Dr James Christian's Outputs (149)

Helmholtz solitons: a new angle in nonlinear science
Presentation / Conference
Chamorro-Posada, P., McDonald, G., Sanchez-Curto, J., & Christian, J. Helmholtz solitons: a new angle in nonlinear science. Presented at Nonlinear Evolution Equations and Dynamical Systems (NEEDS), L’Ametlla de Mar, Spain

The ubiquitous nonlinear SchrÄodinger (NLS) equation models soliton propagation in many di®erent scenarios. In a nutshell, the NLS equation describes the slow modulation of the envelope of a linear wave when propagating in a weakly nonlinear medium.... Read More about Helmholtz solitons: a new angle in nonlinear science.

Peristaltic flow of non-Newtonian, compressible fluid with non-zero boundary slip
Presentation / Conference
Tsiklauri, D., Christian, J., & McDonald, G. Peristaltic flow of non-Newtonian, compressible fluid with non-zero boundary slip. Poster presented at Materials Congress: Institute of Materials, Minerals, and Mining (IoM3), London, UK

In Tsiklauri & Beresnev, Phys Rev E 64, 036303 (2001), we investigated new phenomena brought about into the classic peristaltic mechanism by the inclusion of non-Newtonian effects based on the model of a Maxwell fluid. In Tsiklauri, J Acoust Soc Am 1... Read More about Peristaltic flow of non-Newtonian, compressible fluid with non-zero boundary slip.

Peristaltic wave propagation in compressible Maxwell fluids with boundary slip
Presentation / Conference
Christian, J., Tsiklauri, D., & McDonald, G. Peristaltic wave propagation in compressible Maxwell fluids with boundary slip. Poster presented at Condensed Matter and Materials Physics Conference, University of Exeter, UK

Boundary slip has recently been observed by Craig et al. [Phys Rev Lett 87, 054504 (2001)]. Complementing this work, Tsiklauri [J Acoust Soc Am 112, 843 (2002)] incorporated non-zero boundary slip into a theoretical model of fluid-saturated porous me... Read More about Peristaltic wave propagation in compressible Maxwell fluids with boundary slip.

Helmholtz solitons in non-Kerr media
Presentation / Conference
Christian, J., McDonald, G., & Chamorro-Posada, P. Helmholtz solitons in non-Kerr media. Poster presented at 25th European Quantum Electronics Conference (CLEO Europe/EQEC), Munich, Germany

Spatial optical soliton propagation in a planar waveguide is often modelled by a Non-Linear Schrödinger
(NLS) type equation. Such systems are paraxial in nature, and cannot describe accurately off-axis propagation at nontrivial angles. The NLS equat... Read More about Helmholtz solitons in non-Kerr media.

Helmholtz-Manakov solitons
Presentation / Conference
Christian, J., McDonald, G., & Chamorro-Posada, P. Helmholtz-Manakov solitons. Presented at 25th European Quantum Electronics Conference (CLEO Europe/EQEC), Munich, Germany

The propagation of a spatial vector soliton beam in a Kerr planar waveguide is typically described by the Manakov equation [1]. However, the assumption of beam paraxiality breaks the rotational symmetry of the wave propagation problem. Manakov-based... Read More about Helmholtz-Manakov solitons.

Fresnel diffraction from polygonal apertures
Presentation / Conference
Huang, J., Christian, J., & McDonald, G. Fresnel diffraction from polygonal apertures. Poster presented at 25th European Quantum Electronics Conference (CLEO Europe/EQEC), Munich, Germany

We present, for the first time, two complementary analytical techniques for calculating the Fresnel diffraction patterns from a polygonal aperture illuminated by a plane wave. These frameworks are exact, in that they do not involve any further approx... Read More about Fresnel diffraction from polygonal apertures.

Nonlinear wave phenomena at optical boundaries: spatial soliton refraction
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. Nonlinear wave phenomena at optical boundaries: spatial soliton refraction. Presented at 2nd CSE Doctoral School Postgraduate Research Conference, University of Salford, Greater Manchester, UK

The behaviour of light at the interface between different materials underpins the entire field of Optics. Arguably
the simplest manifestation of this phenomenon – the reflection and refraction characteristics of (infinitely-wide) plane waves at the... Read More about Nonlinear wave phenomena at optical boundaries: spatial soliton refraction.

New modelling applications for Helmholtz soliton theory : from single interfaces to waveguide arrays
Thesis
McCoy, E. New modelling applications for Helmholtz soliton theory : from single interfaces to waveguide arrays. (Thesis). University of Salford

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 backgro... Read More about New modelling applications for Helmholtz soliton theory : from single interfaces to waveguide arrays.

The diffraction of monsters from complex apertures
Thesis
Middleton-Spencer, H. (in press). The diffraction of monsters from complex apertures. (Dissertation). University of Salford

The research presented in this MSc thesis is concerned with understanding the way incoming electromagnetic waves are diffracted by various different types of scattering screens. These classes of problem are fundamental in the laser optics community,... Read More about The diffraction of monsters from complex apertures.