Generalised Kerr Microcomb Physics in Synchronously Driven Systems

In this thesis, the generation of microcombs under complex, non-trivial, and/or higher-order cavity conditions is explored, both in theory & simulation, and in practical experimentation. Pulse-driving of microresonators is investigated for the generation and temporal guiding of localised dissipative structures. The effect of pulse-driving in contrast to constant-wave driving is explored in terms of energy conversion efficiency and the nonlinear transfer of noise from the input to the output light. The generation of localised dissipative structures under arbitrary dispersion is investigated, including for dissipative solitons in pure or perturbed anomalous dispersion, switching waves in normal dispersion, and zero-dispersion solitons that exist in pure third-order dispersion between anomalous and normal. The existence of these localised dissipative structures in non-trivial resonators where the propagation constants vary with distance is studied, with particular attention for longitudinally modulated dispersion. In these resonators, coherent higher-order dispersive waves on solitons, and the emergence of Faraday-wave satellite structures on switching waves are experimentally observed and analysed according to Floquet theory.