Topological structures of and for light

Topology is an invaluable tool to elucidate the properties of physical systems. Typically, it refers to instances where an entity has so-called topological protection, which means that the entity cannot disappear if small changes are made to the system. In this lecture I will address two illustrations of topological protection in light fields.
The first relates to optical singularities, which can have a topological charge. I will experimentally show that the charge of both phase- and polarization singularities plays a role in how they are distributed in space and also in the way they are created and annihilated. The second relates to the behavior of light in photonic nanostructures of which the properties have a non-trivial topology. We experimentally investigated the propagation of edge states between topologically non-trivial photonic crystals. I will show how the propagation direction is related to the far-field optical spin of the modes. Time allowing I will address the heterogeneity of the spatial distribution of the near-field optical spin of the mode, which is of importance to quantum optical application of these states.