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Compared with symmetric directional couplers (DCs), asymmetric DCs constructed by two or over two different parallel waveguides offer a more flexible structure and allow for easier expansion of mode channels. In this Letter, we propose a kind of asymmetric topological DC based on two different valley photonic crystal waveguides (VPCWs). According to the coupled-mode theory, phase matching induces the complete coupling for the guide modes of two different VPCWs, whereas significant phase mismatching indicates no coupling occurs. Furthermore, the asymmetric topological DCs exhibit backscattering immunity and anti-disturbance robustness owing to the topological edge states (TESs), which greatly improve the performance of asymmetric DCs. We further design a new, to the best of our knowledge, kind of topological polarization beam splitter (TPBS) at the communication wavelength of 1550 nm by ensuring that the transverse electric mode satisfies the phase matching condition, while the transverse magnetic mode is phase-mismatched. The simulated results demonstrate that the proposed TPBS exhibits highly effective polarization separation and is robust against defects. This design holds significant potential for applications in optical communication systems.
He et al. (Tue,) studied this question.