Similarities in the form of the Schrodinger equation that governs the behaviour of electronic wavefunctions, and Maxwell’s equations which govern the behaviour of electromagnetic waves, allow ideas that originated in solid state physics to be easily applied to electromagnetic waves in photonic structures. While electrons moving through a semiconductor experience a periodic variation in charge, in a photonic crystal electromagnetic waves experience a periodic variation in refractive index. This leads to ideas such as bandstructure being applicable to the one and two dimensional photonic crystals used in this work. The following work will contain theoretical and experimental studies of the transmission through, and electric fields within, one dimensional photonic crystals. A slow variation in the structure of these crystals will lead to the bandstructure shifting, with an photonic analogy of electronic Bloch oscillations and Wannier-Stark ladders being seen in these structures. The two dimensional photonic crystals will be shown, through Hamiltonian ray tracing, to support both stable and chaotic ray paths. Examination of the phase space reveals the existence of ‘Dynamical Barriers’, regions in phase space supporting stable ray trajectories that divide separate regions in which the ray trajectories are chaotic. Various manners in which the bandstructure may be varied will be presented, along with a proposed switch that may be made using these structures. While the ray tracing will be carried out in photonic crystals in the limit of infinitesimally thin dielectric sheets, the model will then be developed to show the bandstructure of a photonic crystal made from finite width dielectric sheets, with examples of dispersion surfaces for these structures being presented.

This thesis describes a theoretical and numerical study of quantum transport and optical effects through an array of self-assembled InAs quantum dots grown in the intrinsic region of a GaAs p-i-n junction. We present a numerical simulation of this system and compare the generated transport and elecroluminescence results to recent experimental data. The simulation first calculates the quantum tunnelling, excitonic recombination, and relaxation rates within the dots, and then uses a stochastic model to simulate carriers entering and leaving the array. We highlight a number of features within the simulation, which shed light on similar features seen in experimental data. In particular, we demonstrate the importance of including the effects of the Coulomb interactions between the carriers, as this is shown be necessary for the simulated and experimental results to match closely. We also investigate a model of Auger processes which is shown to produce up-conversion luminescence, and study the effect of varying the location of the array within the intrinsic region. Additionally we present a master equation approach, which we use to describe a correlated tunnelling regime, in which the Coulomb interaction between an electron and a hole forces them to tunnel alternately onto a single dot before recombination. We produce current and photon noise predictions for both tunnelling and recombination limited regimes. We also investigate this phenomena for a pair of interacting dots, and find a number of two dot configurations which are able to produce current and electroluminescence. We present current and photo-current rate predictions for each case, and associated current and photon noise results.

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Magnetization processes in a sintered Nd-Fe-B permanent magnet (NEOMAX-35) were examined on a small scale using a Hall-effect microprobe with an active area 75 μm on a side. Probes were made by evaporating bismuth through a stencil mask onto glass slides. Experiments were performed by placing a probe onto the polished pole face of a Nd-Fe-B magnet and inserting the probe-magnet assembly into an electromagnet. Barkhausen steps, indicating rapid domain wall motion, were observed (superimposed upon the blank probe signal) in the demagnetization of a fully magnetized magnet. Magnetization traces for a thermally demagnetized Nd-Fe-B magnet did not exhibit measurable Barkhausen steps until a field of approximately 1.2 T was applied. The following observations were made for two thermally demagnetized samples which were cycled through minor hysteresis loops (maximum applied field of approximately 2 T): (1) virgin magnetization traces did not contain measurable Barkhausen steps, however all other forward and reverse magnetization traces did; (2) the initial reverse magnetization trace exhibited more and larger Barkhausen steps than subsequent traces; and (3) some Barkhausen steps were repeatable, that is, occurring at approximately the same field on each subsequent forward or reverse trace. Hall voltage signals were on the order of millivolts for probe currents of 10 mA.

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