Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

IMPROVED SAMPLE INTRODUCTION SYSTEMS FOR INDUCTIVELY COUPLED PLASMA OPTICAL EMISSION SPECTROMETRY AND THEIR APPLICATION TO THE ANALYSIS OF SIMPLE AND COMPLEX MATRICES

The objective of this thesis is to explore new and improved methods for greater sample introduction efficiency and enhanced analytical performance with inductively coupled plasma optical emission spectrometry (ICP-OES). Three projects are discussed in which the capabilities and applications of ICP-OES are expanded: 1. In the first project, a conventional ultrasonic nebuliser was modified to replace the heater/condenser with an infrared heated pre-evaporation tube. In continuation from previous works with pre-evaporation, the current work investigated the effects of heating with infrared block and rope heaters on two different ICP-OES instruments. Comparisons were made between several methods and setups in which temperatures were varied. By monitoring changes to sensitivity, detection limit, precision, and robustness, and analyzing two certified reference materials, a method with improved sample introduction efficiency and comparable analytical performance to a previous method was established. 2. The second project involved improvements to a previous work in which a multimode sample introduction system (MSIS) was modified by inserting a pre-evaporation tube between the MSIS and torch. The new work focused on applying an infrared heated ceramic rope for pre-evaporation. This research was conducted in all three MSIS modes (nebulisation mode, hydride generation mode, and dual mode) and on two different ICP-OES instruments, and comparisons were made between conventional setups in terms of sensitivity, detection limit, precision, and robustness. By tracking both hydride-forming and non-hydride forming elements, the effects of heating in combination with hydride generation were probed. Finally, optimal methods were validated by analysis of two certified reference materials. 3. A final project was completed in collaboration with ZincNyx Energy Solutions. This project sought to develop a method for the overall analysis of a 12 M KOH zincate fuel, which is used in green energy backup systems. By employing various techniques including flow injection analysis and standard additions, a final procedure was formulated for the verification of K concentration, as well as the measurement of additives (Al, Fe, Mg, In, Si), corrosion products (such C from CO₃²¯), and Zn particles both in and filtered from solution. Furthermore, the effects of exposing the potassium zincate electrolyte fuel to air were assessed.