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We have performed a theoretical study into silicon-on-insulator photonic waveguide arrays. Such waveguides are capable of high levels of light confinement which reinforces the already strong nonlinear response of silicon, making systems involving the waveguidcs ideal for the study of non-linear effects. This study is focussed on two nonlinear processes in relation to the waveguide arrays: optical soli tans and modulational instability, which are often related effects themselves. Optical solitons are pulses localised ill Due or more spatial and/or temporal dimensions which propagate through media -in a. robust, self-reinforcing manner. They require a balance between nonlinearity, diffraction and dispersion. Modulational instability is related to wave-mixing processes whereby photons of a certain frequency arc converted to photons of different frequencies, depending on phase matching and conservation laws. The instability causes the growth of spectral sidebands about a pump pulse, and is often found to occur during soliton propagation. In this thesis a study of the propagation of light within arrays of waveguides is presented, wherein conditions are tuned to promote soliton formation and an emphasis is placed on investigating discrete spatiotemporal solitons. Advantages and disadvantages of employing silicon waveguides for soliton formation are noted with suggestions given to enable minimising of the latter. It is shown that silicon-on-insulator waveguides can provide an excellent medium for supporting discrete spatiotemporal solitons, and where applicable theoretical results have been related to experimental ones performed in tandem . Similar arrays to used to study modulational instability. It is shown that, through exploitation of the supermodes supported by a waveguide array, different degrees of instability, quantified by an amount of 'gain', are possible within the same array. Depending on the initial excitation conditions it is possible for a pulse to experience either large or insignificant amounts of the gain.

A variety of waveguide structures have been analysed for the measurement of the complex dielectric permittivity of liquids. Mode matching techniques are im- plemented to solve the forward problem of computing the scattering parameters for a sample of known permittivity filling a rectangular metal waveguide. Three different sample geometries are used. In the first, the liquid and the sample holder completely fill the waveguide cross section. As a result, only the dominant waveguide modes are matched across the discontinuity interface and an exact an- alytical relation between the S parameters and permittivity can be written. The second and third configurations are concentric cylinders and rectangles respec- tively, partially filling a metal waveguide, hence higher order modes are taken into account in the formulation. For the partially filled rectangular sample, a generalised scattering matrix method to obtain the overall scattering parameters due to the several discontinuity regions. Iterative methods are then introduced to solve the inverse problem of recover- ing the unknown permittivity from simulated or measured scattering parameters. For the partially filled waveguides, because an exact analytical relation does not exist, objective( error) functions are defined and minimized. The partially filled rectangular sample case is extended to obtain the resonant frequency and qual- ity factor of a dielectric loaded resonant cavity, and the results compared to the approximation normally used for the cavity perturbation technique. Finally, a rectangular dielectric waveguide method for liquid measurements was developed. This method has a treatment similar to the well known free space tech- niques. It has a distinct advantage of relaxing the strict requirements of sample dimension associated with metal waveguides, especially at higher frequencies.

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This thesis is focused on a study on the dispersion formulation of the recently appeared ''laminated waveguide". In this framework a new method for the analysis of a wide variety of microwave components like posts, circular junctions or corners in rectangular waveguides is developed. This method can be used to model the posts in the laminated waveguide geometry and this was the main motivation of the present work. The method gives the impedance or admittance matrix of the microwave component by applying discrimination between the localised and accessible modes on the indirect mode matching (IMM) formulation. In all cases the method proved to be fast, very accurate and easy to implement. The application of the IMM technique to the dispersion formulation of the laminated waveguide is undertaken by implementing the Transverse Resonance Method. It is the first time that effort is paid, so that every possible polarisation of both bounded and unbounded modes is considered. In the process a new analytic solution is given for the modelling of the transverse bifurcation. Its significance relies on the the fact that the method of moments is not to be used in the analysis and thus its overall speed is increased. The total procedure is expected to be straightforward and flexible.

A Heterojunction Phototransitor (HPT) is an attractive high-speed photodetector for optical communications, as it can provide high gain and high power. It can also be used to generate millimetre-wave signals using optical heterodyne for radio astronomy and wireless broad-band communications. Edge illuminated 2-terminal HPTs (2T-HPTs) integrated with an optical waveguide are designed and characterised. A small signal model is developed and it simulates the 2T-HPT frequency responses with good accuracy and supplements the measurement to determine its gain and cut-off frequency. This overcomes the requirement to measure the input photocurrent to the 2T-HPT using an exact replica of its PIN structure. The high frequency responses for the longer devices, which give higher saturation current, are limited by the loss of the transmission line. This high loss is also observed by the 2-port characterisation of the back-to-back configured 2T-HPT and gives a trade-off between the cut-off frequency and saturation current in the design. Additional analysis shows that the cut-off frequency is also limited by the large device capacitances. Using scaling of the model, the cut-off frequency is shown to increase to 59.4GHz with a gain of 39dB for a 1mum x 10mum 2T-HPT. The above result shows that the 2T-HPT could be best utilised in a periodic structure (P-TWHPT), with small device area sections connected by short transmission lines. This increases the saturation current level without reducing the cut-off frequency and gain. A P-TWHPT model is developed to simulate and analyse its frequency response. It is shown that the effects of phase matching and reverse input termination are not critical for 2T-HPT structure, as its 3dB bandwidth is limited by the base discharge time constant. A four 5mum x 10mum 2T-HPT section P-TWHPT is simulated with the phase mismatch and without reverse termination. It has a gain of 49dB and a cut-off frequency of 67.5GHz.