Higher order modes and topological phase in the coiled elliptical weakly guiding optical fibres

We study the structure of l = 1 modes in strongly elliptical coiled weakly guiding optical fibres. We establish analytically the expressions for the modes and their polarization corrections. We show that, at certain parameters of the fibre helix, the l = 1 modes are represented in the local Frenet frame by uniform elliptically polarized fields. We demonstrate that the modes turn into circularly polarized fields if the coiling-induced perturbation becomes larger than the intrinsic spin-orbit coupling. In this case the propagation constants comprise geometrically in-duced terms proportional to the spin angular momentum of the mode and a topological phase appears in the system. We show that the presence of such a geometric phase exhibits itself in the rotation of polarization plane of LP mode excited in the fibre. The rotation angle is found to be equal to the solid angle subtended by the coil.