Topological Edge States on Different Domain Walls of Two Opposed Helical Waveguide Arrays

Floquet topological insulators (FTIs) have richer topological properties than static systems. In this work, we designed different domain wall (DW) structures consisting of a Floquet photonic lattice with opposite helical directions. We investigated the existence and types of edge states in three shared coupling structures and the impact of these shared coupling structures on edge states. When two opposite helical lattices share a straight waveguide array coupling, the edge states are localized on the straight waveguide. When two opposite helical lattices share a clockwise (or anticlockwise) helical waveguide array coupling, the DWs consist of zigzag and bearded edges, but the positions of the zigzag and bearded edges of the shared clockwise waveguide array are different from those of the shared anticlockwise waveguide array. The slope and transmission rate of the edge states both vary with the degree of coupling between the shared waveguides. The characteristics of these edge states, such as transmission speed and band gap width, are also affected by the incidence angle, modulation phase factor, and helical radii, and the methods for controlling the edge states in different shared coupling structures are provided. This will help deepen our understanding of how topological structures influence the electronic and photonic properties of materials. This could also lead to combining topology with metasurface-based structured light, which would highlight many novel properties with great application potential for various fields, such as imaging, metrology, communication, quantum information processing, and light–matter interaction.