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Outputs (128)

Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension (2015)
Presentation / Conference
Christian, J., Woodroofe, E., & McDonald, G. (2015, July). Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

The diffraction of plane waves from simple hard-edged apertures constitutes a class of boundary value problem that is well understood in optics, at least within the scalar approximation. Similarly, the diffraction of such waves from fractal apertures... Read More about Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension.

Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes (2015)
Presentation / Conference
Christian, J., Begleris, I., Wickham, S., McDonald, G., & Huang, J. (2015, July). Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

We will report on our latest research into modelling fractal lasers (linear systems that involve geometrically-unstable resonators with inherent magnification), and propose two new classes of cavity configuration. These devices are of fundamental the... Read More about Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes.

Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law (2015)
Presentation / Conference
McCoy, E., Christian, J., Sanchez-Curto, J., & McDonald, G. (2015, July). Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Waves, Karlsruhe, Germany

The interaction of self-localized waves with an abrupt interface is a problem of fundamental importance in many branches of physics, engineering, and applied mathematics. Waveguide optics, for instance, is dominated in an essential way by such consid... Read More about Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law.

Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity (2015)
Presentation / Conference
Carter, L., Christian, J., McDonald, G., & Chamorro-Posada, P. (2015, July). Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Waves, Karlsruhe, Germany

The origin of conventional models for nonlinear optical pulse propagation lies in the ubiquitous slowly-varying envelope approximation (SVEA) accompanied by a Galilean boost to a local-time frame. While such a near-universal procedure typically resul... Read More about Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity.

Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation (2015)
Presentation / Conference
Bostock, C., Christian, J., Leite, A., McDonald, G., & Huang, J. (2015, June). Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

Alan Turing's profound insight into morphogenesis, published in 1952, has provided the cornerstone for understanding the origin of pattern and form in Nature. When the uniform states of a nonlinear reaction-diffusion system are sufficiently stressed,... Read More about Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation.

Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses (2014)
Presentation / Conference
McCoy, E., Christian, J., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. (2014, September). Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses. Presented at 5th European Optical Society Annual Meeting, Berlin, Germany

We report on our most recent results concerning arbitrary-angle spatial soliton refraction at the interface between dissimilar dielectrics, each of which comprises both X(3)and X(5) susceptibilities. Attention is also paid to the oblique injectio... Read More about Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses.

Coupled-waveguide arrays: Oblique injection & soliton propagation (2013)
Presentation / Conference
Christian, J., McCoy, E., & McDonald, G. (2013, June). Coupled-waveguide arrays: Oblique injection & soliton propagation. Presented at College of Science & Technology Research Showcase, University of Salford

The interaction between light beams and periodically-patterned host materials (such as coupled-waveguide arrays or photonic crystals) is a fundamental class of problem in nonlinear optics [1,2]. While oblique (off-axis) propagation effects play a cen... Read More about Coupled-waveguide arrays: Oblique injection & soliton propagation.

Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law (2013)
Presentation / Conference
Yates, R., Christian, J., & McDonald, G. (2013, June). Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law. Presented at College of Science & Technology Research Showcase, University of Salford

The refraction of light waves at planar interfaces is a problem of fundamental interest to the optics community. To date, our Snell’s law-type analyses have considered only families of hyperbolic solitons – robust nonlinear beams that are strongly (e... Read More about Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law.

Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law (2013)
Presentation / Conference
Yates, R., Christian, J., & McDonald, G. (2013, June). Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law. Presented at College of Science & Technology Research Showcase, University of Salford

The refraction of light waves at planar interfaces is a problem of fundamental interest to the optics community. To date, our Snell’s law-type analyses have considered only families of hyperbolic solitons – robust nonlinear beams that are strongly (e... Read More about Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law.