  Interferometers and beam splitters are fundamental building blocks for
photonic neuromorphic and quantum computing machinery. In waveguide-based
photonic integrated circuits, beam-splitting is achieved with directional
couplers that rely on transition regions where the waveguides are adiabatically
bent to suppress back-reflection. We present a novel, compact approach to
introducing guided mode coupling. By leveraging multimodal domain walls between
microwave topological photonic crystals, we use the photonic-spin-conservation
to suppress back-reflection while relaxing the topological protection of the
valley degree of freedom to implement tunable beam splitting. Rapid
advancements in chip-scale topological photonics suggest that the proposed
simultaneous utilization of multiple topological degrees of freedom could
benefit the development of novel photonic computing platforms.
