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 am
plitude 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.
The transverse beam pattern, usually observed in experiment, is a result of averaging the optical-frequency oscillations of the electromagnetic field distributed over the beam cross section. An analytical criterion is derived that these oscillations
are coupled with a sort of rotation around the beam axis. This criterion appears to be in direct relation with the usual definition of the beam orbital angular momentum.
