Novel dynamics of driven nonlinear resonators

Abstract

This Thesis is comprised of theoretical and experimental investigations designed to shed light on novel dynamics of nonlinear optical resonators. The theoretical investigations focus on cavity soliton (CS) dynamics in the presence of pulsed or amplitude modulated driving elds, while the experimental investigation focusses on frequency comb generation in second-order nonlinear microresonators. First, we describe theoretical investigations into the dynamics of CSs in the presence of amplitude inhomogeneities of the driving eld (such as pulsed driving) where the repetition rate of the inhomogeneity and the soliton are synchronised. We show that, in contrast to phase inhomogeneities, CSs are attracted towards (and trapped to) speci c values of the driving eld. We link our ndings to a spontaneous symmetry breaking instability that physically arises from a competition between coherent driving and nonlinear propagation e ects. We then consider the impact due to the presence of desynchronization between the CS and the repetition rate of the inhomogeneity. We show that the trapping positions can be manipulated and even erased, such that single-soliton operation can be assured. Further investigation into the interplay of this desynchronization and stimulated Raman scattering has allowed us to explain recent experimental observations. The experimental portion of this Thesis focusses on the demonstration of internally pumped optical parametric oscillations in a lithium niobate microresonator. We demonstrate through numerical simulations that frequency combs can form around the pump and the second harmonic in a doubly resonant second order nonlinear microresonator. We then report on our experimental method for comb generation in a naturally phase matched lithium niobate microresonator by thermally tuning the birefringence of the crystal. Our observations of cascaded internally pumped optical parametric oscillation producing sidebands around the pump and the second harmonic bring us one step closer to achieving full comb generation in quadratically nonlinear optical microresonators.