Topological Photonics*

We will begin with 1D photonic crystals, in which the Zak phase of the bulk bands can be used to predict the existence of boundary modes. For 2D systems, we show that meticulously designed photonic crystals can achieve the duality condition, enabling the realization of photonic topological insulators which can be regarded as classical wave counterparts of electronic topological insulator. We will also see that symmetry-protected pseudospin states that are guided in air ican be realized simply by imposing certain special electromagnetic boundary conditions. Such systems are unique to EM wave and do not have electronic counterparts. We then discuss the realization of Weyl points in 3D photonic crystals carrying chiral structures. One-way edge modes are found on the boundary of these systems as a result of the synthetic gauge flux emerging from the Weyl nodes. These structures possess single Weyl points, including “type-II” nodes, and Weyl points with topological charges higher then one. Weyl points can also be found in some woodpile photonic crystals. The sign of topological charge will change when the constituent materials change, leading to a topological phase transition and the bands change from topologically trivial to nontrivial. We will see that Weyl-like nodal points can be found in the parameter space of a 1D photonic crystals with complex unit cells. The reflection at the surface of these photonic crystals exhibits phase vortexes, which guarantees the existence of interface states between photonic crystals and any reflecting substrates. In addition, we will see that helical structures that be used to realize three-dimension photonic Dirac points, with four-fold symmetry stabilized by electromagnetic duality symmetry. These systems carry spin-polarized surface arcs that can be realized experimentally.