Special features of the optical-vortex (OV) beams generated by thickholographic elements (HE) with embedded phase singularity are consideredtheoretically. The volume HE structure is based on the 3D pattern ofinterference between an OV beam and a standard reference wave with regularwavefront. The incident beam diffraction is described within the framework of alinear single-scattering model in which the volume HE is represented by a setof parallel thin layers with the "fork" holographic structure. An explicitintegral expression is derived for the complex amplitude distribution of thediffracted paraxial beam with OV. The numerical analysis demonstrates that theHE thickness may essentially influence not only selectivity and efficiency ofthe OV beam generation but also the amplitude and phase profile of thediffracted beam as well as regularities of its propagation. We have studied thegenerated OV morphology and laws of its evolution; in particular, thepossibility of obtaining a circularly symmetric OV beam regardless of thediffraction angle is revealed.
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