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.

Self-efficacy in depression: Bridging the gap between competence and real-world functioning

Background: Depression is the largest contributing factor to years lost to disability, and symptom remission does not always result in functional improvement. Comprehensive analysis of functioning requires investigation both of the competence to perform behaviours, as well as actual performance in the real world. Further, two independent domains of functioning have been proposed: adaptive (behaviours conducive to daily living skills and independent functioning) and interpersonal (behaviours conducive to the successful initiation and maintenance of social relationships). To date, very little is known about the relationship between these constructs in depression, and the factors that may play a key role in the disparity between competence and real-world performance in adaptive and interpersonal functioning. Purpose: This study used a multidimensional (adaptive and interpersonal functioning), multi-level (competence and performance) approach to explore the potential discrepancy between competence and real-world performance in depression, specifically investigating whether self-efficacy (one’s beliefs of their capability to perform particular actions) predicts depressed individuals’ underperformance in the real world relative to their ability. A comparison sample of healthy participants was included to investigate the level of depressed individuals’ impairment, across variables, relative to healthy individuals. Method: Forty-two participants with depression and twenty healthy participants without history of, or current, psychiatric illness were recruited in the Kingston, Ontario community. Competence, self-efficacy, and real-world functioning all in both adaptive and interpersonal domains, and symptoms were assessed during a single-visit assessment. Results: Relative to healthy individuals, depressed individuals showed significantly poorer adaptive and interpersonal competence, adaptive and interpersonal functioning, and significantly lower self-efficacy for adaptive and interpersonal behaviours. Self-efficacy significantly predicted functional disability both in the domain of adaptive and interpersonal functioning. Interpersonal self-efficacy accounted for significant variance in the discrepancy between interpersonal competence and functioning. Conclusions: The current study provides the first data regarding relationships among competence, functioning, and self-efficacy in depression. Self-efficacy may play an important role in the deployment of functional skills in everyday life. This has implications for therapeutic interventions aimed at enhancing depressed individuals’ engagement in functional activities. There may be additional intrinsic or extrinsic factors that influence the relationships among competence and functioning in depression.

The Economic Case for Electric Mining Equipment and Technical Considerations Relating to their Implementation

Underground hardrock mining can be very energy intensive and in large part this can be attributed to the power consumption of underground ventilation systems. In general, the power consumed by a mine’s ventilation system and its overall scale are closely related to the amount of diesel power in operation. This is because diesel exhaust is a major source of underground air pollution, including diesel particulate matter (DPM), NO2 and heat, and because regulations tie air volumes to diesel engines. Furthermore, assuming the size of airways remains constant, the power consumption of the main system increases exponentially with the volume of air supplied to the mine. Therefore large diesel fleets lead to increased energy consumption and can also necessitate large capital expenditures on ventilation infrastructure in order to manage power requirements. Meeting ventilation requirements for equipment in a heading can result in a similar scenario with the biggest pieces leading to higher energy consumption and potentially necessitating larger ventilation tubing and taller drifts. Depending on the climate where the mine is located, large volumes of air can have a third impact on ventilation costs if heating or cooling the air is necessary. Annual heating and cooling costs, as well as the cost of the associated infrastructure, are directly related to the volume of air sent underground. This thesis considers electric mining equipment as a means for reducing the intensity and cost of energy consumption at underground, hardrock mines. Potentially, electric equipment could greatly reduce the volume of air needed to ventilate an entire mine as well as individual headings because they do not emit many of the contaminants found in diesel exhaust and because regulations do not connect air volumes to electric motors. Because of the exponential relationship between power consumption and air volumes, this could greatly reduce the amount of power required for mine ventilation as well as the capital cost of ventilation infrastructure. As heating and cooling costs are also directly linked to air volumes, the cost and energy intensity of heating and cooling the air would also be significantly reduced. A further incentive is that powering equipment from the grid is substantially cheaper than fuelling them with diesel and can also produce far fewer GHGs. Therefore, by eliminating diesel from the underground workers will enjoy safer working conditions and operators and society at large will gain from a smaller impact on the environment. Despite their significant potential, in order to produce a credible economic assessment of electric mining equipment their impact on underground systems must be understood and considered in their evaluation. Accordingly, a good deal of this thesis reviews technical considerations related to the use of electric mining equipment, especially ones that impact the economics of their implementation. The goal of this thesis will then be to present the economic potential of implementing the equipment, as well as to outline the key inputs which are necessary to support an evaluation and to provide a model and an approach which can be used by others if the relevant information is available and acceptable assumptions can be made.