On the coupling of two helical circular waveguides

Coupling between optical waveguides has always been an important topic. By using the finite element modeling 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 the previous studies. Our numerical results show that for the two-fold rotationally symmetric cases, a series of intersections will appear in the effective index curves of the two composite modes with increasing twist rate and as we point out, this is related to the different increases 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 we report for the first time, to our best knowledge, on the asymmetric coupling between the two waveguides. It is found that intensity distributions in the two waveguides are no longer equivalent but azimuthally dependent.