We have studied the coupling effect of topological photonic states in a double-channel magneto-optical photonic crystal waveguide by introducing a two-layer ordinary alumina (Al2O3) photonic crystal as the coupling layer. Interestingly, for the structure with the same widths of the two channels, the electromagnetic wave propagates one-way to the right side and exhibits wave-like path within the waveguide due to the coupling effect of topological photonic states. This unique property provides an effective way to achieve desired power ratio between two right outputs by terminating the structure at different length of waveguide. Moreover, the power ratio can be tuned by the external magnetic field conveniently. As for an asymmetric waveguide with different channel widths, there exist two asymmetric one-way topological photonic states (i.e., the odd-like and even-like modes) in the bandgap. The eigenfield analyses show that the electric field of odd-like mode is stronger in the lower channel, while that of even-like mode is contrary. As the old-like mode propagates rightwards, electromagnetic waves in the two channels couple with each other via the coupling layer, then the power in the upper channel gradually transfers to the lower channel, and finally reach almost 100% transmittance in the lower output. However, the case for the even-like mode is totally contrary. These results hold great promise for many application fields such as signal transmission, optical modulation, and the design of topological devices.
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