We have studied the coupling effect of topological photonic states in a double-channel magneto-optical photonic crystal waveguide by introducing a two-stranded ordinary Al2O3 photonic crystal as the coupling layer. There exist both M1 (odd) and M2 (even) one-way modes simultaneously in the bandgap. Interestingly, M1 mode is always a fast-light mode with large group velocity (vg) and large group velocity dispersion (GVD) regardless what the radius (RA) of Al2O3 rods is. However, when RA is appropriate, M2 mode becomes a very slow-light mode exhibiting near-zero vg and zero GVD simultaneously. The physical reason of such slow-light is attributed to the strong coupling effect between the one-way edge modes in both sub-waveguides. Furthermore, the simulation results show that the robustness of both the fast- and slow-light modes are extremely strong against perfect electric conductor defect and the one-way transmittance is close to 100%. Besides, the PEC defect can cause significant phase delay. These results hold promise for many fields such as signal processing, optical modulation, and the design of various topological devices.

We have studied the transmission properties of odd/even one-way modes and their reversible conversion in a double-channel waveguide consisting of two magneto-optical photonic crystals (MOPCs) sandwiched with Al2O3 PC. There exist two pairs of even and odd modes, i.e., M1(even)/M2(odd) or M3(odd)/M4(even) modes, for the double-channel waveguides with one- or two-stranded coupling layer of Al2O3 rods, respectively. Among them, the M1, M2, and M3 modes are caused by the weak coupling strength of two sub-waveguides, while the M4 mode results from the strong coupling effect and supports dispersionless slow-light propagation. Furthermore, we realize the reversible conversion between odd and even modes (i.e., between M1 and M2 modes, or M3 and M4 modes) in the one- or two-stranded structure, respectively, by adjusting the length and position of the perfect electric conductor (PEC) defect properly to cause the desired significant phase delay along the upper and lower equivalent transmission paths. Additionally, we find that the robustness of the M1 even mode is poor because of extra excitations of counter-propagation modes near the right Brillouin boundary, while the other three modes have extremely strong robustness against PEC defects and their one-way transmittances are nearly 100%. These results hold promise for many fields, such as slow-light modulation and the design of topological devices.