Optical vortices in twisted optical fibres with torsional stress

We solve the vector wave equation for twisted weakly guiding optical fibres using perturbation theory. It is demonstrated that the core modes of such fibres with azimuthal number l = 1 are presented by two circularly polarized optical vortices (OVs) with the unit topological charge and conventional TE and TM modes. We have also shown that the modes with l > 1 are formed by the circularly polarized OVs with the higher-order topological charges. All OVs are found to be robust under small external perturbations of the fibre's parameters. The corresponding propagation constants have been found and it is shown that the corrections induced by the twist are proportional to the total angular momentum of the OV. It is shown that, under certain conditions, the propagation through the twisted fibre of a linearly polarized OV with the unit topological charge is accompanied by rotation of the polarization plane, while the propagation of a circularly polarized Hermit-Gauss mode HG(01) is accompanied by rotation of the intensity pattern.