Skip to main content

Research Repository

Advanced Search

Outputs (148)

Dynamics and chaos in extensible pendulum systems (2024)
Presentation / Conference
Jafari, M., & Christian, J. (2024, March). Dynamics and chaos in extensible pendulum systems. Paper presented at 11th Undergraduate Mathematics Conference "Tomorrow's Mathematicans Today" (TMT 2024), University of Greenwich (hosted online), UK

A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion (2023)
Journal Article
Elatrash, L., Chadwick, E., El-Mazuzi, R., Christian, J. M., Wang, Y., Adamu, H. A., & Chadwick, E. (in press). A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion. Computers and Fluids, 266, https://doi.org/10.1016/j.compfluid.2023.106064

The problem studied was the non-reciprocal cyclic swimming motion of three spheres linked with axially aligned retractable arms in Stokes flow. The arms are assumed to be able to retract at a steady speed to half their length, and then at a later tim... Read More about A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion.

Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems (2023)
Journal Article
Huo, K., Yang, R., Jia, H., He, Y., & Christian, J. (2023). Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems. Nonlinear Dynamics, https://doi.org/10.1007/s11071-023-08574-9

Seeking analytical solutions of nonlinear Schrödinger (NLS)-like equations remains an open topic. In this paper, we revisit the general inhomogeneous nonautonomous NLS (inNLS) equation and report on exact similaritons under generic constraint relati... Read More about Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems.

Dynamics on ₵ with generalized Newton-Raphson maps: Julia sets, uncertainty dimension, and periodic orbits (2023)
Presentation / Conference
Christian, J., & Jensen, G. (2023, April). Dynamics on ₵ with generalized Newton-Raphson maps: Julia sets, uncertainty dimension, and periodic orbits. Poster presented at 64th British Applied Mathematics Colloquium (BAMC 2023), University of the West of England and University of Bristol, UK

The Newton-Raphson (NR) method is a well-known iterative scheme for approximating the roots of functions. Deployed on the complex plane, ₵, perhaps its most famous application is to finding the cube roots of –1. One often regards any specific outco... Read More about Dynamics on ₵ with generalized Newton-Raphson maps: Julia sets, uncertainty dimension, and periodic orbits.

Vector cnoidal waves in spatiotemporal propagation: exact solutions beyond slowly-varying envelopes (2023)
Presentation / Conference
Christian, J., & McAteer, É. (2023, April). Vector cnoidal waves in spatiotemporal propagation: exact solutions beyond slowly-varying envelopes. Presented at 64th British Applied Mathematics Colloquium (BAMC 2023), University of the West of England and University of Bristol, UK

Cnoidal waves are periodic solutions to certain classes of nonlinear partial differential equations (PDEs). They are fundamental excitations in theories of waves and their more familiar localized counterparts––solitons––typically emerge as limits.... Read More about Vector cnoidal waves in spatiotemporal propagation: exact solutions beyond slowly-varying envelopes.

The effect of coherent coupling nonlinearity on modulation instability and rogue wave excitation (2022)
Journal Article
and rogue wave excitation. Communications in Nonlinear Science and Numerical Simulation, 106246. https://doi.org/10.1016/j.cnsns.2021.106246

We study modulation instability (MI) in both anomalous and normal dispersion regimes of a coherently coupled system. It is found that there exist three types of MI spectra with distinct characteristics termed baseband, passband, and zero-baseband b... Read More about The effect of coherent coupling nonlinearity on modulation instability and rogue wave excitation.

On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson (2020)
Journal Article
Christian, J., & Middleton-Spencer, H. (2020). On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson. College Mathematics Journal, 51(2), 95-114. https://doi.org/10.1080/07468342.2020.1703452

We consider a systematic generalization of the well-known cube roots of -1 problem to include the Nth roots. The associated fractal basin boundaries are computed, and we also explore how sensitive this class of systems is to fluctuations at its input... Read More about On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson.

Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons (2019)
Journal Article
Yang, R., Gao, J., Jia, H., Tian, J., & Christian, J. (2020). Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons. Optics Communications, 459, 125025. https://doi.org/10.1016/j.optcom.2019.125025

Similarity transformation and Hirota bilinearization are deployed to derive exact bright and dark ultrashort one- and two-similariton solutions of a nonautonomous cubic-quintic nonlinear Schrödinger equation. Such wave packets may emerge when group... Read More about Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons.

The theory and application of eulerlets (2019)
Journal Article
Chadwick, E., Christian, J., Kapoulas, A., & Chalasani, K. (2019). The theory and application of eulerlets. Physics of Fluids, 31(4), 047106. https://doi.org/10.1063/1.5088132

Consider a fixed body in a uniform flow field in the limit as the Reynolds number approaches infinity and the flow field remains steady. Instead of using standard techniques and theory for describing the problem, a new method is employed based upon t... Read More about The theory and application of eulerlets.

Using eulerlets to model steady uniform flow past a circular cylinder (2018)
Journal Article
Chadwick, E., Christian, J., & Chalasani, K. (2018). Using eulerlets to model steady uniform flow past a circular cylinder. European Journal of Computational Mechanics, 27(5-6), 469-478. https://doi.org/10.1080/17797179.2018.1550960

Consider uniform, steady flow past a circular cylinder at Reynolds numbers 26, 36 and 40 before the flow becomes unsteady. Model the flow by using eulerlets, new Green’s functions for Euler flow. This is the first time this eulerlet model has been us... Read More about Using eulerlets to model steady uniform flow past a circular cylinder.

Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems (2018)
Journal Article
Christian, J., McDonald, G., Lundie, M., & Kotsampaseris, A. (2018). Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems. Physical Review A, 98(5), 053843. https://doi.org/10.1103/PhysRevA.98.053843

We consider an envelope equation with space-time symmetry for describing scalar waves in systems with spatiotemporal dispersion and a generic saturable nonlinearity. Exact bright and gray solitons are derived by direct integration methods and coordin... Read More about Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. II. Saturable systems.

Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems (2018)
Journal Article
Christian, J., McDonald, G., & Kotsampaseris, A. (2018). Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems. Physical Review A, 98(5), 053823. https://doi.org/10.1103/PhysRevA.98.053842

A generic envelope equation is proposed for describing the evolution of scalar pulses in systems with spatiotemporal dispersion and cubic-quintic nonlinearity. Our analysis has application, for instance, in waveguide optics where the physical origin... Read More about Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems.

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity (2017)
Journal Article
Christian, J., & Lundie, M. (2017). Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity. Journal of Nonlinear Optical Physics and Materials, 26(02), https://doi.org/10.1142/S0218863517500242

We present, to the best of our knowledge, the first exact dark spatial solitons of a nonlinear Helmholtz equation with a self-defocusing saturable refractive-index model. These solutions capture oblique (arbitrary-angle) propagation in both the forwa... Read More about Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity.

Spontaneous spatial fractal pattern formation in dispersive systems (2017)
Journal Article
Huang, J., Christian, J., & McDonald, G. (2017). Spontaneous spatial fractal pattern formation in dispersive systems. Journal of Nonlinear Optical Physics and Materials, 26(01), https://doi.org/10.1142/S0218863517500096

We report spontaneous spatial optical fractal patterns in a ring cavity containing a thin slice of diffusive Kerr-type material. The Turing threshold instability condition is derived through linear analysis, and static patterns are found to be descri... Read More about Spontaneous spatial fractal pattern formation in dispersive systems.

Exact dipole solitary wave solution in metamaterials with higher-order dispersion (2016)
Journal Article
Min, X., Yang, R., Tian, J., Xue, W., & Christian, J. (2016). Exact dipole solitary wave solution in metamaterials with higher-order dispersion. Journal of Modern Optics, 63(Sup.3), 544-550. https://doi.org/10.1080/09500340.2016.1185178

We present an exact dipole solitary wave solution in a mutual modulation form of bright and dark solitons for a higher-order nonlinear Schrödinger equation with third- and fourth-order dispersion in metamaterials (MMs) using an ansatz method. Based... Read More about Exact dipole solitary wave solution in metamaterials with higher-order dispersion.

Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity (2015)
Presentation / Conference
Carter, L., Christian, J., McDonald, G., & Chamorro-Posada, P. (2015, July). Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Waves, Karlsruhe, Germany

The origin of conventional models for nonlinear optical pulse propagation lies in the ubiquitous slowly-varying envelope approximation (SVEA) accompanied by a Galilean boost to a local-time frame. While such a near-universal procedure typically resul... Read More about Vector dark solitons in systems with spatiotemporal dispersion and cubic nonlinearity : solutions and stability, transformations and relativity.

Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension (2015)
Presentation / Conference
Christian, J., Woodroofe, E., & McDonald, G. (2015, July). Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

The diffraction of plane waves from simple hard-edged apertures constitutes a class of boundary value problem that is well understood in optics, at least within the scalar approximation. Similarly, the diffraction of such waves from fractal apertures... Read More about Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension.

Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes (2015)
Presentation / Conference
Christian, J., Begleris, I., Wickham, S., McDonald, G., & Huang, J. (2015, July). Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

We will report on our latest research into modelling fractal lasers (linear systems that involve geometrically-unstable resonators with inherent magnification), and propose two new classes of cavity configuration. These devices are of fundamental the... Read More about Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes.

Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law (2015)
Presentation / Conference
McCoy, E., Christian, J., Sanchez-Curto, J., & McDonald, G. (2015, July). Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Waves, Karlsruhe, Germany

The interaction of self-localized waves with an abrupt interface is a problem of fundamental importance in many branches of physics, engineering, and applied mathematics. Waveguide optics, for instance, is dominated in an essential way by such consid... Read More about Nonlinear Helmholtz wave refraction & Goos-Hänchen shifts in nonparaxial optics : angles and interfaces, solitons and Snell's law.

Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation (2015)
Presentation / Conference
Bostock, C., Christian, J., Leite, A., McDonald, G., & Huang, J. (2015, June). Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

Alan Turing's profound insight into morphogenesis, published in 1952, has provided the cornerstone for understanding the origin of pattern and form in Nature. When the uniform states of a nonlinear reaction-diffusion system are sufficiently stressed,... Read More about Multi-Turing instabilities & spontaneous patterns in discrete nonlinear systems : simplicity and complexity, cavities and counterpropagation.

Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses (2014)
Presentation / Conference
McCoy, E., Christian, J., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. (2014, September). Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses. Presented at 5th European Optical Society Annual Meeting, Berlin, Germany

We report on our most recent results concerning arbitrary-angle spatial soliton refraction at the interface between dissimilar dielectrics, each of which comprises both X(3)and X(5) susceptibilities. Attention is also paid to the oblique injectio... Read More about Single interfaces and coupled-waveguide arrays: off-axis nonparaxial analyses.

Ultrabroad-band Raman light: Linear detuning & gain suppression (2013)
Presentation / Conference
Kelly, R., Christian, J., & McDonald, G. (2013, June). Ultrabroad-band Raman light: Linear detuning & gain suppression. Presented at College of Science & Techology Research Showcase, University of Salford

Ultrabroad-band multifrequency Raman generation is a (laser-driven) resonant-symmetric two-colour pumping technique for exciting polychromatic light beams that are characterized by potentially very wide “top-hat” temporal bandwidths [1]. The spectra... Read More about Ultrabroad-band Raman light: Linear detuning & gain suppression.

Diffraction of fractal light: New frontiers for the mathematics of edge waves (2013)
Presentation / Conference
Mylova, M., McDonald, G., & Christian, J. (2013, June). Diffraction of fractal light: New frontiers for the mathematics of edge waves. Presented at College of Science & Technology Research Showcase, University of Salford

The diffraction pattern produced by a plane wave (i.e., a perfectly uniform wavefront) scattering from an infinite hard edge is well-described by the Fresnel integral [1]. Such one-dimensional (1D) edge waves [see Fig. 1(a)] turn out to be truly elem... Read More about Diffraction of fractal light: New frontiers for the mathematics of edge waves.

Kaleidoscope lasers: Polygonal boundary conditions & geometrical instabilities (2013)
Presentation / Conference
McDonald, G., Christian, J., & Huang, J. (2013, June). Kaleidoscope lasers: Polygonal boundary conditions & geometrical instabilities. Presented at College of Science & Technology Research Showcase, University of Salford

Kaleidoscope lasers are geometrically unstable cavities with a feedback mirror that has the shape of a regular polygon [1]. Early calculations of the transverse eigenmodes of these systems hinted toward a fractal (or multi-scale) characteristic, but... Read More about Kaleidoscope lasers: Polygonal boundary conditions & geometrical instabilities.

Spontaneous spatial fractal patterns: Towards nonparaxial nonlinear ring cavities (2013)
Presentation / Conference
Bostock, C., Christian, J., & McDonald, G. (2013, June). Spontaneous spatial fractal patterns: Towards nonparaxial nonlinear ring cavities. Presented at College of Science & Technology Reserach Showcase, University of Salford

Spontaneous pattern formation in optical ring cavities containing a nonlinear (e.g., Kerr-type) material [see Fig. 1(a)] has been studied extensively for the past three decades. A notable trend in the literature over recent years has been a shift awa... Read More about Spontaneous spatial fractal patterns: Towards nonparaxial nonlinear ring cavities.

The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit (2013)
Presentation / Conference
Readman, S., Christian, J., Bostock, C., & McDonald, G. (2013, June). The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit. Presented at College of Science & Technology Research Showcase, University of Salford

An optical ring cavity filled with an absorptive material is a fundamental spontaneous pattern-forming system [1]. Analyses of Turing bifurcations in these (uni-directional) cavity configurations [see Fig. 1(a)] can be simplified by deploying the thi... Read More about The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit.

The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system (2013)
Presentation / Conference
Patel, S., Christian, J., Bostock, C., & McDonald, G. (2013, June). The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system. Presented at College of Science & Technology Research Showcase, University of Salford

The nonlinear Fabry-Pérot (FP) cavity [see Fig. 1(a)] is a generalization of the classic diffusive Kerr slice with a single feedback mirror [1,2]. Such apparent simplicity is deceptive. Historically, analysis of the FP geometry has proved to be a non... Read More about The nonlinear fabry-pérot cavity: Complexity in a simple optical feedback system.

Coupled-waveguide arrays: Oblique injection & soliton propagation (2013)
Presentation / Conference
Christian, J., McCoy, E., & McDonald, G. (2013, June). Coupled-waveguide arrays: Oblique injection & soliton propagation. Presented at College of Science & Technology Research Showcase, University of Salford

The interaction between light beams and periodically-patterned host materials (such as coupled-waveguide arrays or photonic crystals) is a fundamental class of problem in nonlinear optics [1,2]. While oblique (off-axis) propagation effects play a cen... Read More about Coupled-waveguide arrays: Oblique injection & soliton propagation.

Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law (2013)
Presentation / Conference
Yates, R., Christian, J., & McDonald, G. (2013, June). Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law. Presented at College of Science & Technology Research Showcase, University of Salford

The refraction of light waves at planar interfaces is a problem of fundamental interest to the optics community. To date, our Snell’s law-type analyses have considered only families of hyperbolic solitons – robust nonlinear beams that are strongly (e... Read More about Algebraic soliton refraction: New wave contexts for nonlinear Snell’s law.

Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts (2013)
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. (2013, June). Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts. Presented at College of Science & Technology Research Showcase, University of Salford

In this presentation, we give the first detailed overview of spatial soliton refraction at the planar interface between materials whose nonlinear polarization has contributions from both X(3)and X(5)susceptibilities [1]. The governing equation is of... Read More about Refraction at interfaces with X(5) nonlinearity: Snell’s law & Goos-Hänchen shifts.

Coupled spatiotemporal waves: New paradigms in vector soliton physics (2013)
Presentation / Conference
Ashley, J. T., Christian, J., & McDonald, G. (2013, June). Coupled spatiotemporal waves: New paradigms in vector soliton physics. Presented at College of Science & Technology Research Showcase, University of Salford

In this presentation, we propose a novel spatiotemporal generalization of Menyuk’s classic equations [1] describing the propagation of two nonlinearly-coupled waves in a dispersive optical system (such as a fibre or planar waveguide). Our approach is... Read More about Coupled spatiotemporal waves: New paradigms in vector soliton physics.

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.

Dark & anti-dark spatiotemporal solitons: From cubic to cubic-quintic systems (2013)
Presentation / Conference
Cowey, R., Christian, J. M., & McDonald, G. S. (2013, June). Dark & anti-dark spatiotemporal solitons: From cubic to cubic-quintic systems. Presented at College of Science & Technology Research Showcase, University of Salford, Greater Manchester M5 4WT, U.K

The origin of conventional models for optical pulse propagation lies in the universal slowly-varying envelope approximation (SVEA) accompanied by a Galilean boost to the local time frame. However, Biancalana and Creatore [1] have recently pointed out... Read More about Dark & anti-dark spatiotemporal solitons: From cubic to cubic-quintic systems.

Helmholtz bright spatial solitons and surface waves at power-law optical interfaces (2012)
Journal Article
Christian, J., McCoy, E., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. (2012). Helmholtz bright spatial solitons and surface waves at power-law optical interfaces. Journal of Atomic, Molecular, and Optical Physics, 2012, 137967. https://doi.org/10.1155/2012/137967

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.

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.

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.

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.

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.

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.

Cavity-enhanced broadband light generation (2011)
Presentation / Conference
Rose, C., McDonald, G., & Christian, J. (2011, June). Cavity-enhanced broadband light generation. Poster presented at College Research Showcase Day, University of Salford, Greater Manchester, UK

Broadband (multiline frequency) light 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... Read More about Cavity-enhanced broadband light generation.

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.

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.

Spontaneous self-synchronization mechanism for attosecond pulses (2008)
Presentation / Conference
Mcdonald, G., & Christian, J. (2008, August). Spontaneous self-synchronization mechanism for attosecond pulses. Poster presented at National Photonics Conference, Photon 08, Heriot-Watt University, Edinburgh, UK

Ultra-broadband multi-frequency Raman generation is a long-established technique for producing temporal bandwidths that can be of the order of the pump frequency. However, higher-than-optimal intensity beams reduce the bandwidth generated. Many works... Read More about Spontaneous self-synchronization mechanism for attosecond pulses.

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.

Unstable resonators with Gosper-island boundary conditions : virtual-source computation of fractal eigenmodes
Presentation / Conference
Christian, J., & Huang, J. Unstable resonators with Gosper-island boundary conditions : virtual-source computation of fractal eigenmodes. Poster presented at 29th European Quantum Electronics Conference (CLEO Europe / EQEC), Munich, Germany

The Gosper island is a well-known fractal belonging to a family of self-similar “root 7” curves constructed from a simple iterative algorithm [1]. One begins with a regular hexagon (the initiator, corresponding to iteration n = 0) with sides of refer... Read More about Unstable resonators with Gosper-island boundary conditions : virtual-source computation of fractal eigenmodes.

Electromagnetic diffraction by fractal dusts, triangles and carpets : a Kirchhoff approach to circulation
Presentation / Conference
a Kirchhoff approach to circulation. Poster presented at 30th European Quantum Electronics Conference (CLEO Europe / EQEC), Munich, Germany

The diffraction of plane waves by perfectly-conducting thin screens is of fundamental physical and mathematical interest in electromagnetics [1]. Classic laser-optics experiments involve both open (single- and double-slit arrangements) and closed (ci... Read More about Electromagnetic diffraction by fractal dusts, triangles and carpets : a Kirchhoff approach to circulation.

Scattering of electromagnetic waves by cantor screens : Rayleigh-Sommerfeld integrals on complex domains
Presentation / Conference
Christian, J., & Middleton-Spencer, H. Scattering of electromagnetic waves by cantor screens : Rayleigh-Sommerfeld integrals on complex domains. Poster presented at 30th European Quantum Electronics Conference (CLEO Europe / EQEC), Munich, Germany

The scattering of light from fractal screens has been a topic of sustained interest in optics for many decades. A common thread weaving together much of the theoretical literature is the scalar approximation, wherein the polarization state of the ele... Read More about Scattering of electromagnetic waves by cantor screens : Rayleigh-Sommerfeld integrals on complex domains.

Discrete nonlinear Schrödinger equations for periodic optical systems : pattern formation in \chi(3) coupled waveguide arrays
Presentation / Conference
pattern formation in \chi(3) coupled waveguide arrays. Presented at 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019), Vienna University of Technology, Austria

Discrete nonlinear Schrödinger equations have been used for many years to model the propagation of light in optical architectures whose refractive index profile is modulated periodically in the transverse direction. Typically, one considers a modal... Read More about Discrete nonlinear Schrödinger equations for periodic optical systems : pattern formation in \chi(3) coupled waveguide arrays.

Electromagnetic scattering problems on perfectly-conducting complex domains: from Rayleigh-Sommerfeld integrals toward fractal screens
Presentation / Conference
Christian, J., & Middleton-Spencer, H. Electromagnetic scattering problems on perfectly-conducting complex domains: from Rayleigh-Sommerfeld integrals toward fractal screens. Presented at 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019), Vienna University of Technology, Austria

The diffraction of light by an aperture in an otherwise perfectly conducting plane screen of infinite extent is a phenomenon of fundamental interest in electromagnetics. Here, we consider classes of problems where the aperture domain is complex (p... Read More about Electromagnetic scattering problems on perfectly-conducting complex domains: from Rayleigh-Sommerfeld integrals toward fractal screens.

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.

Dissipative solitons of a spatiotemporal Ginzburg-Landau equation
Presentation / Conference
Cooper, A., Christian, J., Bresnahan, D., McDonald, G., & Chamorro-Posada, P. Dissipative solitons of a spatiotemporal Ginzburg-Landau equation. Presented at Quantum Electronics and Photonics Conference (Photon14/QEP-21), Imperial College London, UK

Diffraction of fractal light by simple apertures
Presentation / Conference
Mylova, M., Christian, J., & McDonald, G. Diffraction of fractal light by simple apertures. Presented at Quantum Electronics and Photonics Conference (Photon14/QEP-21), Imperial College London, UK

We propose and investigate, for the first time to our knowledge, an entirely new regime in wave physics  the diffraction of fractal waves from simple apertures. A selection of new analyses and physical predictions will be given for experimental g... Read More about Diffraction of fractal light by simple apertures.

Spatiotemporal vector solitons in nonlinear optical systems with \chi(3) susceptibility
Presentation / Conference
Ashley, J., Christian, J., McDonald, G., & Chamorro-Posada, P. Spatiotemporal vector solitons in nonlinear optical systems with \chi(3) susceptibility. Presented at 5th European Optical Society Annual Meeting, Berlin, Germany

A new model is proposed for describing coupled optical waves propagating in a system with linear dispersion (both group-velocity and spatial contributions) \chi(3 nonlinear susceptibility. The modulational instability problem is solved in full, and... Read More about Spatiotemporal vector solitons in nonlinear optical systems with \chi(3) susceptibility.

Multi-turing instabilities in Fabry-Perot resonators and discrete microcavities
Presentation / Conference
Bostock, C., Christian, J., McDonald, G., Leite, A., & Huang, J. Multi-turing instabilities in Fabry-Perot resonators and discrete microcavities. Presented at 5th European Optical Society Annual Meeting, Berlin, Germany

We report on research concerning spontaneous spatial fractal pattern formation in passive nonlinear optical cavities (both ring-resonator and Fabry-Pérot geometries). A new model for light propagation inside discrete coupled cavities is proposed... Read More about Multi-turing instabilities in Fabry-Perot resonators and discrete microcavities.

Diffraction of fractal optical fields by simple apertures
Presentation / Conference
Christian, J., Mylova, M., & McDonald, G. Diffraction of fractal optical fields by simple apertures. Presented at 5th European Optical Society Annual Meeting, Berlin, Germany

We propose and investigate, for the first time to our knowledge, an entirely new regime in wave physics  the diffraction of fractal waves from simple apertures. A selection of new analyses and physical predictions will be given for experimental... Read More about Diffraction of fractal optical fields by simple apertures.

Unstable cavity lasers - from kaleidoscopes to snowflakes
Presentation / Conference
Christian, J., Begleris, I., McDonald, G., & Huang, J. Unstable cavity lasers - from kaleidoscopes to snowflakes. Presented at 5th European Optical Society Annual Meeting (EOSAM 2014), Berlin, Germany

The snowflake laser is proposed  a new class of unstable resonator whose feedback mirror has the shape of the von Koch snowflake. Theoretical analysis is undertaken with two-dimensional virtual source theory, and predictions of novel mode patt... Read More about Unstable cavity lasers - from kaleidoscopes to snowflakes.

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 spatiotemporal wave equation with a dual power-law nonlinearity
Presentation / Conference
Cowey, R., Christian, J., & McDonald, G. The spatiotemporal wave equation with a dual power-law nonlinearity. Poster presented at Salford Postgraduate Annual Research Conference (SPARC 2013), University of Salford

Solitons and soliton-like emergent phenomena appear ubiquitously throughout nonlinear science. These waves are truly fundamental entities, transcending the physical details of a system and resulting whenever linear dispersion (which tends to broaden... Read More about The spatiotemporal wave equation with a dual power-law nonlinearity.

Spatiotemporal dark and anti-dark solitons in cubic-quintic photonic systems
Presentation / Conference
Cowey, R., Christian, J., & McDonald, G. Spatiotemporal dark and anti-dark solitons in cubic-quintic photonic systems. Presented at Salford Postgraduate Annual Research Conference (SPARC 2013), University of Salford

In a recent publication, Christian et al. [Phys. Rev. Lett. vol. 108, art. no. 034101 (2012)] developed a novel mathematical formalism for describing pulses in generic wave-based systems. When applied to optical geometries, their proposed class of (... Read More about Spatiotemporal dark and anti-dark solitons in cubic-quintic photonic systems.

Helmholtz surface wave propagation along nonlinear interfaces
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. Helmholtz surface wave propagation along nonlinear interfaces. Poster presented at Salford Postgraduate Annual Research Conference (SPARC 2013), University of Salford

When two dissimilar nonlinear photonic materials are placed together, the boundary between them forms an optical interface. A light beam (typically from a laser source) may then travel along the boundary as a surface wave, remaining trapped within t... Read More about Helmholtz surface wave propagation along nonlinear interfaces.

Giant Goos-Hänchen shifts and soliton refraction in systems with χ(5) susceptibility
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. Giant Goos-Hänchen shifts and soliton refraction in systems with χ(5) susceptibility. Presented at Salford Postgraduate Annual Research Conference (SPARC 2013), University of Salford

A full understanding of how a spatial solitons (a unique type of nonlinear light beam) behave when the encounter the boundary between two dissimilar media is still some way off. On the one hand, light-interface interactions underpin essentially all... Read More about Giant Goos-Hänchen shifts and soliton refraction in systems with χ(5) susceptibility.

Vector spatial solitons beyond the slowly-varying envelope approximation
Presentation / Conference
Bostock, C., Christian, J., & McDonald, G. Vector spatial solitons beyond the slowly-varying envelope approximation. Poster presented at Salford Postgraduate Annual Research Conference (SPARC 2013), University of Salford

The simultaneous propagation of two spatially-overlapping and differently-coloured laser beams (e.g., at infra-red and green wavelengths) in photonic waveguides has attracted much attention since the early 1990s [Shalaby & Barthelemy, IEEE J. Quantum... Read More about Vector spatial solitons beyond the slowly-varying envelope approximation.

Spontaneous spatial fractal light patterns in simple nonlinear cavities
Presentation / Conference
Bostock, C., Christian, J., & McDonald, G. Spontaneous spatial fractal light patterns in simple nonlinear cavities. Presented at Salford Postgraduate Annual Research Conference (SPARC 2013), University of Salford

Nature furnishes us with a wide variety of patterns that, fundamentally, tend to fall into one of two categories: simple (characterized by a dominant scale-length or “size”) or fractal (containing comparable levels of detail spanning decimal orders o... Read More about Spontaneous spatial fractal light patterns in simple nonlinear cavities.

Arbitrary-angle interaction of spatial solitons with layered photonic structures
Presentation / Conference
layered photonic structures. Presented at Salford Postgraduate Annual Research Conference (SPARC 2012), University of Salford, Greater Manchester, UK

The behaviour of light at the interface between different adjoining materials underpins the entire field of Optics. In nonlinear photonics, a fundamental geometry comprises a spatial soliton incident on the planar boundary between two dissimilar Ker... Read More about Arbitrary-angle interaction of spatial solitons with layered photonic structures.

Stability of two-colour spatial solitons in Helmholtz vector beam models
Presentation / Conference
in Helmholtz vector beam models. Presented at Salford Postgraduate Annual Research Conference (SPARC 2012), University of Salford, Greater Manchester, UK

This presentation will cover a few very basic aspects of our latest research into how laser beams behave when they travel through some types of materials. In particular, we are interested in the properties of overlapping light beams with different c... Read More about Stability of two-colour spatial solitons in Helmholtz vector beam models.

Spontaneous spatial fractal patterns in simple linear and nonlinear optical cavities
Presentation / Conference
linear and nonlinear optical cavities. Presented at European Optical Society Annual Meeting (EOSAM 2012), Aberdeen, Scotland, UK

We present an overview of our research on the fractal-generating properties of two distinct optical cavities: fractal eigenmodes of linear systems with inherent magnification, and spontaneous spatial fractals in nonlinear systems. Our latest research... Read More about Spontaneous spatial fractal patterns in simple linear and nonlinear optical cavities.

Nonparaxial refraction laws in optics: from non-Kerr interfaces to waveguide arrays
Presentation / Conference
from non-Kerr interfaces to waveguide arrays. Presented at European Optical Society Annual Meeting (EOSAM 2012), Aberdeen, Scotland, UK

Angular effects play a central role in essentially all non-trivial optical configurations, and can be well-described within a Helmholtz-type nonparaxial framework. We report recent results modelling spatial solitons interacting with cubic-quintic mat... Read More about Nonparaxial refraction laws in optics: from non-Kerr interfaces to waveguide arrays.

Spatial dispersion and spatiotemporal solitons in cubic-quintic optical waveguides
Presentation / Conference
in cubic-quintic optical waveguides. Presented at European Optical Society Annual Meeting (EOSAM 2012), Aberdeen, Scotland, UK

We report on fresh developments in the field of spatiotemporal optical solitons. A host of new analytical and numerical predictions for light pulses in nonlinear waveguides will be detailed, which have a simple physical interpretation. Tantalizing c... Read More about Spatial dispersion and spatiotemporal solitons in cubic-quintic optical waveguides.

Helmholtz dark spatial optical solitons for a defocusing saturable nonlinearity
Presentation / Conference
defocusing saturable nonlinearity. Presented at European Optical Society Annual Meeting (EOSAM 2012), Aberdeen, Scotland, UK

We report on our latest developments in the field of Helmholtz soliton theory: the derivation of exact dark spatial optical solitons for a defocusing saturable nonlinearity. A raft of new physical predictions is made, and extensive analysis (via bot... Read More about Helmholtz dark spatial optical solitons for a defocusing saturable nonlinearity.

Nonparaxial refraction laws for spatial solitons at cubic-quintic material interfaces
Presentation / Conference
cubic-quintic material interfaces. Presented at National Photonics Conference, Photon12, University of Durham, UK

The behaviour of light at the interface between different materials essentially underpins the entire field of Optics. In nonlinear photonics, a building-block geometry comprises a spatial soliton incident on the planar boundary between two dissimila... Read More about Nonparaxial refraction laws for spatial solitons at cubic-quintic material interfaces.

Helmholtz spatial solitons and oblique propagation in coupled-waveguide arrays
Presentation / Conference
Christian, J., McCoy, E., McDonald, G., Sanchez-Curto, J., & Chamorro-Posada, P. Helmholtz spatial solitons and oblique propagation in coupled-waveguide arrays. Presented at National Photonics Conference, Photon12, University of Durham, UK

The interaction between light waves and layered host media is a fundamental class of problem in nonlinear photonics. For example, the interest may lie with studying the behaviour of a spatial optical soliton: (i) at the planar boundary between other... Read More about Helmholtz spatial solitons and oblique propagation in coupled-waveguide arrays.

Helmholtz dark spatial solitons in waveguides with defocusing saturable materials
Presentation / Conference
with defocusing saturable materials. Presented at National Photonics Conference, Photon12, University of Durham, UK

Angular configurations play a fundamental role in essentially all nonlinear photonic architectures: from beam multiplexing applications, to scattering at a single interface, to evolution inside patterned optical structures. Equations of the nonline... Read More about Helmholtz dark spatial solitons in waveguides with defocusing saturable materials.

Two-colour spatial optical solitons: new stability analyses for off-axis propagation
Presentation / Conference
new stability analyses for off-axis propagation. Presented at National Photonics Conference, Photon12, University of Durham, UK

Two-colour spatial optical solitons comprise a pair of stationary continuous-wave light beams at two well-separated temporal frequencies. The components overlap in the propagation plane and are coupled through system nonlinearity (e.g., the Kerr-typ... Read More about Two-colour spatial optical solitons: new stability analyses for off-axis propagation.

Instabilities and Helmholtz vector solitons in nonlinearly-coupled optical systems
Presentation / Conference
nonlinearly-coupled optical systems. Presented at Second Annual Student Conference on Complexity Science (SCCS 2012), University of Gloucestershire, UK

The propagation of, and interaction between, multiple waves is a fundamental problem in physical science. The interplay between linear and nonlinear processes – such as diffraction (wave spreading) and self-/cross-phase modulation (wave compressing)... Read More about Instabilities and Helmholtz vector solitons in nonlinearly-coupled optical systems.

Propagation properties of Helmholtz power-law nonlinear surface waves
Presentation / Conference
nonlinear surface waves. Presented at Second Annual Student Conference on Complexity Science (SCCS 2012), University Gloucestershire, UK

Optical surface waves are a fundamental class of excitation in inhomogeneous nonlinear photonic systems. This type of laser light satisfies a Helmholtz-type governing equation, and is subject to certain boundary conditions. It also has an asymmetri... Read More about Propagation properties of Helmholtz power-law nonlinear surface waves.

Nonparaxial refraction and giant Goos-Hänchen shifts at nonlinear optical interfaces
Presentation / Conference
at nonlinear optical interfaces. Presented at Second Annual Student Conference on Complexity Science (SCCS 2012), University of Gloucestershire

The scattering of spatial optical solitons (self-localizing beams of laser light) at the interface between two dissimilar materials is a problem of fundamental importance in nonlinear photonics. Theoretical analyses must take into account a highly c... Read More about Nonparaxial refraction and giant Goos-Hänchen shifts at nonlinear optical interfaces.

Spatial soliton refraction at cubic-quintic material interfaces
Presentation / Conference
McCoy, E., Christian, J., & McDonald, G. Spatial soliton refraction at cubic-quintic material interfaces. Poster presented at Salford Postgraduate Annual Research Conference (SPARC 11), University of Salford, Greater Manchester, UK

In their most general form, wave–interface problems are inherently angular in nature. For instance, the interaction between light waves and material boundaries essentially defines the entire field of optics [1]. The seminal works of Aceves et al. [2,... Read More about Spatial soliton refraction at cubic-quintic material interfaces.

From Turing instability to fractals
Presentation / Conference
Huang, J., Christian, J., McDonald, G., Jahanpanah, J., & Chamorro-Posada, P. From Turing instability to fractals. Presented at Nonlinear Photonics Topical Meeting, Quebec City, Canada

Complexity focuses on commonality across subject areas and forms a natural platform for multidisciplinary activities. Typical generic signatures of complexity include: (i) spontaneous occurrence of simple patterns (e.g. stripes, squares, hexagons) em... Read More about From Turing instability to fractals.

Helmholtz solitons: a new angle in nonlinear optics
Presentation / Conference
Christian, J., McDonald, G., Chamorro-Posada, P., & Sanchez-Curto, J. Helmholtz solitons: a new angle in nonlinear optics. Poster presented at Nonlinear Photonics Topical Meeting, Quebec City, Canada

We rigorously show that nonparaxial optical beams are not necessarily ultranarrow [1-3]. While existing paraxial models constrain considerations of broad beams to vanishingly-small propagation angles relative to the longitudinal (i.e. z) direction,... Read More about Helmholtz solitons: a new angle in nonlinear optics.

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.