically. The volume HE structure is based on the 3D pattern of
interference between an OV beam and a standard reference wave with regular
wavefront. The incident beam diffraction is described within the framework of a
linear single-scattering model in which the volume HE is represented by a set
of parallel thin layers with the "fork" holographic structure. An explicit
integral expression is derived for the complex amplitude distribution of the
diffracted paraxial beam with OV. The numerical analysis demonstrates that the
HE thickness may essentially influence not only selectivity and efficiency of
the OV beam generation but also the amplitude and phase profile of the
diffracted beam as well as regularities of its propagation. We have studied the
generated OV morphology and laws of its evolution; in particular, the
possibility of obtaining a circularly symmetric OV beam regardless of the
diffraction angle is revealed.
