Dr James Christian's Outputs (150)

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.

Helmholtz bright spatial solitons and surface waves at power-law optical interfaces (2012)
Journal Article

We consider arbitrary-angle interactions between spatial solitons and the planar boundary between two optical materials with a single power-law nonlinear refractive index. Extensive analysis has uncovered a wide range of new qualitative phenomena in... Read More about Helmholtz bright spatial solitons and surface waves at power-law optical interfaces.

Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons (2012)
Journal Article
II. Modulational instabilities and dark Kerr solitons. Physical Review A, 86(2), 023839. https://doi.org/10.1103/PhysRevA.86.023839

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with... Read More about Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons.

Helmholtz spatial solitons: towards a theory of ultranarrow optical beams (2012)
Presentation / Conference
Walsh, T., McDonald, G., & Christian, J. (2012, June). Helmholtz spatial solitons: towards a theory of ultranarrow optical beams. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

Spatial optical solitons are self-localizing and self-stabilizing beams of light that propagate with a stationary (invariant) intensity profile. Such nonlinear wave states may arise when a beam's natural tendency to diffract is exactly compensated by... Read More about Helmholtz spatial solitons: towards a theory of ultranarrow optical beams.

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.

Spatial solitons at interfaces: nonparaxial refraction & giant Goos-Hänchen shifts (2012)
Presentation / Conference
nonparaxial refraction & giant Goos-Hänchen shifts. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

The behaviour of light at interfaces underpins, in an essential way, the entire field of optics: almost all technological device designs and architectures rely on the interplay between material mismatches (that define the interface) and the 'degree o... Read More about Spatial solitons at interfaces: nonparaxial refraction & giant Goos-Hänchen shifts.

Helmholtz dark solitons: oblique propagation, saturable materials & bistability (2012)
Presentation / Conference
oblique propagation, saturable materials & bistability. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

Dark spatial optical solitons comprise a uniform background wave that is modulated by an obliquely-propagating 'dip' in the light intensity profile. Appearing throughout nonlinear science, these universal entities possess a phase topology that endows... Read More about Helmholtz dark solitons: oblique propagation, saturable materials & bistability.

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.

Vector spatial solitons: off-axis nonparaxiality in coupled Helmholtz equations (2012)
Presentation / Conference
in coupled Helmholtz equations. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

Vector spatial solitons are complex optical beams with several distinct components. These components (which may be bright-like and/or dark-like) are localized in space and tend to overlap strongly in the propagation plane, thereby allowing the interp... Read More about Vector spatial solitons: off-axis nonparaxiality in coupled Helmholtz equations.

Spontaneous spatial fractal pattern formation in absorptive systems (2012)
Journal Article
Huang, J. G., Christian, J. M., & McDonald, G. S. (2012). Spontaneous spatial fractal pattern formation in absorptive systems. Journal of Nonlinear Optical Physics and Materials, 21(2), 1-9. https://doi.org/10.1142/S021886351250018X

We predict, for the first time to our knowledge, that purely-absorptive nonlinearity can support spontaneous spatial fractal pattern formation. A passive optical ring cavity with a thin slice of saturable absorber is analyzed. Linear stability analys... Read More about Spontaneous spatial fractal pattern formation in absorptive systems.

Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves (2012)
Journal Article
I. Bright Kerr solitons and cnoidal waves. Physical Review A, 86(2), 023838. https://doi.org/10.1103/PhysRevA.86.023838

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-vel... Read More about Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves.

Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics (2012)
Journal Article
Christian, J., McDonald, G., Hodgkinson, T., & Chamorro-Posada, P. (2012). Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics. Physical Review Letters, 108(3), 034101-1. https://doi.org/10.1103/PhysRevLett.108.034101

A generic nonparaxial model for pulse envelopes is presented. Classic Schro¨dinger-type descriptions of
wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the
local time frame. By abandoning these two... Read More about Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics.

Two-colour optical fields: modulational instabilities and vector spatial solitons (2011)
Presentation / Conference
Bostock, C., Christian, J., & McDonald, G. (2011, November). Two-colour optical fields: modulational instabilities and vector spatial solitons. Presented at 2nd CSE Doctoral School Postgraduate Research Conference, University of Salford, Greater Manchester

The propagation of a light beam at a single optical frequency – or colour – in a Kerr-type planar waveguide is an elementary configuration in photonics [1,2]. Under two classic assumptions: (i) that the transverse extent of the
beam is much greater... Read More about Two-colour optical fields: modulational instabilities and vector spatial solitons.

Optical fractals: characterization, cavities, coherence and connections (2011)
Presentation / Conference
Mcdonald, G., Christian, J., Walsh, T., & Huang, J. (2011, September). Optical fractals: characterization, cavities, coherence and connections. Presented at 11th International Conference on Laser and Fiber Optics Networks Modeling, LFNM'2011, Kharkov, Ukraine

Uniform and regular systems can generate optical fractals. After characterizing different fractal-generating systems, emphasis is placed on the roles of boundary conditions and cavity feedback. New aspects of linear and nonlinear optical fractals are... Read More about Optical fractals: characterization, cavities, coherence and connections.

Pulses with relativistic and pseudo-relativistic aspirations (2011)
Presentation / Conference
Lundie, M., Lancaster, G., Hodgkinson, T., Christian, J., Mcdonald, G., & Chamorro-Posada, P. (2011, July). Pulses with relativistic and pseudo-relativistic aspirations. Presented at Waves 2011 - 10th International Conference on Mathematical and Numerical Aspects of Waves, Vancouver, Canada

Temporal solitons are robust self-localizing pulses that play a pivotal role in modern understandings of nonlinear wave phenomena. Here, we propose a new approach for describing pulses in dispersive nonlinear systems. By retaining the fuller generali... Read More about Pulses with relativistic and pseudo-relativistic aspirations.

White light lasers (2011)
Presentation / Conference
Rose, C., McDonald, G., & Christian, J. (2011, June). White light lasers. Poster presented at SEE Celebration of Research, University of Salford, Greater Manchester, 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 a novel process that is ac... Read More about White light lasers.

Snell's law for nonlinear beams (2011)
Presentation / Conference
Christian, J., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. (2011, June). Snell's law for nonlinear beams. Poster presented at SEE Celebration of Research, University of Salford, Greater Manchester, UK

The refraction of plane waves at a uniform boundary between dissimilar linear dielectric materials is perhaps one of the oldest and best-understood phenomenon in optics. In contrast, the behaviour of a beam with a finite transverse cross-section is m... Read More about Snell's law for nonlinear beams.

Relativistic effects in non-relativistic systems (2011)
Presentation / Conference
McDonald, G., Christian, J., & Hodgkinson, T. (2011, June). Relativistic effects in non-relativistic systems. Poster presented at SEE Celebration of Research, University of Salford, Greater Manchester, UK

We propose a new model for describing the evolution of scalar optical pulses in Kerr-type planar waveguides and optical fibres. The wave envelope satisfies a dimensionless equation and its solutions are thus endowed with some intriguing and mystical... Read More about Relativistic effects in non-relativistic systems.

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.

The role of boundary conditions in kaleidoscope laser modes (2011)
Presentation / Conference
McDonald, G., Christian, J., & Huang, J. (2011, June). The role of boundary conditions in kaleidoscope laser modes. Poster presented at College Research Showcase Day, University of Salford, Greater Manchester, UK

The complex character of transverse eigenmodes in one-dimensional (1D) unstable cavity lasers has been known for many years [1]. Early collaborations showed that the origin of such fractal (i.e., multiple spatial scale) structure lies in a subtle int... Read More about The role of boundary conditions in kaleidoscope laser modes.