Weyl points in classical waves

Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Depending on the total Berry flux coming out from the monopoles, Weyl points have different charges; While in terms of the signs of group velocities around the Weyl points, there are two types of Weyl points, type-I and type-II, both are topologically nontrivial but exhibit very different physical properties. For instance, the density of state is zero at a type-I Weyl point; while that of type-II Weyl point is rather large just like the hyperbolic metamaterials. In this talk, I will talk about both types of Weyl points, and also Weyl points with different charges. I will start my talk with a tight-binding model and then show that actually Weyl points can be constructed easily using coupled resonance cavities. Such idea can be extended to waveguide systems. For the waveguide systems, we show that for each fixed values of kz, the systems are acoustic analogues of the topological Haldane model, and hence we can have one-way edge modes which are robust to kz-preserved scattering. We then design an electromagnetic wave system to experimentally show such robustness. Also in this system, we find Weyl points with charges higher than one. I will also briefly discuss the possible realizations of Weyl points in the optical frequency region. After that, I will talk about constructing Weyl points using homogenous metamaterials. Though tuning the nonlocal effect, the system can possess both types of Weyl points. I will also give a physical realization of such metamaterial consisting of an array of metal wires in the shape of elliptical helixes.