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.

THE ROLE OF LIPOPROTEIN(a)/APOLIPOPROTEIN(a) IN ENDOTHELIAL DYSFUNCTION: MECHANISTIC STUDIES IN VASCULAR ENDOTHELIUM

Multiple lines of evidence suggest that elevated plasma lipoprotein(a) (Lp(a)) concentrations are a significant risk factor for the development of a number of vascular diseases including coronary heart disease and stroke. Lp(a) consists of a low-density lipoprotein (LDL)-like moiety and an unique glycoprotein, apolipoprotein(a) (apo(a)), that is covalently attached to the apolipoproteinB-100 (apoB-100) component of LDL by a single disulfide bond. Many studies have suggested a role for Lp(a) in the process of endothelial dysfunction. Indeed, Lp(a) has been shown to increase both the expression of adhesion molecules on endothelial cells (EC), as well as monocyte and leukocyte chemotactic activity in these cells. We have previously demonstrated that Lp(a), through its apo(a) moiety, increases actomyosin-driven EC contraction which, as a consequence, increases EC permeability. In this thesis, we have demonstrated a role for the strong lysine-binding site in the kringle IV type 10 domain of apo(a) in increasing EC permeability, which occurs through a Rho/Rho kinase-dependent pathway. We have further validated these findings using mouse mesenteric arteries in a pressure myograph system. We also have dissected another major signaling pathway initiated by apo(a) that involves in a disruption of adherens junctions in EC. In this pathway, apo(a)/Lp(a) activates the PI3K/Akt/GSK3β-dependent pathway to facilitate nuclear translocation of beta-catenin. In the nucleus beta-catenin induced the expression of cyclooxygenase-2 (COX-2) and the secretion of prostaglandin E2 (PGE2) from the EC. Finally, we have presented data to suggest a novel inflammatory role for apo(a) in which it induces the activation of nuclear factor-kappaB through promotion of the dissociation of IkappaB from the inactive cytoplasmic complex; this allows the nuclear translocation of NFkappaB with attendant effects on the transcription of pro-inflammatory genes. Taken together, our findings may facilitate the development of new drug targets for mitigating the harmful effects of Lp(a) on vascular EC which corresponds to an early step in the process of atherogenesis.