Tunable topological boundary modes enabled by synthetic translation dimension

Topological boundary modes, which are localized at the edge of topological materials, have received significant attention for their various applications in robust waveguides, optical cavities, and topological lasers. To envision their further applications in tunable devices, we propose and demonstrate a scheme to dynamically manipulate topological boundary modes by exploiting the two translation parameters of photonic crystals. We find that the translation not only transports the Wannier state similar to conventional Thouless pumping but also induces a nonzero Chern number in the two-dimensional synthetic space while preserving the time-reversal symmetry in the real space. Through changing the translation, gapless and tunable topological boundary modes are demonstrated. As a specific application, we show a dynamic bandpass filter with real-time tuning over 100% bandgap, a capability that cannot be achieved with only one translation parameter. Our design opens a venue for the development of tunable topological devices based on synthetic parameter dimension and can be generalized to other bosonic systems.