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.

EFFECTS OF BUBBLE-FACILITATED VOC TRANSPORT FROM LNAPL SMEAR ZONES ON VAPOR INTRUSION

Light non-aqueous phase liquid (LNAPL) sources can pose a significant threat to indoor air through vapour intrusion (VI). Most conceptual and numerical models of VI assume that the transport of volatile organic compounds (VOCs) is a diffusion-limited process. Recently, alternate conditions have been identified that could lead to faster transport, including the presence of preferential pathways and methanogenic gas production. In this study, an additional mechanism that could lead to faster transport was investigated: bubble-facilitated VOC transport from LNAPL smear zones. A laboratory investigation was preformed using pentane in one-dimensional laboratory columns and two-dimensional visualization experiments. Results of the column experiments showed that average VOC mass fluxes in the bubble-facilitated columns were over two orders of magnitude greater than in the diffusion-limited columns. In addition, the flux signal was intermittent, consistent with expectations of bubble-facilitated transport as bubbles expand, mobilize and are released to the vadose zone at various times during the test. The results from the visualization experiments showed gas fingers growing and mobilizing over time, which supports the findings of the column experiments. In conclusion, these results demonstrate the potential for bubble-facilitated VOC transport to affect mass transfer in LNAPL smear zones, and lead to increased indoor air concentrations by VI.