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.

CLASHES IN CONFINEMENT: MEN’S GENDERED EXPERIENCES WITH CONFLICT IN CANADIAN PRISONS

This dissertation presents the results of in-depth qualitative interviews with twenty-three formerly imprisoned men regarding their lived experience with prison conflict and the pain of incarceration. The results suggest that prison is a gendered ‘total institution’ (Goffman 1961). The pains that men experience in prison are uniquely gendered in that the deprivations imposed by incarceration– deprivation of autonomy, liberty, goods and services, heterosexual sex, and security (Sykes 1958) – in the reverse, define idealized masculinity as it is currently socially constructed: self-reliance, independence, toughness or invulnerability, material and economic success, and heterosexual prowess. From these shared deprivations emerges a gendered code of conduct that perpetuates a hierarchy among incarcerated men by constructing violent masculinity as a subcultural norm. The results suggest that the gender code in prison represents a set of rules that create opportunities for men to police each other’s gender performance and make claims to masculine statuses. Because status is inextricably tied to survival in this context, many men feel pressured to perform violent masculinities in prison despite privately subscribing to a non-violent sense of self-concept. The results suggest that violence is an expressive and instrumental resource for men in prison. A gender theory of prison violence, methodological findings, theoretical implications, ethical considerations and the short and long term aftermath of violent prison conflict are discussed.

Expanding our Constitutional Horizons: A Comprehensive Study of Quasi-Constitutionality in Canada

A number of laws in Canada which uphold rights are referred to as quasi-constitutional by the courts in recognition of their special importance. Quasi-constitutional statutes are enacted through the regular legislative process, although they are being interpreted and applied in a fashion which has become remarkably similar to constitutional law, and are therefore having an important affect over other legislation. Quasi-constitutionality has surprisingly received limited scholarly attention, and very few serious attempts at explaining its significance have been made. This dissertation undertakes a comprehensive study of quasi-constitutionality which considers its theoretical basis, its interpretation and legal significance, as well as its similarities to comparable forms of law in other Commonwealth jurisdictions. Part I examines the theoretical basis of quasi-constitutionality and its relationship to the Constitution. As a statutory and common law form of fundamental law, quasi-constitutionality is shown to signify an association with the Canadian Constitution and the foundational principles that underpin it. Part II proceeds to consider the special rules of interpretation applied to quasi-constitutional legislation, the basis of this interpretative approach, and the connection between the interpretation of similar provisions in quasi-constitutional legislation and the Constitution. As a statutory form of fundamental law, quasi-constitutional legislation is given a broad, liberal and purposive interpretation which significantly expands the rights which they protect. The theoretical basis of this approach is found in both the fundamental nature of the rights upheld by quasi-constitutional legislation as well as legislative intent. Part III explores how quasi-constitutional statutes affect the interpretation of regular legislation and how they are used for the purposes of judicial review. Quasi-constitutional legislation has a significant influence over regular statutes in the interpretative exercise, which in some instances results in conflicting statutes being declared inoperable. The basis of this form of judicial review is demonstrated to be rooted in statutory interpretation, and as such it provides an interesting model of rights protection and judicial review that is not conflated to constitutional and judicial supremacy.