Vector erf-Gaussian beams: fractional optical vortices and asymmetric TE and TM modes

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 envelope. We have revealed that the initial distributions of the transverse electric and transverse magnetic fields have a far from standard form but at the far diffraction field the field distributions recover nearly the symmetric form.