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.

Adiposity, Sex Hormones, and Repetitive Element DNA Methylation in Healthy Postmenopausal Women

INTRODUCTION: Low levels of methylation within repetitive DNA elements, such as long interspersed nuclear element-1 (LINE-1) and Alu repeats, are believed to epigenetically predispose an individual to cancer and other diseases. The extent to which lifestyle factors affect the degree of DNA methylation within these genomic regions has yet to be fully understood. Adiposity and sex hormones are established risk factors for certain types of cancer and other illnesses, particularly amongst postmenopausal women. The aim of the current investigation is to assess the impact of adiposity and sex hormones on LINE-1 and Alu methylation in healthy postmenopausal women. METHODS: A cross-sectional study was conducted using baseline data from an ancillary study of the Alberta Physical Activity and Breast Cancer Prevention (ALPHA) Trial. Current adiposity was measured using a dual-energy x-ray absorptiometry (DXA) scan, computed tomography (CT) scan, and balance beam scale. Historical weights were self-reported in a questionnaire. Current endogenous sex hormone concentrations were measured in fasting blood serum. Estimated lifetime number of menstrual cycles was used as a proxy for cumulative exposure to ovarian sex hormones. Repetitive element methylation was quantified in white blood cells using a pyrosequencing assay. Linear regression was used to model the relations of interest while adjusting for important confounders. RESULTS: Adiposity and serum estrogen concentrations were positively related to LINE-1 methylation but were not associated with Alu methylation. Cumulative ovarian sex hormone exposure had a “U-shaped” relation with LINE-1 regardless of folate intake and a negative relation with Alu methylation amongst low folate consumers. Androgens were not associated with repetitive element DNA methylation in this population. CONCLUSION: Adiposity and estrogens appear to play a role in maintaining high levels of repetitive element DNA methylation in healthy postmenopausal women. LINE-1 methylation may be a mechanism whereby estrogen exposure protects against cardiovascular and neurodegenerative illnesses. These results add to the growing body of literature showing how the epigenome is shaped by our lifestyle choices. Future prospective studies assessing the relation between levels of repetitive element DNA methylation in healthy individuals and subsequent disease risk are needed to better understand the clinical significance of these results.