TOPOLOGICAL PHOTONICS: NESTED FREQUENCY COMBS AND EDGE MODE TAPERING

Abstract

Topological photonics has emerged in recent years as a powerful paradigm for the designof photonic devices with novel functionalities. These systems exhibit chiral or helical edge states that are confined to the boundary and are remarkably robust against certain defects and imperfections. While several applications of topological photonics have been demonstrated, such as robust optical delay lines, quantum optical interfaces, lasers, waveguides, and routers, these have largely been proof-of-principle demonstrations. In this dissertation, we present the design and generation of the first topological frequency comb. While on-chip generation of optical frequency combs using nonlinear ring resonators has led to numerous applications of combs in recent years, they have predominantly relied on the use of single-ring resonators. Here, we combine the fields of linear topological photonics and frequency microcombs and experimentally demonstrate the first frequency comb of a new class in an array of hundreds of ring resonators. Through high-resolution spectrum analysis and out-of- plane imaging we confirm the unique nested spectral structure of the comb, as well as the confinement of the parametrically generated light. Additionally, we present a theoretical study of a new kind of valley-Hall topological photonic crystal that utilizes a position dependent perturbation (or “mass-term”) to manipulate the width of the topological edge modes. We show that this approach, due to the inherent topological robustness of the system, can result in dramatic changes in mode width over short distances with minimal losses. Additionally, by using a topological edge mode as a waveguide mode, we decouple the number of supported modes from the waveguide width, circumventing challenges faced by more conventional waveguide tapers.