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We have considered the paraxial vector erf-Gaussian beams with fielddistribution in the form of the error function that are shaped by the cone ofplane waves with a fractional step of the azimuthal phase distributionmodulated by the Gaussian envelope. We have revealed that the initialdistributions of the transverse electric and transverse magnetic fields havethe form far from standard ones but at the far diffraction field the fielddistributions recover nearly the symmetric form. We have also revealed that thehalf-charged vortices in one of the field components can propagates up to theRayleigh length without essential structural transformations but then splitsinto an asymmetric net of singly charged vortices.

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