Interaction Between Two One-Way Waveguides

The interaction between two (parallel) one-way waveguides formed by photonic crystals is investigated theoretically. It is shown that when the two waveguides support modes propagating in opposite directions, they can effectively interact with each other only within a narrow guiding region where their propagation constants are nearly zero. In this coupling window, the waveguides are contra-directionally coupled and the efficiency grows monotonously with the coupling length, reaching 100% as the coupling length is large enough. When the one-way waveguides support the modes propagating in the same direction, they may be efficiently coupled through the whole guiding regime, and their coupling exhibits the same behavior as the conventional uniform waveguides. The coupling between the one-way waveguides is first analyzed with the coupled-mode approximation and then verified by rigorous numerical simulation.