Analytical studies of spatial and temporal confinement in stimulated Raman scattering
The work presented in this thesis is a description of theoretical techniques for spatial and temporal confinement in the small signal regime of Stimulated Raman Scattering with a pump laser beam. The aim of this work is to provide where possible a mathematical model for the effects of confinement on both the pump, and the Raman generated Stokes fields, whilst at the same time to give some idea of the tools available to the theoretician pursuing this end. Particular attention has been paid to the (existing) domains over which relatively simple mathematical models are applicable, and also to provide bounds on the applicability of both original and existing results. Both the Maxwell and Lagrange formulation of the (electromagnetic) propagation problem are developed in this work. The paraxial ray equation which arises from the former is investigated in some detail; results are presented which give the full set of refractive index variations for which this equation is separable (and therefore potentially soluble) under an arbitrary transformation. The Lagrange formulation is employed to solve the spatial confinement problem which may arise from the use of a waveguide or a focussed pump beam. The traditional Maxwell formulation is used to provide the solutions to the temporal confinement problem. Where possible, results are presented which combine the solutions from both domains to obtain a model for simultaneous spatial and temporal confinement.