Outline of the thesis

This thesis is based on our contributions to the project NAIS concerning the modeling and simulation of microresonators as tunable wavelength filters. Here we investigate a frequency domain spatial coupled mode theory based model of 2-D circular integrated optical microresonators. The formulation requires the propagation constants of the cavity segment (bent waveguide) modes and the scattering matrices of the bent-straight waveguide couplers. The former quantities characterize the wave propagation along the cavity segments, and the latter quantities characterize the response of the couplers. We proceed as follows:

• Chapter 2 explores the classical frequency domain model of the wave propagation along curved interfaces. We implemented routines for complex order Bessel functions, which allow to compute the bend modes and their propagation constants, and also to visualize the bend field propagation.
• Chapter 3 presents a parameter-free spatial coupled mode theory model of bent-straight waveguide couplers derived from variational principles. With access to the analytical bent waveguide modes, we could implement the above model, and investigate it systematically.
• Chapter 4 describes in detail the 2-D model for circular microresonators, and explains how to evaluate effectively their spectral response. Tunability of microresonators is an essential feature from the application point of view. This chapter also describes how the effect of small changes of the cavity refractive index on the spectral response of the resonators can be estimated by perturbational expressions.
• Chapter 5 contains the conclusions of the present work and a brief outlook.