Crystalline Whispering Gallery Mode Resonators
High quality (Q) optical resonators find applications in many fields of science and in- dustry. They serve as narrowband linear frequency filters, laser cavities and are used in high-performance sensing experiments. In a resonator, the field intensity can be enhanced by orders of magnitude compared to the field driving the resonator. This property makes them a valuable tool for studying and exploiting nonlinear effects and to enhance light-matter interaction in general. In this work, we explore an important subtype of dielectric resonators, the so called whispering gallery mode (WGM) resonator. Essentially, such a resonator is a convex shaped, usually rotationally symmetric dielectric material with small optical losses. The light is guided close to the boundary, but almost entirely within the dielectric by total internal reflection (TIR). The modes of WGM resonators can exhibit very high Q factors and confine light on a small footprint resulting in high field intensities within the ma- terial. Together with their monolithic design offering high stability, they are a natural choice for nonlinear optics experiments. Furthermore, the evanescent field component of the TIR interacts with the environment of the resonator causing the great success of WGM resonators in bio- and refractometric sensing experiments. Here, we focus on WGM resonators made from a single crystalline material. In addition to the already mentioned favorable properties, they can exhibit birefringence and second order nonlinearities enabling highly efficient phase-matched three wave mixing between vastly different frequencies. These resonators have to be fabricated mechanically by high precision single point di- amond turning and polishing to maintain the single crystal nature and to ensure an optically smooth surface. We optimized this fabrication technique and are now able to reach material limited Q factors in magnesium fluoride and lithium niobate resonators. The narrow bandwidth of the modes of a magnesium fluoride WGM resonator and its refractive index being very close to that of water motivated us to conduct refractometric sensing experiments in aqueous environment. Due to the small difference of the refrac- tive indices between the resonator and the environment, the evanescent field extends deep into the surrounding water. This increases the sensitivity compared to other mate- rials commonly used for sensing considerably. We were able to show that even mm-sized magnesium fluoride resonators can compete with two orders of magnitude smaller fused silica spheres. In addition, the thermal properties and the birefringence of magnesium fluoride allow for sophisticated temperature stabilization schemes. In that context, we investigated an exotic type of resonator where the optic axis of the crystal is tilted with respect to the symmetry axis of the resonator. Such a resonator exhibits still very high Q factors. Furthermore, we showed that the modes of such a res- onator are, in general, elliptically polarized and the polarization depends on the position on the resonator rim. This raised the question whether such a system could be used for sensing of chirality. Our results and estimations show, however, that the effect imposed by chirality would be most likely too small compared to other effects to be measurable efficiently. We demonstrate that birefringence can also be used to couple selectively to one of the two polarization families usually excited in a z-cut resonator, while the coupling to the re- spective other polarization remains entirely suppressed. Selective coupling will improve nonlinear conversion experiments such as single photon generation or third harmonic generation in WGM resonators since it allows to tune coupling rates to the pump and signal modes independently. In that context we expanded the existing theory for prism coupling and are now able to provide a modified condition for coupling of WGMs to a prism. The developed theory allowed us furthermore to calculate the far field pattern of outcoupled WGMs as a function of the resonator geometry. Finally, we demonstrate efficient nonlinear up-conversion of microwave signals into the optical domain using an all-resonant lithium niobate resonator. We discuss theoreti- cally that this requires a very precisely fabricated resonator geometry to achieve phase- matching for a given set of frequencies. We show how such a resonator can be iteratively fabricated and demonstrate the so far best reported conversion efficiency of continuous wave microwave signals around 80GHz into the telecom band. The up-converted signal preserves the phase information of the input microwave signal and can be efficiently detected by optical methods like heterodyning. We discuss the noise properties of such a receiver and find that it could outperform state-of-the-art THz detectors at room temperature by orders of magnitudes. Depending on the actual implementation of the optical detection, the smallest, thermally limited, detectable power could be as small as 10 −17 W at 300K.
Optische Resonatoren mit hohen Gütefaktoren (