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All Outputs (107)

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.

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.

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.

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.

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.

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.

The spatiotemporal ginzburg-landau equation: Dissipative solitons & stability (2013)
Presentation / Conference
Bresnahan, D., Christian, J., & McDonald, G. (2013, June). The spatiotemporal ginzburg-landau equation: Dissipative solitons & stability. Presented at College of Science & Technology Research Showcase, University of Salford

The complex Ginzburg-Landau (GL) equation describes universal wave propagation in dispersive systems that also exhibit competition between amplification and dissipation [1,2]. The balance between dispersive effects (group-velocity dispersion and self... Read More about The spatiotemporal ginzburg-landau equation: Dissipative solitons & stability.

Coupled spatiotemporal waves: New paradigms in vector soliton physics (2013)
Presentation / Conference
Ashley, J. T., Christian, J., & McDonald, G. (2013, June). Coupled spatiotemporal waves: New paradigms in vector soliton physics. Presented at College of Science & Technology Research Showcase, University of Salford

In this presentation, we propose a novel spatiotemporal generalization of Menyuk’s classic equations [1] describing the propagation of two nonlinearly-coupled waves in a dispersive optical system (such as a fibre or planar waveguide). Our approach is... Read More about Coupled spatiotemporal waves: New paradigms in vector soliton physics.

Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts (2013)
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. (2013, June). Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts. Presented at College of Science & Technology Research Showcase, University of Salford

In this presentation, we give the first detailed overview of spatial soliton refraction at the planar interface between materials whose nonlinear polarization has contributions from both X(3)and X(5)susceptibilities [1]. The governing equation is of... Read More about Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts.

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.

The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit (2013)
Presentation / Conference
Readman, S., Christian, J., Bostock, C., & McDonald, G. (2013, June). The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit. Presented at College of Science & Technology Research Showcase, University of Salford

An optical ring cavity filled with an absorptive material is a fundamental spontaneous pattern-forming system [1]. Analyses of Turing bifurcations in these (uni-directional) cavity configurations [see Fig. 1(a)] can be simplified by deploying the thi... Read More about The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit.

The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system (2013)
Presentation / Conference
Patel, S., Christian, J., Bostock, C., & McDonald, G. (2013, June). The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system. Presented at College of Science & Technology Research Showcase, University of Salford

The nonlinear Fabry-Pérot (FP) cavity [see Fig. 1(a)] is a generalization of the classic diffusive Kerr slice with a single feedback mirror [1,2]. Such apparent simplicity is deceptive. Historically, analysis of the FP geometry has proved to be a non... Read More about The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system.

Ultrabroad-band Raman light: Linear detuning & gain suppression (2013)
Presentation / Conference
Kelly, R., Christian, J., & McDonald, G. (2013, June). Ultrabroad-band Raman light: Linear detuning & gain suppression. Presented at College of Science & Techology Research Showcase, University of Salford

Ultrabroad-band multifrequency Raman generation is a (laser-driven) resonant-symmetric two-colour pumping technique for exciting polychromatic light beams that are characterized by potentially very wide “top-hat” temporal bandwidths [1]. The spectra... Read More about Ultrabroad-band Raman light: Linear detuning & gain suppression.

Diffraction of fractal light: New frontiers for the mathematics of edge waves (2013)
Presentation / Conference
Mylova, M., McDonald, G., & Christian, J. (2013, June). Diffraction of fractal light: New frontiers for the mathematics of edge waves. Presented at College of Science & Technology Research Showcase, University of Salford

The diffraction pattern produced by a plane wave (i.e., a perfectly uniform wavefront) scattering from an infinite hard edge is well-described by the Fresnel integral [1]. Such one-dimensional (1D) edge waves [see Fig. 1(a)] turn out to be truly elem... Read More about Diffraction of fractal light: New frontiers for the mathematics of edge waves.

Spontaneous spatial fractal patterns: Towards nonparaxial nonlinear ring cavities (2013)
Presentation / Conference
Bostock, C., Christian, J., & McDonald, G. (2013, June). Spontaneous spatial fractal patterns: Towards nonparaxial nonlinear ring cavities. Presented at College of Science & Technology Reserach Showcase, University of Salford

Spontaneous pattern formation in optical ring cavities containing a nonlinear (e.g., Kerr-type) material [see Fig. 1(a)] has been studied extensively for the past three decades. A notable trend in the literature over recent years has been a shift awa... Read More about Spontaneous spatial fractal patterns: Towards nonparaxial nonlinear ring cavities.

Kaleidoscope lasers: Polygonal boundary conditions & geometrical instabilities (2013)
Presentation / Conference
McDonald, G., Christian, J., & Huang, J. (2013, June). Kaleidoscope lasers: Polygonal boundary conditions & geometrical instabilities. Presented at College of Science & Technology Research Showcase, University of Salford

Kaleidoscope lasers are geometrically unstable cavities with a feedback mirror that has the shape of a regular polygon [1]. Early calculations of the transverse eigenmodes of these systems hinted toward a fractal (or multi-scale) characteristic, but... Read More about Kaleidoscope lasers: Polygonal boundary conditions & geometrical instabilities.

Instabilities & boundary conditions: fractal mode patterns in kaleidoscope lasers (2012)
Presentation / Conference
fractal mode patterns in kaleidoscope lasers. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

The multi-scale - or fractal - nature of transverse modes in one-dimensional (1D) unstable cavity lasers has been known since the late 1990s [1]. Early collaborations with some members of our Group demonstrated that the origin of fractality (which de... Read More about Instabilities & boundary conditions: fractal mode patterns in kaleidoscope lasers.

Spatiotemporal pulse propagation: connections to special relativity theory (2012)
Presentation / Conference
connections to special relativity theory. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

We propose a more complete model for describing the evolution of scalar optical pulses in nonlinear waveguides. The electromagnetic wave envelope u satisfies a dimensionless spatiotemporal governing equation that is of a fully-second-order form. Wit... Read More about Spatiotemporal pulse propagation: connections to special relativity theory.