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This thesis discusses the wavelength stabilisation of semiconductor lasers for WDM applications. The motivation is to explore the potential of a novel athermal WDM laser with much less wavelength drift than conventional lasers, and without the traditional external temperature compensation units. The study is mainly theoretical, but some experimental work is included. Based on the Cambridge time domain model, intensive simulation has been done to investigate the design space of DBR lasers. Although the structure of the initial prototype DBR model is simple, the simulation output results are rather complex. All the main parameters such as grating length, grating coupling strength, total laser cavity length and waveguide scattering loss are varied. Results obtained agree with current measurements on DBR lasers, and support dimensions and structures derived empirically. Based upon the above results, simulation work then goes further towards the athermal WDM laser idea which employs negative temperature coefficient material to physically compensate the frequency variation with temperature. A polymer widely used in optical waveguides is one candidate. Having reviewed temperature dependent parameters in semiconductor lasers, we incorporated these into the Cambridge Time Domain model. It predicts a wavelength shift of about 0.75 nm over a 100^oC range at wavelength of 1500 nm where about 9nm would be expected from a normal DFB laser. It also reveals other complex and interesting behaviour, which is likely to give several useful insights into the behaviour of tuneable and other forms of DBR and BFB lasers. An experiment to verify the athermal effect of a polymer has been done. Focussed ion beam etch was employed to form a deep grating in near-conventional FP laser, and the grating voids were filled with the polymer. Lasing action with good wavelength stability was observed, though the particular structure employed is probably not capable of single mode operation over a wide temperature range.

In this thesis, we focus on three different optical models possessing accelerating solitons, namely, propagation of beams in photorefractive media with diffusion, pulse propagation in fibre links using sliding-frequency filters and pulse propagation governed by the NLS equation with intrapulse Raman scattering. In each case, an ordinary differential equation (ODE) is obtained from the partial differential equation (PDE) through a similarity variable reduction. Then, we investigate parameter ranges for which solutions exist and their normal mode stability. Integration of the PDE is also used to confirm acceleration regime and stability properties. The three accelerating solitons have the common characteristic that the asymptotics of both the ODE and the stability eigenvalue problem involve solutions to Airy equations. This characteristic allows us to use Airy functions and their asymptotic properties in our analytic and numerical evaluations. It also implies that, in using Evans function ideas in a stability analysis, a significant modification is necessary. The asymptotics must be described in terms of appropriate recessive choices of Airy functions. This leads to a novel modification of the Evans function method, which is then applied in the search for eigenvalues, allowing the identification of unstable and internal (oscillatory) modes when they exist. The prediction of these modes is shown to agree with direct numerical integration of the PDEs.

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