Pancharatnam’s phase induced by spin-orbit interaction in weakly guiding twisted elliptical fibres

We derive the expressions for modes of weakly guiding twisted elliptical fibres and the polarization corrections to the scalar propagation constant of these modes in the framework of Jones matrix formalism in the re?ectionless approximation. Using these results, we demonstrate that the topological Pancharatnam’s phase in the twisted elliptical fibre appears due to spin-orbit coupling in fibres and is absent in the scalar approximation.