Bulk-Edge Correspondence and Multiplexing Topological Routings in Gyromagnetic Photonic Weyl Metamaterials

The bulk-edge correspondence principle stands among topological photonics'most impactful and broadly relevant theoretical breakthroughs. In this work, various topological phases are systematically studied and establish the bulk-edge correspondence in three-dimensional (3D) gyromagnetic photonic Weyl metamaterials. It is proved that the Weyl points with nonzero chiralities are the critical points of multiple topological phase transitions. Based on rigorous theoretical analysis, the comprehensive depictions of the topological phase diagrams are further mapout for multi-type bulk-edge correspondences in gyromagnetic metamaterials. It is demonstrated that topological edge state sexist not only on a vacuum-metamaterial boundary but also on more general different topological phases metamaterial-metamaterial boundary. Notably, the copropagating topological edge states physically originate from the nonzero large gap Chern numbers. Moreover, multichannel and multiplexing topological photonic routings are realized by leveraging the unique characteristics of unidirectional and scattering-immunity edge states. Itis theoretically reveal that the physical mechanisms of producing such multiplexing topological photonic routings are caused by the gap Chern number-locking properties of the chiral and copropagating topological edge waves.