  A vector wave analysis of nondiffracting beams propagating along a
birefringent chiral crystal for the case of tensor character both of the
optical activity and linear birefringence is presented, fields of eigen modes
satisfying vector wave equation. We have written characteristic equations and
found propagation constants and amplitude parameters of eigen modes. We have
shown that the field of eigen modes is non-uniformly polarized in the beam
cross-section. We have revealed that even a purely chiral crystal without a
linear birefringent can generate optical vortices in an initially vortex-free
Bessel beam.
