Helical core optical fibers maintaining propagation of a solitary optical vortex

We study theoretically the mode structure of few-mode helical core optical fibers with small (up to a wavelength order) values of the helix pitch. We demonstrate that in such fibers, at certain values of pitch the fundamental HE₁₁ mode strongly hybridizes with $l=1$ optical vortices and the forbidden zone appears in the spectra of such hybrid modes, which results in their attenuation. We have shown that within the spectrum gap, the only forward-propagating guiding modes are represented by two circularly polarized optical vortices with opposite polarization and the same topological charge so that upon excitation of such a fiber with a circularly polarized beam, only a solitary optical vortex could be excited in it. Such ``monovortex'' fibers are found to be analogous to conventional monomode fibers that maintain the propagation of the HE₁₁ mode.