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We consider the paraxial propagation of nondiffracting singular beams insidenatural biaxial and biaxially-induced birefringent media in vicinity of one ofthe optical axes in terms of eigenmode vortex-beams, whose angular momentumdoes not change upon propagation. We have predicted a series of new opticaleffects in the natural biaxial crystals such as the stable propagation ofvector singular beams bearing the coupled optical vortices with fractionaltopological charges, the conversion of the zero-order Bessel beam with auniformly distributed linear polarization into the radially-, azimuthally- andspirally-polarized beams and the conversion of the space-variant linearpolarization in the combined beam with coupled vortices. We have revealed thatthe field structure of the vortex-beams in the biaxially-induced crystalsresembles that in the natural biaxial crystals and form the vector structureinherent in the conical diffraction. However, the mode beams in this case donot change the propagation direction as it takes place inside natural biaxialcrystals.

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