Whispering-Gallery Mode Microresonators as Tunable Optical Parametric Oscillators

Abstract

In this thesis, investigation of the continuous and discrete tunability properties of optical parametric oscillations within crystalline whispering-gallery mode resonators is undertaken. These ultra-high finesse, compact devices represent an exciting platform for the generation of new spectral components through nonlinear optical phenomena. Specicically, the Kerr nonlinearity of magnesium uoride microresonators induces the four-wave mixing process to convert an input pump beam into two spectrally equidistant sidebands. Through careful engineering of dispersion characteristics, sideband tuning is achieved. Firstly, the fundamental mechanism driving parametric gain within dielectric cavities with generalised dispersion is formalised in the lumped and mean-field model. This analysis uncovers parametric gain sidelobes of two diering modulation instability regimes that would otherwise be hidden if a direct linear stability analysis is taken on the mean- field model. A comparison between the two models with higher-order dispersion is used to determine the threshold of validity when taking the approximation. The geometry of whispering-gallery mode resonators permits the coexistence of higher-order spatial modes. Each mode possesses dierent dispersion characteristics, therefore, there are multiple phase-matching curves possible within a single microresonator. These can then be leveraged to almost triple the available tunability range. Parametric sidebands generated through the four-wave mixing process must have comparable coherence to the driving beam for any useful applications. This is confirmed by measuring their spectral linewidth against the pump laser using the delayed selfheterodyne interferometry technique. We demonstrate that the three waves do indeed share similar linewidths. Lastly, experimental techniques outlining the observations of continuous and discrete tunability of parametric oscillations within a single resonator resonance is presented. The sidebands are found to be continuously tunable and experience the same frequency shift as the pump. We demonstrate over 10 GHz of continuous tunability in parametric sidebands produced by these crystalline microresonators. In addition to continuous tunability, discrete jumps of a single free spectral range or more can be induced through only picometre changes in the pump wavelength.