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Dr James Christian's Outputs (149)

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.

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.

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.