A Nonlocal Effective Medium Description of Topological Weyl Metamaterials

Effective medium theory lays the foundation for the development of metamaterials-artificially engineered photonic medium with subwavelength building blocks. However, the nonlocal effects, which are difficult to be incorporated into the effective medium description, are usually unavoidable in most metamaterial systems due to the finite lattice constant, preventing a precise modeling of wave propagation inside a metamaterial of large scale. On the other hand, recent development shows that nonlocal effect is essential for designing certain topological photonic systems such as ideal Weyl metamaterial. The properties of topological metamaterials rely on nonlocal effects, which, for example, determine whether a Weyl degeneracy formed by the linear crossing between a longitudinal and a transverse mode belongs to type I or type II. Here a nonlocal effective medium description of topological metamaterials is developed. For the first time, it is possible to calculate the wave propagation inside this complex medium in a large-scale based on general numerical programs. To show the potential of the approach, wave propagation inside and at the boundary of a photonic ideal Weyl system are thoroughly studied in this work. By reformulating the electric field equation, the method paves the way toward comprehensive engineering of metamaterials with unrestricted nonlocality.