Photonic-crystal waveguides and patterned materials: new modelling applications for Helmholtz soliton theory

Spatial solitons are localized, self-stabilizing beams of light that can become the dominant electromagnetic modes of a dielectric planar waveguide . They can arise when material effects (nonlinearly-induced refractive-index changes) oppose diffractive broadening, resulting in beams with propagation-invariant intensity profiles. Such stationary states of light - spatial solitons - have become a universal feature of the nonlinear photonics literature since their inception in the mid 1960s. Intrinsic robustness against perturbations makes spatial solitons ideal candidates for use in a diverse range of proposed device applications and, to this day, they remain an integral part of both theoretical and experimental research.Angular considerations lie at the heart of optics. For instance, even the simplest experimental arrangements - the overlapping of two beams , or a single beam impinging obliquely on a material interface - have intrinsic angle-dependent (off-axis) characteristics. These systems cannot be adequately described by conventional (paraxial) modelling approaches, where angles (defined with respect to a reference axis) are constrained to be negligibly or near-negligibly small. Moreover, interaction and single-interface scenarios are elementary building block geometries from which many of the most exotic and sophisticated configurations (e.g., induced waveguiding, optical switching, processing and storing of optical information, optical computing) are constructed. Intellectual investment in the understanding of oblique-propagation effects is thus fundamental to optical science in general, and essential for the effective design and realization of future photonic devices and architectures.A highly active branch of current photonics research considers light evolving in periodically-patterned media. Conventionally, there are two main classes of periodic structure: coupled-waveguide arrays (CWAs) and photonic crystals (PCs). Referring to Fig. 1, CWA (PC) configurations tend to involve modulations in the refractive-index profile that are predominantly perpendicular (parallel) to the beam axis. While both configurations are equivalent to a multi-layer interface problem, their relationship is much more subtle. By approaching these systems with angular considerations firmly in mind, it becomes apparent that CWAs and PCs are geometrically identical structures - they are related by a rotation. Such a connection is masked in paraxial modelling, where rotational effects are strictly limited by inherent approximations. As a result of this insight alone, it is clear that Helmholtz modelling becomes essential for studying oblique propagation of light across patterned structures.Despite the pivotal role played by angular effects in nonlinear photonics, this territory remains largely uncharted. Helmholtz soliton theory is uniquely placed to address oblique-incidence problems within a mathematically elegant and computationally accessible framework. It provides the ideal platform for designing novel devices whose operation relies on intrinsic angular characteristics. The proposed research project is a potential gold mine for scientific publications and new device applications, with the advantage that theoretical predictions are immediately testable in the laboratory.