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.

Teen Girls’ Perspectives on Their Current Dietary Habits and Food Choices: A Qualitative Study in Jeddah, Saudi Arabia

Rapid socioeconomic development in Saudi Arabia, as a result of oil revenues, has had profound effects on people’s lifestyles, including the transformation of people’s dietary habits. Such dietary transformations, known as the nutrition transition, are common in countries undergoing rapid socioeconomic changes. This transition is significant in Saudi Arabia as the traditional Saudi diet is considered a healthy one. Adoption of the Western diet has had negative health effects on the Saudi population, especially adolescents. As evidenced in many studies, adolescents are the most affected population when it comes to changes in dietary habits and physical activity. Adolescence is a vulnerable stage of life when dietary habits are developed, often lasting into adulthood, and may not be easily changed. In the case of Saudi Arabia, youth or adolescents represent almost 60% of the population; therefore, the eating habits they develop now could have profound consequences for population health in the future. To develop effective health promotion strategies, it is important to understand the sociocultural factors that influence the dietary habits and food choices of Saudi teens. I conducted two semi-structured, open-ended interviews, using photo-elicitation techniques, with 12 Saudi girls, aged 15-16 years. Analysis of the data shows four factors that pulled the participants toward eating home cooked traditional food and five factors that pushed participants away from eating home cooked traditional foods. The research suggests that despite the attractiveness of modern, Western ways of eating for Saudi teen girls, parents still play a key role in encouraging and supporting them to eat healthy food.