Berry's phase for optical vortices in coiled optical fibres

We study theoretically the manifestation of Berry's topological phase in the propagation of higher order (l >= 1) modes of helical weakly guiding fibres. We have shown that in coiled fibres higher order modes are represented either by pure circular optical vortices (at l > 1) or by circular optical vortices and the TE and TM modes (at l = 1). We have established that pure modes upon propagation in coiled fibres acquire an additional topological phase proportional to the intrinsic angular momentum of the mode and to the solid angle subtended by one helix coil. We have studied the influence of this geometric phase on the propagation of composite fields in helical fibres. We have shown that the topological effects result in an overall rotation of the intensity and polarization patterns. We have found that the angle of the pattern rotation is equal to the solid angle subtended by one coil. We have also shown that the angle by which the local polarizations rotate does not coincide, in a general case, with the angle of the pattern rotation: for certain cases it was found to be proportional to the angular momentum of the constituent modes.