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Dr James Christian's Outputs (149)

Helmholtz solitons: fresh perspectives and new angles in photonics (2008)
Presentation / Conference
Christian, J., Mcdonald, G., & Chamorro-Posada, P. (2008, August). Helmholtz solitons: fresh perspectives and new angles in photonics. Poster presented at National Photonics Conference, Photon 08, Heriot-Watt University, Edinburgh, UK

Spatial solitons are self-localizing optical beams that can evolve with a stationary intensity profile when diffraction is off-set by material nonlinearity. Classic descriptions of spatial solitons [1] involve the paraxial approximation, which can im... Read More about Helmholtz solitons: fresh perspectives and new angles in photonics.

Soliton solutions of the nonlinear Helmholtz equation: propagation properties, interface effects and new families of exact solutions (2008)
Presentation / Conference
Chamorro-Posada, P., Sanchez-Curto, J., McDonald, G., & Christian, J. (2008, June). Soliton solutions of the nonlinear Helmholtz equation: propagation properties, interface effects and new families of exact solutions. Presented at Annual International Conference "Days on Diffraction" 2008, St. Petersburg, Russia

The properties of spatial optical solitons are most often studied using nonlinear Schroedinger (NLS) equations. These model the slow modulation the envelope of a linear wave solution experiences when propagation takes place in a wealky nonlinear medi... Read More about Soliton solutions of the nonlinear Helmholtz equation: propagation properties, interface effects and new families of exact solutions.

Helmholtz solitons: Maxwell’s equations, interfaces, bistability & counterpropagation (2008)
Presentation / Conference
Chamorro-Posada, P., Sanchez-Curto, J., Grikurov, V., McDonald, G., & Christian, J. (2008, June). Helmholtz solitons: Maxwell’s equations, interfaces, bistability & counterpropagation. Presented at Days on Diffraction, 2008. DD '08 International Conference, St. Petersburg, Russia

We give a brief overview of some new results in Helmholtz soliton theory. Firstly, fundamental considerations are made in terms of new contexts for Helmholtz solitons that arise directly from Maxwells equations. We then detail applications of Helmhol... Read More about Helmholtz solitons: Maxwell’s equations, interfaces, bistability & counterpropagation.

Helmholtz-Manakov solitons (2006)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2006). Helmholtz-Manakov solitons. Physical Review E, 74(6), 066612. https://doi.org/10.1103/PhysRevE.74.066612

A novel spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (H-M) equation, for describing the evolution of broad multi-component self-trapped beams in Kerr-type media. By omitting the slowly-varying envelope approximation, the... Read More about Helmholtz-Manakov solitons.

Korteweg-de Vries description of Helmholtz-Kerr dark solitons (2006)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2006). Korteweg-de Vries description of Helmholtz-Kerr dark solitons. https://doi.org/10.1088/0305-4470/39/50/004

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturb... Read More about Korteweg-de Vries description of Helmholtz-Kerr dark solitons.

Fresnel diffraction and fractal patterns from polygonal apertures (2006)
Journal Article
Huang, J., Christian, J., & McDonald, G. (2006). Fresnel diffraction and fractal patterns from polygonal apertures. https://doi.org/10.1364/JOSAA.23.002768

Two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures under uniform illumination are detailed. In particular, a simple expression for the diffracted field from constituent edges is derived. These results have fu... Read More about Fresnel diffraction and fractal patterns from polygonal apertures.

Broadband nonlinear optics: fractals, white light and multiplexing (2005)
Presentation / Conference
McDonald, G., Christian, J., Huang, J., Laughton, G., Chamorro-Posada, P., & Sanchez-Curto, J. (2005, February). Broadband nonlinear optics: fractals, white light and multiplexing. Presented at New Trends in Nonlinear Optics, Univesity of Strathclyde, Glasgow, UK

We will present an overview of some recent works that collectively fall under the banner of “broadband nonLinear optics”. Firstly, a generic mechanism for the spontaneous formation of spatial optical fractals has been proposed. Willie’s classic singl... Read More about Broadband nonlinear optics: fractals, white light and multiplexing.

Chaotic scattering problems with polygons and polyhedra: exit basins and uncertainty fractal dimension
Presentation / Conference
Christian, J. Chaotic scattering problems with polygons and polyhedra: exit basins and uncertainty fractal dimension. Poster presented at 4th IMA Conference on Nonlinearity and Coherent Structures, University of Loughborough (online)

The Gaspard-Rice (GR) problem provides a paradigm for studying ballistic scattering in a
plane, and it exhibits the phenomenon of sensitive dependence on initial conditions. The
classic incarnation comprises a point-particle projectile reflecting s... Read More about Chaotic scattering problems with polygons and polyhedra: exit basins and uncertainty fractal dimension.

Spontaneous patterns from Ablowitz-Ladik equations: cavity boundary conditions, instabilities, and mean-field theory
Presentation / Conference
cavity boundary conditions, instabilities, and mean-field theory. Presented at 4th IMA Conference on Nonlinearity and Coherent Structures, University of Loughborough (online)

In physics, the discrete nonlinear Schrödinger (dNLS) equation plays a key role in modelling wave
propagation in periodic systems. Optical architectures typically involve light confined to a set of
waveguide channels with nearest-neighbour coupling... Read More about Spontaneous patterns from Ablowitz-Ladik equations: cavity boundary conditions, instabilities, and mean-field theory.

Multi-Turing instabilities and spatial patterns in discrete systems : simplicity and complexity, cavities and counterpropagation
Presentation / Conference
Bostock, C., Christian, J., Leite, A., McDonald, G., & Huang, J. Multi-Turing instabilities and spatial patterns in discrete systems : simplicity and complexity, cavities and counterpropagation. Poster presented at 6th European Optical Society Annual Meeting (EOSAM 2016), Berlin Adlershof, Germany

The spontaneous pattern-forming properties of three discrete nonlinear optical
systems are investigated, including the proposal of two new physical contexts for
coupled-waveguide geometries. Linear analyses predict Turing threshold instability
spe... Read More about Multi-Turing instabilities and spatial patterns in discrete systems : simplicity and complexity, cavities and counterpropagation.

Vector waves with spatiotemporal dispersion and \chi(3) nonlinearity : transformations and relativity, solitons and stability
Presentation / Conference
Carter, L., Christian, J., & McDonald, G. Vector waves with spatiotemporal dispersion and \chi(3) nonlinearity : transformations and relativity, solitons and stability. Poster presented at 6th European Optical Society Annual Meeting (EOSAM 2016), Berlin Adlershof, Germany

A vector model, fully-second-order in both space and time, is proposed for coupled
electromagnetic modes in nonlinear waveguides. Our formalism has strong overlaps
with the special relativity. Exact two-component solitons are derived, asymptotic
a... Read More about Vector waves with spatiotemporal dispersion and \chi(3) nonlinearity : transformations and relativity, solitons and stability.

Complex Ginzburg-Landau equations with space-time symmetry : attenuation and amplification, solitons and shockwaves
Presentation / Conference
Barrow, P., Christian, J., & McDonald, G. Complex Ginzburg-Landau equations with space-time symmetry : attenuation and amplification, solitons and shockwaves. Poster presented at 6th European Optical Society Annual Meeting (EOSAM 2016), Berlin Adlershof, Germany

We present an overview of our research into space-time-symmetrized complex Ginzburg-Landau equations, going beyond the traditional assumption of slowly-varying
envelopes. Exact analytical solitary solutions are detailed, and their stability properti... Read More about Complex Ginzburg-Landau equations with space-time symmetry : attenuation and amplification, solitons and shockwaves.

Fresnel diffraction patterns from fractal apertures : boundaries and circulation, pentaflakes and islands
Presentation / Conference
Christian, J., McDonaldg, G., Kotsampaseris, A., & Huang, J. Fresnel diffraction patterns from fractal apertures : boundaries and circulation, pentaflakes and islands. Presented at 6th European Optical Society Annual Meeting (EOSAM 2016), Berlin Adlershof, Germany

We present a theoretical and numerical analysis of near-field diffraction patterns from
hard-edged apertures whose shapes correspond to the iterations of (closed) classic
fractal curves. The Fresnel (paraxial) area integral is transformed into a ci... Read More about Fresnel diffraction patterns from fractal apertures : boundaries and circulation, pentaflakes and islands.

On the diffraction of monsters : Weierstrass and Young, analysis and edge-waves
Presentation / Conference
Christian, J., & McDonald, G. On the diffraction of monsters : Weierstrass and Young, analysis and edge-waves. Presented at 6th European Optical Society Annual Meeting (EOSAM 2016), Berlin Adlershof, Germany

We report on recent research developments investigating the diffraction of fractal
(i.e., multi-scale) light waves from simple hard-edged apertures. A bandwidth-limited
Weierstrass function is used as a physical model for illumination, and a formal... Read More about On the diffraction of monsters : Weierstrass and Young, analysis and edge-waves.