Transforming transformation optics via generalised refraction

Generalised refraction is a topic which has, thus far, garnered far less attention than it deserves. The purpose of this thesis is to highlight the potential that generalised refraction has to offer with regards to imaging and its application to designing new passive optical devices. Specifically in this thesis we will explore two types of gener- alised refraction which takes place across a planar interface: refraction by generalised confocal lenslet arrays (gCLAs), and refraction by ray-rotation sheets. We will show that the corresponding laws of refraction for these interfaces produce, in general, light-ray fields with non-zero curl, and as such do not have a corresponding outgoing waveform. We will then show that gCLAs perform integral, geometrical imaging, and that this enables them to be considered as approximate realisations of metric tensor interfaces. The concept of piecewise transformation optics will be introduced and we will show that it is possible to use gCLAs along with other optical elements such as lenses to design simple piecewise transformation-optics devices such as invisibility cloaks and insulation windows. Finally, we shall show that ray-rotation sheets can be interpreted as performing geometrical imaging into complex space, and that as a consequence, ray-rotation sheets and gCLAs may in fact be more closely related than first realised. We conclude with a summary of potential future projects which lead naturally from the results of this thesis.

Examination of myocardial electrophysiology using novel panoramic optical mapping techniques

Optical mapping of voltage signals has revolutionised the field and study of cardiac electrophysiology by providing the means to visualise changes in electrical activity at a high temporal and spatial resolution from the cellular to the whole heart level under both normal and disease conditions. The aim of this thesis was to develop a novel method of panoramic optical mapping using a single camera and to study myocardial electrophysiology in isolated Langendorff-perfused rabbit hearts. First, proper procedures for selection, filtering and analysis of the optical data recorded from the panoramic optical mapping system were established. This work was followed by extensive characterisation of the electrical activity across the epicardial surface of the preparation investigating time and heart dependent effects. In an initial study, features of epicardial electrophysiology were examined as the temperature of the heart was reduced below physiological values. This manoeuvre was chosen to mimic the temperatures experienced during various levels of hypothermia in vivo, a condition known to promote arrhythmias. The facility for panoramic optical mapping allowed the extent of changes in conduction timing and pattern of ventricular activation and repolarisation to be assessed. In the main experimental section, changes in epicardial electrical activity were assessed under various pacing conditions in both normal hearts and in a rabbit model of chronic MI. In these experiments, there was significant changes in the pattern of electrical activation corresponding with the changes in pacing regime. These experiments demonstrated a negative correlation between activation time and APD, which was not maintained during ventricular pacing. This suggests that activation pattern is not the sole determinant of action potential duration in intact hearts. Lastly, a realistic 3D computational model of the rabbit left ventricle was developed to simulate the passive and active mechanical properties of the heart. The aim of this model was to infer further information from the experimental optical mapping studies. In future, it would be feasible to gain insight into the electrical and mechanical performance of the heart by simulating experimental pacing conditions in the model.