The Nested Topological Band-Gap Structure for the Periodic Domain Walls in a Photonic Super-Lattice

We study the nested topological band-gap structure of one-dimensional (1D) photonic super-lattices. One cell of the super-lattice is composed of two kinds of photonic crystals (PhCs) with different topologies so that there is a domain wall (DW) state at the interface between the two PhCs. We find that the coupling of periodic DWs could form a new band-gap structure inside the original gap. The new band-gap structure could be topologically nontrivial, and a topological phase transition can occur if the structural or material parameters of the PhCs are tuned. Theoretically, we prove that the Hamiltonian of such coupled DWs can be reduced to the simple Su–Schrieffer–Heeger (SSH) model. Then, if two super-lattices carrying different topological phases are attached, a new topological interface state can occur at the interface between the two super-lattices. Finally, we find the nested topological band-gap structure in two-dimensional (2D) photonic super-lattices. Consequently, such nested topological structures can widely exist in complex super-lattices. Our work improves the topological study of photonic super-lattices and provides a new way to realize topological interface states and topological phase transitions in 1D and 2D photonic super-lattices. Topological interface states in super-lattices are sensitive to frequency and have high accuracy, which is desired for high-performance filters and high-finesse cavities.