Mathematical and Physical Aspects of Topologically Protected States

Aspects of topological photonics in two and three dimensions

Mikael Rechtsman

Pennsylvania State University


Topological insulators are solid-state materials whose transport properties are immune to defects and disorder due to underlying topological order. Perhaps the first such phenomenon was the quantum Hall effect, wherein the Hall conductivity is quantized and hence extremely robust. In this talk, I will present the experimental observation of the topological protection of the transport of photons (rather than electrons in the solid state) in a complex dielectric structure. I will then present the observation of optical Weyl points in the context of three-dimensional photonic crystals. Time permitting, I will discuss our experimental results for the topological protection of mid-gap cavity modes.