On the coupling of two helical waveguides

Coupling between optical waveguides has always been an important topic. By using the finite element method (FEM) based on a helicoidal coordinate system, we present a detailed study of the couplings between two helical coupled circular waveguides, showing several important aspects that were not found in previous studies. Our numerical results show that for the two-fold rotationally symmetric cases, intersections will appear in the effective index curves of the two composite modes with increasing twist rate, and we have found that this is related to the different increases of the composite modes in the helical path and the emergence of high-order harmonics. Further, for the one-fold rotationally symmetric structures formed by the two waveguides with the same radical but different azimuthal positions, as the twist rate increases, we observe the emerging asymmetric modal distributions of the composite modes, indicating that couplings between the two waveguides are no longer equivalent.