A general study of beams produced by a computer-generated hologram representing a diffraction grating with fringe
bifurcation is presented. Properties of output beams are considered in connection with violation of ideal geometrical
conditions: the input beam shape variations, its shifts and inclinations with respect to the grating. The basic
consequences are: (i) presence the "ripple" structure in both amplitude and phase distributions (especially in the nearfield
zone) caused by diffraction on the phase singularity (bifurcation point); (ii) in contrast to usual Gaussian beams
with exponential amplitude fall-off, diffracted beams demonstrate the power-law decay at the beam periphery; (iii) when
the incident beam axis is shifted from the grating center, an output beam with off-axial optical vortex is formed whose
spatial evolution tends to the pattern of self-similar rotation. Trajectories of featuring points of the generated optical-vortex
beam show regular angular deviation from the nominal positions, which grow with the incident beam shift
magnitude and with topological charge of the vortex produced.
Two types of paraxial light beams which show a sort of rotation around the propagation axis are studied. In beams with
"intrinsic" rotation (e.g., superpositions of Laguerre-Gaussian modes having the same waist and Gaussian envelope
radius) the transverse structure rotates during the free beam propagation because of certain internal reasons. The
transverse structure experiences the self-similar transformation, in which every point of the beam cross section moves as
if it performs a centrifugal fly-off due to inertia. In case of "extrinsic" rotation, a beam is set in rotation due to action of
some rotatory optical system. Such beams can be represented as superpositions of angular harmonics with different
frequencies. This "forced" rotation causes the angular momentum of the rotating beam which is proportional but
directed oppositely to the angular velocity ofthe rotation. This mechanical feature is associated with the complicated 3D
helical structure ofthe forcedly rotating beams.
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