Linear and nonlinear applications of miniaturized silicon nitride microresonators

Photonic integrated circuits (PICs) are the subject of massive interest due to the range of applications they can provide at a huge scale while building on well-established CMOS technologies. One of the critical parameters defining a technology's maturity level is its implementation in an operational environment. Optical frequency combs (microcombs) generated using on-chip microresonators have proved vital for multiple industrial and research applications. However, like many other technologies, microcombs based on PICs are restricted to a well-stabilized lab environment. The full photonic integration of soliton microcombs in a single, compact, and electrically-driven package would allow mass-manufacturable devices compatible with emerging high-volume applications such as laser-based ranging (LIDAR), or sources for dense wavelength division multiplexing for data center based optical interconnects. Another obstacle is establishing optical packaging protocol allowing the miniaturization and portability of this platform. The current thesis work aims at the miniaturization of the microcombs system based on ultra-low loss \ce{Si3N4} microresonator providing a path toward its applicability at a broader scale. Two approaches have been established for miniaturization based on application requirements. The first approach uses fast optical feedback originating from a \ce{Si3N4} microresonator known as "self-injection-locking." By directly coupling a multi-frequency laser diode to the \ce{Si3N4}, self-injection locking first leads to narrow linewidth single-mode lasing and subsequently enables the generation of the optical frequency comb. Moreover, the soliton state is initiated by changing the current simplifying conventional soliton generation mechanism and reducing the overall footprint to 1 cm$^3$. In the second approach, a more generic protocol of optical packaging is implemented, enabling the interfacing of \ce{Si3N4} based microcomb with standard fiber modules. The requirements of high input power and broadband coupling for frequency comb generation separate microresonator packaging from conventional packaging. Initially, packaging protocols are established, enabling device operation at high power ($>$ 2.5 W) and low temperature. The first application of a packaged soliton microcombs module demonstrates ultra-fast (nanoseconds timescale) circuit switching for the data center in collaboration with Microsoft Research (MSR), Cambridge. This study carried out at MSR Cambridge, shows the potential of a soliton microcomb as a multiwavelength source for future datacenter and the importance of optical packaging to enable the demonstration on a system level. Further validation of the generic optical packaging approach is done by interfacing a photonic integrated \ce{Si3N4} based microresonator inside a transmission electron microscope (TEM) to modulate the electron beam with the linear and nonlinear intracavity field. The introduction of integrated photo