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.

Design and Synthesis of Acridine-Based Macrocyclic G-Quadruplex DNA Ligands

DNA sequences that are rich in the guanine nucleic base possess the ability to fold into higher order structures called G-quadruplexes. These higher level structures are formed as a result of two sets of four guanine bases hydrogen-bonding together in a planar arrangement called a guanine quartet. Guanine quartets subsequently stack upon each other to form quadruplexes. G-quadruplexes are mainly localized in telomeres as well as in oncogene promoters. One unique and promising therapeutic approach against cancer involves targeting and stabilizing G-quadruplexes with small molecules, generally in order to suppress oncogene expression and telomerase enzyme activity; the latter has been found to contribute to “out-of control” cell growth in ca. 80-85% of all cancer cells and primary tumours while being absent in normal somatic cells. In this work, we present efforts towards designing and synthesizing acridine-based macrocycles (Mh) and (Mb) with the purpose of providing potential G4 ligands that are suited for selective binding to G4 vs. duplex DNA, and stabilize G-quadruplex structures. Two ligands described in this study include an acridine core which provides an aromatic surface capable of π-π interactions with the surface of G-quadruplexes. The successful synthesis of 4,5-diaminoacridine is described in chapter 2, as an essential fragment of the macrocycles (Mh) and (Mb). In order to investigate the synthetic method for macrocyclization, model compounds composing almost half of the designed macrocycles were explored. As discussed in chapter 3, the synthesis of the model compound for (Mb) turned out to be challenging. However, as a step towards the synthesis of (Mh), the synthesis of the hydrogen-containing model compound, which is almost half of the desired macrocycle (Mh) was achieved in our group and proved to be promising.