Nontrivial topology from simple photonic structures

Within the emerging area of topological photonics, which seeks to discover novel topological physics effects in photonic systems, much of the efforts have been devoted to discover non-trivial topology in photonic band structures. On the other hand, there are also interesting topological effects in other aspects of photonics. In this talk, as one of the examples, we discuss the non-trivial topology that arises from the dependency of the scattering matrix of a photonic crystal slab on the angles of incidence. We show that these scattering matrices can exhibit non-trivial topology, which leads to complete polarization conversion, as well as the capability for generation of arbitrary polarization by varying only the input angles. Being topological, these effects are robust to frequency variation, and thus is naturally broad-band.