Abstract
Optical resonators are fundamentally important building blocks for quantum optics. They enable crucial processes such as optical parametric oscillation. Among these resonators, whispering-gallery resonators stand out due to a number of unique favourable characteristics. They combine low loss, small mode volumes and easy tuning of coupling into a monolithic package that can be made out of many crystalline or non-crystalline materials. Their low loss allows high intracavity field strengths, which enables nonlinear optics with low input powers. The resonators explored here are carved out of single crystals and polished – a technique which still produces the lowest optical loss.
We provide in-depth explanations of nonlinear optics and various phase-matching methods applicable to whispering-gallery resonators. The theory of XY-cut phase matching is expanded upon by developing a number of complex yet intuitive approximations. We display how momentum can be gained for phase matching from the rotating polarisation of transverse-magnetic modes, by using an electro-optic conversion scheme where the microwave frequency electric field oscillates in unison and therefore has an azimuthal number of zero.
A second-harmonic generation scheme is demonstrated implementing XY-cut phase matching. An anisotroptic prism is combined with the anisotroptic resonator to selectively couple to a single polarisation of light, enhancing the usable second-harmonic light considerably.
We show how nonlinear optical processes can be tuned by looking at a Kerr process that generates widely-detuned sidebands. We first look at how to predict the generated wavelengths over such a large range by carefully considering the dispersion of the resonator. Then, we see how we can finely tune the generated sidebands by leveraging changing resonator temperature and mode detuning.
We provide theory and calculations to predict the strength of third-harmonic generation and its inverses. Various production schemes are examined and in the end one is chosen. Unfortunately only minor success is obtained. 10 nW of third-harmonic light is successfully coupled out of a magnesium fluoride resonator. Higher conversion efficiencies were obtained, but without extraction of the generated light. Other promising possibilities for generation of entangled triplet photons, as well as third-order optical parametric oscillation are discussed.