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.

Restrictions on Aliens in the United Kingdom, 1914-1919 : a Study of the Origins and Political Background of the Aliens Restrictions Acts of 1914 and 1919.

At first glance the Aliens Restriction Act of 1914, which was introduced and passed on the first day of World War One, seems a hasty and ill-prepared piece of legislation. Actually, when examined in the light of Arthur Marwick's thesis that war is a forcing house for pre-existent social and governmental ideas, it becomes clear that the act was not after all the product of hastily formed notions. In point of fact it followed the precedent of detailed draft clauses produced in 1911 by a sub-committee of the Committee of Imperial Defence established to consider the treatment of aliens in the event of war. Indeed the draft clauses and the restrictions embodied in the 1914 act were strikingly similar to restrictions on aliens legislated in 1793. Hostility to aliens had been growing from 1905 to 1914 and this hostility blossomed into xeno-phobia on the outbreak of war, a crucial precondition for the specifically anti-enemy fears of the time. In 1919 the Aliens Restriction (Amendment) Bill was introduced into parliament to extend temporarily the provisions of the 1914 act thus permitting the Home Secretary to plan permanent, detailed legislation. Two minority groups of MPs with extreme views on the treatment of aliens were prominent in the debates on this bill. The extreme Liberal group which advocated leniency in the treatment of aliens had little effect on the final form of the bill, but the extreme Conservative group, which demanded severe restrictions on aliens, succeeded in persuading the government to include detailed restrictions. Despite its allegedly temporary nature, the Aliens Restriction (Amendment) Act of 1919 was renewed annually until 1971.

Terrain Controls and Landscape-Scale Susceptibility Modelling of Active-Layer Detachments, Sabine Peninsula, Melville Island, Nunavut

Modelling the susceptibility of permafrost slopes to disturbance can identify areas at risk to future disturbance and result in safer infrastructure and resource development in the Arctic. In this study, we use terrain attributes derived from a digital elevation model, an inventory of permafrost slope disturbances known as active-layer detachments (ALDs) and generalised additive modelling to produce a map of permafrost slope disturbance susceptibility for an area on northern Melville Island, in the Canadian High Arctic. By examining terrain variables and their relative importance, we identified factors important for initiating slope disturbance. The model was calibrated and validated using 70 and 30 per cent of a data-set of 760 mapped ALDs, including disturbed and randomised undisturbed samples. The generalised additive model calibrated and validated very well, with areas under the receiver operating characteristic curve of 0.89 and 0.81, respectively, demonstrating its effectiveness at predicting disturbed and undisturbed samples. ALDs were most likely to occur below the marine limit on slope angles between 3 and 10° and in areas with low values of potential incoming solar radiation (north-facing slopes).

¬FISH DISTRIBUTIONS IN LAKE ONTARIO’S EASTERN BASIN AND THE UPPER ST. LAWRENCE RIVER: AN ANALYSIS USING GIS AND OCCUPANCY MODELLING TECHNIQUES

Predictive models of species distributions are important tools for fisheries management. Unfortunately, these predictive models can be difficult to perform on large waterbodies where fish are difficult to detect and exhaustive sampling is not possible. In recent years the development of Geographic Information Systems (GIS) and new occupancy modelling techniques has improved our ability to predict distributions across landscapes as well as account for imperfect detection. I surveyed the nearshore fish community at 105 sites between Kingston, Ontario and Rockport, Ontario with the objective of modelling geographic and environmental characteristics associated with littoral fish distributions. Occupancy modelling was performed on Round Goby, Yellow perch, and Lepomis spp. Modelling with geographic and environmental covariates revealed the effect of shoreline exposure on nearshore habitat characteristics and the occupancy of Round Goby. Yellow Perch, and Lepomis spp. occupancy was most strongly associated negatively with distance to a wetland. These results are consistent with past research on large lake systems indicate the importance of wetlands and shoreline exposure in determining the fish community of the littoral zone. By examining 3 species with varying rates of occupancy and detection, this study was also able to demonstrate the variable utility of occupancy modelling.