Dr Graham McDonald's Outputs (169)

Spontaneous spatial fractals: universal contexts and applications (2011)
Presentation / Conference
Mcdonald, G., Christian, J., Heyes, A., Millington, N., Walsh, T., & Huang, J. (2011, May). Spontaneous spatial fractals: universal contexts and applications. Presented at CLEO Europe - EQEC 2011, Munich, Germany

We report on our latest research in the field of spontaneous spatial fractal patterns. New analyses, results and potential applications are reported for nonlinear ring cavities and kaleidoscope laser systems.

Total non-refraction angle at Kerr defocusing interfaces (2011)
Presentation / Conference
Sánchez-Curto, J., Chamorro-Posada, P., & Mcdonald, G. (2011, February). Total non-refraction angle at Kerr defocusing interfaces. Presented at QUONLOP 2011, Meeting of the Quantum Optics and Nonlinear Optics Committee of SEDOPTICA, University of Valladolid, Spain

Spatial soliton refraction at interfaces separating two nonlinear media has traditionally been studied in terms of the paraxial Nonlinear Schrödinger (NLS) Equation, thus restricting the validity of results to vanishingly small angles of incidence. T... Read More about Total non-refraction angle at Kerr defocusing interfaces.

Black and gray Helmholtz Kerr soliton refraction (2011)
Journal Article
Sanchez-Curto, J., Chamorro-Posada, P., & McDonald, G. (2011). Black and gray Helmholtz Kerr soliton refraction. Physical Review A, 83(1), 013828. https://doi.org/10.1103/PhysRevA.83.013828

efraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell’s law is derived that describes gray soliton refraction, in addition to capturing the... Read More about Black and gray Helmholtz Kerr soliton refraction.

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.

A potential new light source for nuclear fusion (2010)
Presentation / Conference
Rose, C., McDonald, G., & Christian, J. (2010, November). A potential new light source for nuclear fusion. Presented at 1st CSE Doctoral School Postgraduate Research Conference, University of Salford, Greater Manchester

Lasers typically emit light of one or two, well-defined, frequencies (or ‘colours’). However, numerous applications arise if such light can be converted into a broad, multi-frequency (e.g. ‘multi-colour’) comb of laser beams. Applications range from... Read More about A potential new light source for nuclear fusion.

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.

Refraction of grey solitons at defocusing Kerr interfaces (2010)
Presentation / Conference
Sanchez-Curto, J., Chamorro-Posada, P., & Mcdonald, G. (2010, September). Refraction of grey solitons at defocusing Kerr interfaces. Presented at 5th International Conference on Advanced Optoelectronics & Lasers, CAOL 2010, Sevastopol, Crimea, Ukraine

We present a generalized Snell’s law that governs grey soliton refraction at the interface separating two defocusing
Kerr media. The analysis, based on the Helmholtz theory, is valid for arbitrary angles of incidence and reveals that grey solitons u... Read More about Refraction of grey solitons at defocusing Kerr interfaces.

Optical soliton pulses with relativistic characteristics (2010)
Presentation / Conference
Mcdonald, G., Christian, J., & Hodgkinson, T. (2010, September). Optical soliton pulses with relativistic characteristics. Presented at 5th International Conference on Advanced Optoelectronics & Lasers, CAOL 2010, Sevastopol, Crimea, Ukraine

The slowly varying envelope approximation and the ensuing Galilean boost to a local time frame are near-universal features of conventional scalar pulse models. Here, we will give an overview of our recent progress with a new approach to nonlinear pul... Read More about Optical soliton pulses with relativistic characteristics.

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.

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.

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.

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.

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.

Black and grey soliton refraction at interfaces (2010)
Presentation / Conference
Sánchez-Curto, J., Chamorro-Posada, P., & McDonald, G. (2010, August). Black and grey soliton refraction at interfaces. Poster presented at National Photonics Conference, Photon 10, Southampton, UK

The behaviour of grey solitons incident on Kerr defocusing interfaces is studied within the framework of Helmholtz theory. We report that the refraction of grey solitons is governed by a generalized Snell's law whose validity extends to arbitrary ang... Read More about Black and grey soliton refraction at interfaces.

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 dark solitons at nonlinear defocusing interfaces (2010)
Presentation / Conference
Sanchez Curto, J., Chamorro-Posada, P., & McDonald, G. (2010, June). Helmholtz dark solitons at nonlinear defocusing interfaces. Presented at Nonlinear Photonics (NP, Karlsruhe, Germany

Dark Kerr soliton refraction at planar boundaries is analysed and simulated for the first time. A universal law of Kerr spatial soliton refraction is derived. Strong parameter sensitivity of gray soliton refraction is also uncovered.

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.

Dark solitons at nonlinear interfaces (2010)
Journal Article
Sanchez-Curto, J., Chamorro-Posada, P., & McDonald, G. (2010). Dark solitons at nonlinear interfaces. Optics Letters, 35(9), 1347-1349. https://doi.org/10.1364/OL.35.001347

The refraction of dark solitons at a planar boundary separating two defocusing Kerr media is simulated and analyzed, for the first time (to our knowledge). Analysis is based on the nonlinear Helmholtz equation and is thus valid for any angle of incid... Read More about Dark solitons at nonlinear interfaces.