New modelling applications for Helmholtz soliton theory : from single interfaces to waveguide arrays

This thesis details an exploration of the behaviour of spatial optical solitons (self-collimated, self-stabilising light beams) interacting with the interface between classes of nonlinear dielectric materials.Chapter 1 gives the theoretical background to the thesis by introducing the soliton concept, material interfaces and the Helmholtz model. The second chapter discusses the reflection and refraction characteristics of soliton beams incident on the planar boundary between dissimilar cubic-quintic materials. The deployment of Helmholtz soliton theory allows for the simultaneous consideration of: (i) arbitrary angles of incidence, reflection and refraction (relative to the interface), and (ii) finite beam waists (as opposed to infinitely-wide plane waves). Despite an abundance of literature concerning solitons at interfaces, there appears to be no published research addressing refraction in the presence of cubic-quintic optical nonlinearity (and certainly none in arbitrary-angle contexts). Excellent agreement is generally found between theoretical predictions from a generalised Snell’s law and results from extensive computer simulations. In Chapter 3, these novel analyses have been complemented by further investigations into other fundamental aspects of optical refraction, namely Goos-Hänchen shifts and critical angle prediction. Both aspects are the first of their kind in the cubic-quintic regime.The fourth chapter considers surface wave propagation along the interface between two dissimilar power-law materials; this research has already contributed to a published peer reviewed paper [J. M. Christian et al., "Helmholtz bright spatial solitons and surface waves at power-law optical interfaces," Journal of Atomic, Molecular & Optical Physics 2012 (2012), art. no. 137967]. The chapter also expands upon that paper by giving a more detailed account of surface wave stability properties.Chapter 5 provides an in-depth computational study into beam propagation in coupled waveguide arrays (materials whose refractive index is periodically patterned) and there appears to be a link between the beam's critical angle and the depth of the modulation of the array.The thesis concludes with a summary of findings and suggestions surrounding the implications of this novel research