We have considered the paraxial vector erf-Gaussian beams with field distribution in the form of the error function that are shaped by the cone of plane waves with a fractional step of the azimuthal phase distribution modulated by the Gaussian envelo
pe. We have revealed that the initial distributions of the transverse electric and transverse magnetic fields have the form far from standard ones but at the far diffraction field the field distributions recover nearly the symmetric form. We have also revealed that the half-charged vortices in one of the field components can propagates up to the Rayleigh length without essential structural transformations but then splits into an asymmetric net of singly charged vortices.
We have theoretically predicted the gigantic spikes of the orbital angular momentum caused by the conversion processes of the centered optical vortex in the circularly polarized components of the elliptic vortex beam propagating perpendicular to the
crystal optical axis. We have experimentally observed the conversion process inside the subwave deviations of the crystal length. We have found that the total orbital angular momentum of the wave beam is conserved.
The splitting of a single optical vortex into four separate ones in a singular beam is theoretically and experimentally described for the propagation of light obliquely through a uniaxial crystal. Also we found the condition under which the new-born
vortices in each four individual beams propagate independently without dislocation reactions and have different locations in all beams for any crystal lengths.
