Unidirectional self-imaging in multiple shifted photonic crystal interfaces.

In this study, we investigate the unidirectional self-imaging phenomenon in the shifted photonic crystal (PC) heterostructure. A spin-locked topological edge state, which originates from the mismatch of the Wannier center positions, can propagate along the shifted PC interface without backscattering. When the neighboring shifted PC interfaces are close enough, the coupling between the edge states happens, and coupled edge states (CES) can be found. Based on the finite element method (FEM) simulation, the spin-locked multimode interference (MMI) and self-imaging phenomenon of CES, including paired and symmetrical interference, are achieved in multiple shifted PC interfaces. To illustrate the application of the frequency splitters, the T-shaped and double cross-shaped structures with backscattering immunity and spin-locked characteristics are proposed. Our work provides an alternative way toward the design of a topological splitter by utilizing the photonic frequency and spin degrees of freedom at the same time.