Dr James Christian's Outputs (28)

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.

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.

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.

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.