The fine structure of the vortex-beams in the biaxial and biaxially-induced birefringent media caused by the conical diffraction

We consider the paraxial propagation of nondiffracting singular beams inside natural biaxial and biaxially-induced birefringent media in vicinity of one of the optical axes in terms of eigenmode vortex-beams, whose angular momentum does not change upon propagation. We have predicted a series of new optical effects in the natural biaxial crystals such as the stable propagation of vector singular beams bearing the coupled optical vortices with fractional topological charges, the conversion of the zero-order Bessel beam with a uniformly distributed linear polarization into the radially-, azimuthally- and spirally-polarized beams and the conversion of the space-variant linear polarization in the combined beam with coupled vortices. We have revealed that the field structure of the vortex-beams in the biaxially-induced crystals resembles that in the natural biaxial crystals and form the vector structure inherent in the conical diffraction. However, the mode beams in this case do not change the propagation direction as it takes place inside natural biaxial crystals.