The goal of topological photonics is to understand and harness the robustness of topologically protected transport of light in nanostructures, such as photonic crystals. In the first part of my defense, I will discuss our experimental observation of charge-2 Weyl points at IR wavelengths in three-dimensional micro-printed photonic crystals. These Weyl points are protected both by topology and symmetry, allowing for their observation in photonic crystals with a low refractive-index contrast. Furthermore, we also predict and observe the splitting of the charge-2 Weyl point into two charge-1 Weyl points along preferred directions in momentum space.  

In the second part of my defense, I will show that polarization and corner charge, two topological invariants thought to be ill-defined in Chern insulators, are in fact meaningful under some circumstances. I will demonstrate the implications of these invariants for boundary states in Chern insulators using a two-dimensional gyro-magnetic photonic crystal. 

Next, I will show that it is possible to perfectly confine nanocavity modes in two-dimensional photonic crystals that lack a bandgap. The mechanism for confinement is a carefully engineered symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal environment, resulting in a symmetry-protected bound state in the continuum.

In the last part of my defense, I will talk about our recent experimental observation of a reentrant delocalization transition in one-dimensional photonic quasicrystals. Time permitting, I will further show that the experimental platform employed here can also be used for realizing higher-dimensional topological phenomena, such as the formation of Landau levels in inhomogeneously strained Weyl systems.