Silicon photonics, the design and manufacturing of optical structures on silicon wafers using the same process as computer chips, has in the past several years revolutionized high-speed communications between computers and stands primed to further advance sensing, signal processing, and quantum computation. Such photonic devices are the most powerful because they can be manufactured at incredible scale, allowing us to either build them very cheaply or build large systems of photonic components, much like transistors and large-scale integrated circuits. In this dissertation we make a leapfrog improvement in the state of the art of silicon photonics in two different areas: dramatically improving the performance of modulators using graphene and building large-scale silicon optical phased arrays with record-breaking efficiency and output beam quality.

The dissertation is divided into five chapters. In the first, I introduce silicon photonics, discuss its capabilities and limitations, and summarize the key results of the dissertation. In Chapter 2, I lay a theoretical framework for on-chip waveguides and ring resonators with a mathematical notation used throughout the thesis, as well as derive Fourier optics of optical phased arrays from first-principle scattering theory. Chapter 3 details work on graphene ring modulators, including extensive fabrication and measurement details. Chapter 4 continues with theoretical and experimental models of using graphene for highly linear and purely phase-based modulators. Finally, Chapter 5 describes work on chip-scale optical phased arrays and a method for achieving half-wavelength emitter waveguide pitch.