Topological Refraction in Kagome Split-Ring Photonic Insulators

A valley-Hall-like photonic insulator based on [Formula: see text] Kagome split-ring is proposed. Theoretical analysis and numerical calculations illustrate that [Formula: see text] symmetry can be broken not only by global rotation [Formula: see text] but also individual rotation [Formula: see text] of the split rings, providing topological phase transitions. Furthermore, refraction of the edge state from the interface into the background space at Zigzag termination is explored. It is shown that positive/negative refraction of the outgoing beam depends on the type of valley (K or [Formula: see text]), from which the edge state is projected. These results provide a new way to manipulate terahertz wave propagation and facilitate the potential applications in directional collimation, beam splitting, negative refraction image, etc.