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.

A self-contained method of solving the wave equation in the presence of acoustic periodic waves propagating along optical fibres has been developed. As an example, the structure of the modes, and the corresponding spectrum of the propagation constants of an ideal optical fibre in which the flexural acoustic wave propagates have been established. On the basis of the obtained results a rigorous explanation has been given of the experimentally observed effect of the optical frequency upshifting or downshifting, which accompanies the corresponding mode conversion.

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