Generation and conversion of optical vortices in long-period helical core optical fibers

We theoretically study generation and conversion of optical vortices (OVs) in long-period helical core fibers (HCFs) produced by drawing from a perform with an eccentric core. Solving scalar waveguide equation in the helical coordinates we demonstrate that in such fibers topologically induced corrections to scalar propagation constants lead to convergence of spectral curves. At their intersection points a resonance coupling takes place between the fundamental and the vortex modes, as well as the coupling between OVs, whose topological charges differ by unity. This coupling leads to energy exchange between the coupled modes, which is manifested either in conversion of the input fundamental mode into an OV or transformation of an OV into the OV with higher by 1 (or lower, depending on core's helicity) value of the topological charge. This effect can be used for creation of all-fiber generators of singular beams from regular input beams. We also study effect of ellipticity of the core's form on transformation properties of HCFs and show that this leads to splitting of resonance fiber's parameters, at which conversion of left and right circularly polarized input regular beams into OVs occurs. We prove that in long-period HCFs one can neglect this effect due to reduction of polarization mode dispersion in twisted fibers.