Physics of Dissipative Kerr Solitons in Optical Microresonators and Application to Frequency Synthesis

Optical-frequency combs, that is spectra of equidistant coherent optical lines, have revolutionized the precision measurements of time and frequency. In 2007 a new method to generate optical frequency combs was discovered. In contrast to conventional generation methods based on pulsed laser sources, these Kerr combs' or microcombs' are generated entirely via nonlinear frequency conversion in a microresonator pumped by a continuous-wave laser. More recently, the discovery of dissipative soliton formation in these cavities has enabled the generation of low-noise comb states with reproducible spectral envelopes, required in applications. Solitons are pulses of light which retain their shape as they circulate in the resonator, owing to the balance between counter-acting effects. On the one hand, the tendency of the pulse to spread due to anomalous group velocity dispersion is counteracted by the nonlinear self-phase modulation. On the other hand, the losses in the cavity are lifted by the nonlinear parametric gain provided by the driving laser. These states are robust attractors of the nonlinear cavity system under specific driving conditions. In this thesis, the properties and dynamics of dissipative soliton states are studied experimentally in crystalline magnesium fluoride whispering gallery mode resonators. Several methods are developed to accurately determine and control the driving parameters as well as to improve the comb stability. The observations provide an accurate verification of the Lugiato-Lefever equation commonly used to describe the system. Furthermore, unexpected deviations from this canonical model are observed and accounted for with an enriched framework. The improved fundamental understanding and control of the system is applied for the generation of an ultralow-noise microcomb driven with an ultra-stable laser. In combination with a novel transfer oscillator method, this comb is used to synthesize ultralow-noise microwaves via optical frequency division. Lastly, a novel method for synthesizing multiple distinct frequency combs from a single resonator and with a single laser is devised. It relies on multiplexing solitons in different spatial modes of the microresonator. Up to three combs are generated simultaneously from a single device for the first time.