Frenet-Serret analysis of helical Bloch modes in N-fold rotationally symmetric rings of coupled spiralling optical waveguides

Frenet-Serret (FS) analysis has previously been used to track the polarisation state evolution of a mode guided along a spiralling off-axis optical fibre core [1] . Here we present an analytical model, based in the local FS frame, for the properties of helical Bloch modes (HBMs) guided in a rotationally symmetric ring of N coupled cores that spiral around the axis of an optical fibre. The model takes full account of the curvature and torsion of the spiralling waveguides.