Description of a bottle resonator evanescently coupled to a waveguide

Abstract

Optical microresonators are widely used in numerous applications and are also of interest for researching predictions of cavity quantum electrodynamics. In contrast to other microresonators it is possible to tune the resonance frequencies of the bottle resonator by applying a longitudinal stress to any given frequency. Moreover, the resonator modes exhibit two so-called caustics which are advantageous to couple light to the resonator. So far, the interaction of such resonators with fibers have only been described heuristically. In this thesis we will introduce a more solid theoretical framework by using a coupled mode theory for modelling their coupling. Using the coupled mode theory, we will also be able to address the experimentally relevant question whether a so-called conveyor belt can work near a bottle resonator. We will see that the phase-matching between fiber and resonator modes plays a crucial part for this problem. In a next step we will develop models which aim to properly describe the transmission and reflection spectra of our bottle resonator-waveguide system. Scattering matrices will be used to model the interaction between the different modes under consideration. This model will later be extended to also account for scattering between the two counterpropagating resonator modes. Subsequently, we will make use of a non-hermitian model. The most interesting part about this model is that it allows for so-called "chiral modes" to occur which have so far not been experimentally demonstrated. By the term "chiral modes" we mean a nearly-degenerate mode pair where both modes exhibit the same sense of rotation. Our aim will be to investigate how this model is accordable with the ones previously described and which implications the occurrence of chiral modes have. By demanding that no energy shall be created within the resonator, we will derive a condition for the model parameters. This will be our main finding, allowing us to quantitatively describe under which circumstances chiral modes can occur.