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 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.