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All Outputs (169)

Nonlinear interfaces: intrinsically nonparaxial regimes and effects (2009)
Journal Article
Sánchez-Curto, J., Chamorro-Posada, P., & McDonald, G. (2009). Nonlinear interfaces: intrinsically nonparaxial regimes and effects. Journal of Optics A: Pure and Applied Optics, 11(5), 054015. https://doi.org/10.1088/1464-4258/11/5/054015

The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrödinger equation. For instance, large propagation angles are... Read More about Nonlinear interfaces: intrinsically nonparaxial regimes and effects.

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 solitons in power-law optical materials (2007)
Journal Article
Christian, J., McDonald, G., Potton, R., & Chamorro-Posada, P. (2007). Helmholtz solitons in power-law optical materials. Physical Review A, 76(3), 033834. https://doi.org/10.1103/PhysRevA.76.033834

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures broad beam evolution at any angle with respect to the reference direction in a wide range of media, including some se... Read More about Helmholtz solitons in power-law optical materials.

Helmholtz solitons at nonlinear interfaces (2007)
Journal Article
McDonald, G., Chamorro-Posada, P., & Sanchez-Curto, J. (2007). Helmholtz solitons at nonlinear interfaces. Optics Letters, 32(9), 1126-1128. https://doi.org/10.1364/OL.32.001126

The evolution of Helmholtz solitons at the interface separating two Kerr-type media is described by means of a generalized nonlinear Helmholtz equation. The bright soliton solution for this equation and arbitrary media properties are presented. Numer... Read More about Helmholtz solitons at nonlinear interfaces.

Helmholtz bright and boundary solitons (2007)
Journal Article
Christian, J., McDonald, G., & Chamorro-Posada, P. (2007). Helmholtz bright and boundary solitons. Journal of Physics A: Mathematical and Theoretical, 40(7), 1545-1560. https://doi.org/10.1088/1751-8113/40/7/008

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their ampl... Read More about Helmholtz bright and boundary solitons.

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.

Spatial Kerr soliton collisions at arbitrary angles (2006)
Journal Article
Chamorro-Posada, P., & McDonald, G. (2006). Spatial Kerr soliton collisions at arbitrary angles. Physical Review E, 74(3), 036609. https://doi.org/10.1103/PhysRevE.74.036609

The theory of spatial Kerr solitons is extended to colliding beams that are neither almost-exactly copropagating nor almost-exactly counterpropagating. Our new Helmholtz formalism yields results that are consistent with the inherent symmetry of the c... Read More about Spatial Kerr soliton collisions at arbitrary angles.

On the theory of Helmholtz solitons (2006)
Thesis
Christian, J. On the theory of Helmholtz solitons. (Thesis). Salford : University of Salford

This thesis is concerned with spatial optical solitons in (quasi-two
dimensional) planar waveguides, where there is a single longitudinal and
(effectively) a single transverse dimension, and whose symmetry the solutions
respect consistently. A key... Read More about On the theory of Helmholtz solitons.

Spontaneous optical fractal pattern formation (2005)
Journal Article
Huang, J., & McDonald, G. (2005). Spontaneous optical fractal pattern formation. Physical review letters, 94(17), 174101. https://doi.org/10.1103/PhysRevLett.94.174101

We report, for the first time, spontaneous nonlinear optical spatial fractals. The proposed generic
mechanism employs intrinsic nonlinear dynamics both to generate an initial pattern seed and to fill out
structure across decades of spatial scale. W... Read More about Spontaneous optical fractal pattern formation.

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.

Exact analytical helmholtz bright and dark solitons (2004)
Journal Article
Chamorro-Posada, P., & McDonald, G. (2004). Exact analytical helmholtz bright and dark solitons. Proceedings of SPIE, 5582, 154. https://doi.org/10.1117/12.583404

In this paper, exact analytical Helmholtz bright and dark soliton solutions for a Kerr nonlinearity are presented. Numerical simulations verify that these solutions are both robust and act as attractors in nonlinear beam dynamics. Results dealing wit... Read More about Exact analytical helmholtz bright and dark solitons.