Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress

In this paper we consider weakly guiding twisted optical fibres with torsional mechanical stress. We establish the structure of the modes and the propagation constants of such fibres by accounting for the coupling between modes with different azimuthal numbers. It is shown that the principle of the mode formation is based on a sort of selection rule, that allows only the coupling between modes with the same value of total angular momentum. It is demonstrated that the modes are optical vortices bearing the well-defined total angular momentum. Using the obtained mode structure, we show that such twisted fibres transform the incident Gaussian-like mode, possessing spin angular momentum, to the field with orbital angular momentum.