Fabry-Perot Resonators in Guided-Wave Media

Abstract

The objective of this thesis is to study Fabry-Perot resonators in transmission lines and waveguides. Transmission lines and waveguides may be referred to as guided-wave media. A Fabry-Perot resonator is the simplest form of resonator occurring frequently in coupled guided-wave structures, for example dielectric-filled waveguides, lasers, plasmonic waveguides etc. In this thesis, analytical as well as numerical approaches have been adopted to model different resonator problems. Analytical solutions of Maxwell’s equations, derived from first principles, are used whenever possible. The commercially available finite-element-based electromagnetic solver COMSOL Multiphysics has been used throughout the course of this work for numerical full-wave modelling. In addition, a finite difference time-domain (FDTD) code was also developed for numerical full-wave modelling.

This thesis consists of eight chapters. The first chapter is a review of current trends in THz technology and plasmonics, with a brief description of the FDTD technique and how FDTD can be used to model surface plasmon polaritons. Chapter 2 is an overview of scattering parameters in relation to travelling waves, pseudo waves and power waves. Several useful results have been derived in this chapter including, direct formulas for renormalisation of conventional (S-) and power (Sp-)scattering parameters for a two-port network; conversion between S- and Sp-parameters for a multi-port network; and direct formulas for interconversion between S, Z, Y, h, ABCD and T parameters for a two-port network with arbitrary port reference impedances. Chapter 3 deals with challenges in modelling lossy resonant structures by considering the example of a lossy one-dimensional resonator as the walls of the resonator are transformed from perfect electric conductor (PEC) to free space. Chapter 4 discusses excitation of Fabry-Perot eigenmodes in 3-D printed dielectric samples when placed in a waveguide as observed by authors of a recently published paper. Chapter 5 presents a rigorous analysis of Fabry-Perot eigenmode excitation in dielectric filled parallel-plate and circular waveguides. Chapter 6 reviews an S-parameter renormalisation technique for resolving ambiguities in reflectance and transmittance relationships of a two-port network, from noisy measurements. The technique was introduced in a recently published paper. Furthermore, a method for estimation of vector network analyser (VNA) output signal-to-noise ratio is also discussed. Chapter 7 introduces a THz spectroscopy technique based on surface plasmon excitation. Several modelling approaches have been used to model the spectroscopic response of a high resistivity Si slab under a Si prism when surface plasmons are excited on the Si slab using the attenuated total reflection (ATR) scheme. The intended experimental set-up was modelled using different techniques including; dispersion modelling, analytical planar media reflection/transmission modelling from first principles using Maxwell’s equations and full-wave numerical modelling using the FDTD technique and COMSOL Multiphysics frequency domain solver. Chapter 8 is on modelling plasmon propagation in two-dimensional electron system (2-DES) channels in the presence of a magnetic field. The experimental results published by a recent study were modelled using COMSOL Multiphysics and the transmission of the proposed device was computed for the first time, which revealed that the device was too lossy. Based on the simulated results, a new device structure was proposed which could reduce transmission losses by 20 dB.