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.
We study the light propagation in the twisted anisotropic optical fibers endowed with torsional mechanical stress by obtaining the analytical solution o f the vector wave equation. We show that at certain interplay between fiber parameters optical vortex beams o f topological charge l = 0 ,± 1 ,± 2 ,... become the modes o f the fibers in question. To explain the splitting of the optical vortex propagation constants we introduce the notions of orbital birefringence and optical Zeeman effect. Moreover, we unveil that induced by torsional stress circular birefringence makes the vortex beams with the well-defined orbital angular momentum robust against small perturbations characterized by both constant and spatially varying orientation o f a director. We believe that such fibers can be successfully utilized for the long-range robust transmission of information encoded in the light's orbital degrees o f freedom.
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