Dr James Christian's Outputs (150)

Arbitrary-angle scattering of spatial solitons from dielectric optical interfaces (2011)
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. (2011, June). Arbitrary-angle scattering of spatial solitons from dielectric optical interfaces. Poster presented at College Research Showcase Day, University of Salford, Greater Manchester, UK

Wave–interface phenomena appear throughout Nature and are intrinsically angular in character. For instance, the behaviour of light waves at material boundaries underpins the entire field of optics. The seminal works on nonlinear
beam refraction [1]... Read More about Arbitrary-angle scattering of spatial solitons from dielectric optical interfaces.

Relativistic & pseudo-relativistic connections in optical pulse propagation (2011)
Presentation / Conference
Christian, J., McDonald, G., Lundie, M., & Lancaster, G. (2011, June). Relativistic & pseudo-relativistic connections in optical pulse propagation. Poster presented at College Research Showcase Day, University of Salford, Greater Manchester, UK

We explore a more complete model for describing the evolution of scalar optical pulses in generic nonlinear waveguides. The electromagnetic wave envelope satisfies a dimensionless equation that is of the Helmholtz type. Our
approach is to retain the... Read More about Relativistic & pseudo-relativistic connections in optical pulse propagation.

Propagation and stability of two-colour spatial optical solitons (2011)
Presentation / Conference
Bostock, C., Christian, J., & McDonald, G. (2011, June). Propagation and stability of two-colour spatial optical solitons. Presented at College Research Showcase Day, University of Salford, Greater Manchester, UK

Two-colour spatial solitons comprise coupled nonlinear optical beams at two distinct temporal frequencies [1]. The components (which may be bright-like and/or dark-like) are localized in space and tend to overlap, thereby allowing
the interplay betw... Read More about Propagation and stability of two-colour spatial optical solitons.

Research on nonlinear and quantum optics at the photonics and quantum information group of the University of Valladolid (2011)
Journal Article
quantum information group of the University of Valladolid. Optica Pura y Aplicada, 44(2), 211-217

We outline the main research lines in Nonlinear and Quantum Optics of the Group of Photonics and Quantum Information at the University of Valladolid. These works focus on Optical Solitons, Quantum Information using Photonic Technologies and the devel... Read More about Research on nonlinear and quantum optics at the photonics and quantum information group of the University of Valladolid.

Refraction law for self-collimated light beams at material interfaces (2010)
Presentation / Conference
McCoy, E., Christian, J., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. (2010, November). Refraction law for self-collimated light beams at material interfaces. Presented at 1st CSE Doctoral School Postgraduate Research Conference, University of Salford, Greater Manchester, UK

Perhaps the most fundamental electromagnetic phenomenon is the behaviour of light at the interface between dissimilar materials. In fact, the entire field of Optics follows from this single key concept. The reflection and refraction properties of a p... Read More about Refraction law for self-collimated light beams at material interfaces.

Refraction of power-law spatial solitons – the Helmholtz-Snell law (2010)
Presentation / Conference
Christian, J., Sánchez-Curto, J., Chamorro-Posada, P., McDonald, G., & McCoy, E. (2010, September). Refraction of power-law spatial solitons – the Helmholtz-Snell law. Presented at 10th International Conference on Laser and Fiber-Optical Networks Modeling (LFNM), 2010, Sevastopol, Crimea, Ukraine

The behaviour of a scalar optical beam at the boundary between two dissimilar nonlinear media is of fundamental interest in nonlinear photonics. Here, we report the first systematic generalization of our Kerr analyses to a wider class of power-law ma... Read More about Refraction of power-law spatial solitons – the Helmholtz-Snell law.

Kaleidoscope laser properties and new optical fractal contexts (2010)
Presentation / Conference
Christian, J., McDonald, G., Heyes, A., & Huang, J. (2010, September). Kaleidoscope laser properties and new optical fractal contexts. Presented at 5th International Conference on Advanced Optoelectronics & Lasers, CAOL 2010, Sevastopol, Crimea, Ukraine

We present the first detailed account of kaleidoscope laser modes where the equivalent Fresnel number Neq and magnification M may assume arbitrary values. Properties of these linear fractal eigenmodes are explored through extensive numerical computat... Read More about Kaleidoscope laser properties and new optical fractal contexts.

Helmholtz solitons in optical materials with a dual power-law refractive index (2010)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2010). Helmholtz solitons in optical materials with a dual power-law refractive index. Journal of Nonlinear Optical Physics and Materials, 19(3), 389-405. https://doi.org/10.1142/S0218863510005340

A nonlinear Helmholtz equation is proposed for modelling scalar optical beams in uniform planar waveguides whose refractive index exhibits a purely-focusing dual powerlaw
dependence on the electric field amplitude. Two families of exact analytical s... Read More about Helmholtz solitons in optical materials with a dual power-law refractive index.

Universal Snell’s law & bright spatial soliton refraction (2010)
Presentation / Conference
Sánchez-Curto, J., Chamorro-Posada, P., Christian, J., McDonald, G., & McCoy, E. (2010, August). Universal Snell’s law & bright spatial soliton refraction. Poster presented at National Photonics Conference, Photon 10, Southampton, UK

The behaviour of a scalar optical beam at the boundary between two dissimilar Kerr media is of fundamental interest in nonlinear photonics. Since this class of problem is intrinsically nonparaxial, the limitations of conventional (paraxial) theory mu... Read More about Universal Snell’s law & bright spatial soliton refraction.

Optical pulses with spatial dispersion – solitons & relativity (2010)
Presentation / Conference
Christian, J., McDonald, G., Hodgkinson, T., & Chamorro-Posada, P. (2010, August). Optical pulses with spatial dispersion – solitons & relativity. Poster presented at National Photonics Conference, Photon 10, Southampton, UK

We propose a new model for describing the evolution of scalar optical pulses in Kerr-type waveguides. The (normalized) wave envelope u satisfies a governing equation that is of the nonlinear Helmholtz type, where the space and time coordinates are de... Read More about Optical pulses with spatial dispersion – solitons & relativity.

Fractal laser sources: new analyses, results and contexts (2010)
Presentation / Conference
Christian, J., McDonald, G., Heyes, A., & Huang, J. (2010, August). Fractal laser sources: new analyses, results and contexts. Presented at National Photonics Conference, Photon 10, Southampton, UK

A series of significant new extensions concerning fractal light generation are reported. Firstly, we summarise techniques and results from the first full analysis of the linear modes of ‘fractal lasers’ [1] – unstable-cavity geometries with arbitrary... Read More about Fractal laser sources: new analyses, results and contexts.

Novel cavity effects in ultra-broadband multiline Raman generation (2010)
Presentation / Conference
Rose, C., McDonald, G., & Christian, J. (2010, August). Novel cavity effects in ultra-broadband multiline Raman generation. Poster presented at National Photonics Conference, Photon 10, Southampton, UK

Broadband multiline frequency combs present a wealth of applications, ranging from meteorology, sensing and measurements to those potentially in the domain of attosecond science. We report here on detailed investigations of, what we believe is, a nov... Read More about Novel cavity effects in ultra-broadband multiline Raman generation.

Kaleidoscope lasers - Complexity in simple optical systems (2010)
Presentation / Conference
Christian, J., McDonald, G., & Huang, J. (2010, June). Kaleidoscope lasers - Complexity in simple optical systems. Presented at Nonlinear Photonics (NP), Karlsruhe, Germany

We present the first detailed account of modelling kaleidoscope laser modes where the equivalent Fresnel number Neq and magnification M may assume arbitrary values. The convergence toward circularity is also investigated through extensive numerical c... Read More about Kaleidoscope lasers - Complexity in simple optical systems.

Helmholtz pulse propagation & spatially-dispersive light (2010)
Presentation / Conference
Christian, J., Hodgkinson, T., McDonald, G., & Chamorro-Posada, P. (2010, June). Helmholtz pulse propagation & spatially-dispersive light. Presented at Nonlinear Photonics (NP), Karlsruhe, Germany

We present the first detailed account of modelling pulses in Helmholtz-type nonlinear systems with both temporal and spatial dispersion. Exact analytical solitons will be reported, and their stability examined through mathematical analysis and comput... Read More about Helmholtz pulse propagation & spatially-dispersive light.

Bistable dark solitons of a cubic-quintic Helmholtz equation (2010)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2010). Bistable dark solitons of a cubic-quintic Helmholtz equation. Physical Review A, 81(5), https://doi.org/10.1103/PhysRevA.81.053831

We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instabili... Read More about Bistable dark solitons of a cubic-quintic Helmholtz equation.

Helmholtz algebraic solitons (2010)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2010). Helmholtz algebraic solitons. Journal of Physics A: Mathematical and Theoretical, 43(8), https://doi.org/10.1088/1751-8113/43/8/085212

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the pr... Read More about Helmholtz algebraic solitons.

Bistable Helmholtz bright solitons in saturable materials (2009)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2009). Bistable Helmholtz bright solitons in saturable materials. Journal of the Optical Society of America B, 26(12), 2323-2330. https://doi.org/10.1364/JOSAB.26.002323

We present, to the best of our knowledge, the first exact analytical solitons of a nonlinear Helmholtz equation with a saturable refractive-index model. These new two-dimensional spatial solitons have a bistable characteristic in some parameter regim... Read More about Bistable Helmholtz bright solitons in saturable materials.

Turing instability: a universal route to spontaneous spatial fractals (2008)
Presentation / Conference
Huang, J., Christian, J., McDonald, G., & Chamorro-Posada, P. (2008, September). Turing instability: a universal route to spontaneous spatial fractals. Presented at European Optical Society Annual Meeting, Paris, France

We present the first predictions of spontaneous spatial fractal patterns in nonlinear ring cavities. New analyses reveal multi-Turing spectra characteristic of susceptibility
for spontaneous fractals. Extensive computer simulations confirm theoretic... Read More about Turing instability: a universal route to spontaneous spatial fractals.

Wide class of new fractal light sources [Invited plenary paper] (2008)
Presentation / Conference
McDonald, G., Christian, J., & Huang, J. (2008, September). Wide class of new fractal light sources [Invited plenary paper]. Presented at Advanced Optoelectronics and Lasers (CAOL), 2010 International Conference, Alushta, Crimea, Ukraine

Pattern emergence in Naturepsilas complex systems is mostly attributed to a classic Turing instability. There, a single length-scale becomes dominant and this defines a simple emergent structure (for example, a striped or hexagonal pattern). We have... Read More about Wide class of new fractal light sources [Invited plenary paper].

Turing instability: a universal route to spontaneous fractal patterns (2008)
Presentation / Conference
Huang, J., Christian, J., McDonald, G., & Chamorro-Posada, P. (2008, August). Turing instability: a universal route to spontaneous fractal patterns. Poster presented at National Photonics Conference, Photon 08, Heriot-Watt University, Edinburgh, UK

Turing instability is the tendency of the uniform states of a system to become spontaneously patterned in the presence of any small fluctuation [1]. Archetypal Turing- instability patterns include hexagons, squares, stripes, and rings. These simple s... Read More about Turing instability: a universal route to spontaneous fractal patterns.