No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

In recent years, magnetic separation has attracted considerable attention as a technique for the separation of paramagnetic particles from the media carrying them. Equipment may be at least approximately specified by theoretical formulae, or by analysis of the results of laboratory experiments. In general, and neglecting experimental errors, the two methods of predicting separator performance will not agree due to the physical approximations which are necessary to achieve analytical solutions of the resulting equations.

Photonic crystal cavities can confine light to volumes smaller than a cubic wavelength, coupling their photonic modes to embedded quantum dots. Structures with sufficiently low losses and modal volumes can render photon emission reversible, a regime with potential for applications in quantum information processing. Three dimensional photonic crystal cavities are extremely difficult to produce, however two dimensional structures, bound above and below by air, can use the photonic band gap for in-plane confinement, and total internal reflection for 'to the plane' confinement. This thesis concerns itself with the development and utilisation of a method for calculating the mode structure and characteristics of such 'airbridge' cavities. An expansion in terms of the guided modes of an unpatterned dielectric membrane allows us to find the energies and fields of confined states. Loss calculations using periodic boundary conditions are shown to be flawed, and a method is devised, which effectively modifies the bound-ary conditions prior to the loss calculation. Losses are then calculated using Fermi's golden rule, allowing for full analyses of emission rate, directionality and polarisation. This method is highly accurate, and orders of magnitude faster than the widely used finite difference time domain codes. Multiple cavity designs are analysed and optimised. The 'L3' cavity which consists of a line of three holes missed from a hexagonal lattice, with the holes at either end slightly displaced, is then used to consider the effect of membrane refractive index, showing an exponential relationship between refractive index and achievable quality factors. The effects of in-plane disorder are shown to hold influence over the design preference of cavities. Finally, as a step towards a scalable quantum information processing architecture, several geometries are considered for the coupling of parallel 'L3' cavities; splittings are shown to exist in energy, quality factor, and emission polarisation.