Application of TLM for optical microresonators

Optical microresonators can form the basis of all-optical switching and control devices. The presented study is an exploration of the Transmission Line Modelling (TLM) method as a suitable candidate for designing optical microresonators. Chalcogenide glasses were identified as promising materials, with which to fabricate optical microresonators. The study presents the formulation of TLM in two dimensions to model nonmagnetic dielectric materials and a suitable computationally efficient yet flexible software design. Some methods for extracting spectral properties of resonators are compared and the modified difference Prony method was identified as a suitable tool to extract resonant frequencies and Q factors from a limited time signal. When applying TLM to microresonators of sub-wavelength dimensions it was understood that the method of discretisation plays an important role in accurately modelling microresonators. Two novel methods of discretisations -the same area method and the anti-aliasing method- were used to improve the accuracy significantly compared to existing mesh refinement techniques. Perfect matched layers (PMLs) were implemented to improve reflections from domain truncation using several methods. A Convolutional PML(CPML) was identified as the best, but it does not reach the efficiency of PMLs in the Finite Difference Time Domain (FDTD) method. Several frequency dependent refractive index models were proposed and implemented in TLM. A Tauc-Lorentz model was identified as the best fit to the experimental refractive index of three chalcogenide glasses, but a Sellmeier model with one term and a coefficient was efficient for TLM implementation. The main concern in the use of these models within TLM was shown to be the error arising due to mesh dispersion. Kerr nonlinear models were formulated and implemented in TLM and the models applied to the study of a waveguide junction. Compared to an equivalent implementation in a time domain beam propagation method, TLM models better represent the waveguide junction reflections