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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.

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.

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.