  Spatial characteristics of diffracted beams produced by a "fork" hologram
from an incident circular Laguerre-Gaussian beam whose axis differ from the
hologram optical axis are studied theoretically. General analytical
representations for the complex amplitude distribution of a diffracted beam are
derived in terms of superposition of Kummer beams or hypergeometric-Gaussian
beams. The diffracted beam structure is determined by combination of the
"proper" topological charge m of the incident vortex beam and the topological
charge l of the singularity "imparted" by the hologram. Evolution of the
diffracted beam structure is studied in detail for several combinations of m
and l and for various incident beam displacements with respect to the optical
axis of the hologram. Variations of the intensity and phase distribution due to
the incident beam misalignment are investigated and possible applications for
the purposeful optical-vortex beam generation and optical measurements are
discussed.
