The main subject of this thesis is solitons due to degenerate parametric four-wave mixing. Derivation of the governing equations is carried out for both spatial solitons (slab waveguide) and temporal solitons (optical fibre). Higher-order effects that are ignored in the standard paraxial approximation are discussed and estimated. Detailed analysis of conventional solitons is carried out. This includes discovery of various solitons families, linear stability analysis of fundamental and higher-order solitons, development of theory describing nonlinear dynamics of higher-order solitons. The major findings related to the stationary problem are bifurcation of a two-frequency soliton family from an asymptotic family of infinitely separated one-frequency solitons, jump bifurcation and violation of the bound state principle. Linear stability analysis shows a rich variety of internal modes of the fundamental solitons and existence of a stability window for higher-order solitons. Theory for nonlinear dynamics of higher-order solitons successfully predicts the position and size of the stability window, and various instability scenarios. Equivalence between direct asymptotic approach and invariant based approach is demonstrated. A general analytic approach for description of localised solutions that are in resonance with linear waves (quasi-solitons and embedded solitons) is given. This includes normal form theory and approximation of interacting particles. The main results are an expression for the amplitude of the radiating tail of a quasi-soliton, and a two-fold criterion for existence of embedded solitons. Influence of nonparaxiality on soliton stability is investigated. Stationary instability threshold is derived. The major results are shift and decreasing of the size of the stability window for higher-order solitons. The latter is the first demonstration of the destabilizing influence of nonparaxiality on higher-order solitons. Analysis of different aspects of solitons is based on universal approaches and methods. This includes Hamiltonian formalism, consideration of symmetry properties of the model, development of asymptotic models, construction of perturbation theory, application of general theorems etc. Thus, the results obtained can be extended beyond the particular model of degenerate four-wave mixing. All theoretical predictions are in good agreement with the results of direct numerical modeling.

Two colour pumping was used to investigate the short-pulse technique of Multifrequency Raman Generation (MRG) in the transient regime of Raman scattering. In the course of this study we have demonstrated the ability to generate over thirty Raman orders spanning from the infrared to the ultraviolet, investigated the dependence of this generation on the pump intensities and the dispersion characteristics of the hollow-fibre system in which the experiment was conducted, and developed a simple computer model to help understand the exhibited behaviours. These dependence studies have revealed some characteristics that have been previously mentioned in the literature, such as the competition between MRG and self-phase modulation, but have also demonstrated behaviours that are dramatically different than anything reported on the subject. Furthermore, through a simple modification of the experimental apparatus we have demonstrated the ability to scatter a probe pulse into many Raman orders, generating bandwidth comparable to the best pump-probe experiments of MRG. By using a numeric fast Fourier transform, we predict that our spectra can generate pulses as short as 3. 3fs, with energies an order of magnitude larger than pulses of comparable duration that are made using current techniques.

Two colour pumping was used to investigate the short-pulse technique of Multifrequency Raman Generation (MRG) in the transient regime of Raman scattering. In the course of this study we have demonstrated the ability to generate over thirty Raman orders spanning from the infrared to the ultraviolet, investigated the dependence of this generation on the pump intensities and the dispersion characteristics of the hollow-fibre system in which the experiment was conducted, and developed a simple computer model to help understand the exhibited behaviours. These dependence studies have revealed some characteristics that have been previously mentioned in the literature, such as the competition between MRG and self-phase modulation, but have also demonstrated behaviours that are dramatically different than anything reported on the subject. Furthermore, through a simple modification of the experimental apparatus we have demonstrated the ability to scatter a probe pulse into many Raman orders, generating bandwidth comparable to the best pump-probe experiments of MRG. By using a numeric fast Fourier transform, we predict that our spectra can generate pulses as short as 3. 3fs, with energies an order of magnitude larger than pulses of comparable duration that are made using current techniques.

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