Theory and Computation of Intrinsic Propagation Losses and Disorder-Induced Modes in Topological Photonic Crystal Waveguides Using Mode Expansion Techniques
Photonic crystal (PC) slabs are promising optical systems for manipulating the flow of light on the nanoscale as a result of their combined in-plane lattice structure and slab waveguide properties. By introducing a line defect to the two-dimensional lattice, an efficient waveguide is formed that yields regions of fast and slow light. Although conventional PC waveguides are relatively well understood and have been partly optimized in terms of their intrinsic losses, they are prone to significant disorder-induced backscattering and propagation losses. Topological PC slab waveguides have been proposed as a means to help mitigate disorder-induced backscattering and offer additional control of light-matter interactions. However, many topological structures in optics are not yet well understood, due to being relatively new in the field of nanophotonics. In this thesis, we first investigate the intrinsic losses of topological PC slab waveguides using the semianalytical guided mode expansion method for perfectly periodic structures. We show that certain topological structures proposed in the literature are in fact intrinsically very lossy, while other, more recent “valley Hall” structures are able to achieve lossless propagation modes with good bandwidth. Second, we study the role of structural disorder using a Bloch mode expansion technique, which conveniently uses the solutions from the guided mode expansion as input. We find that the disorder-induced modes and impact on the photonic density of states for a topological structure is actually similar or worse than the W1 waveguide, and forms cavity-like modes with very small mode volumes. Future work is required to investigate how to mitigate the potential problems of disorder on these waveguides, and to assess which structures are more robust when coupling to resonators and spin-charged quantum emitters, where the topological waveguides show good promise.