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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.

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.

Dark solitons at nonlinear interfaces (2010)
Journal Article
Sanchez-Curto, J., Chamorro-Posada, P., & McDonald, G. (2010). Dark solitons at nonlinear interfaces. Optics Letters, 35(9), 1347-1349. https://doi.org/10.1364/OL.35.001347

The refraction of dark solitons at a planar boundary separating two defocusing Kerr media is simulated and analyzed, for the first time (to our knowledge). Analysis is based on the nonlinear Helmholtz equation and is thus valid for any angle of incid... Read More about Dark solitons at nonlinear interfaces.

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.

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.

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.

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.