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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.

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.

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.

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.

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.

Exact soliton solutions of the nonlinear Helmholtz equation: communication (2002)
Journal Article
Chamorro-Posada, P., McDonald, G., & New, G. (2002). Exact soliton solutions of the nonlinear Helmholtz equation: communication. Journal of the Optical Society of America B, 19(5), 1216-1217. https://doi.org/10.1364/JOSAB.19.001216

Exact analytical soliton solutions of the nonlinear Helmholtz equation are reported. A lucid generalization of paraxial soliton theory that incorporates nonparaxial effects is found.

Diffractive origin of fractal resonator modes (2001)
Journal Article
New, G., Yates, M., Woerdman, J., & Mcdonald, G. (2001). Diffractive origin of fractal resonator modes. Optics Communications, 193(1-6), 261-266. https://doi.org/10.1016/S0030-4018%2801%2901237-8

The modes of unstable optical resonators possess fractal character. In this paper, the fundamental question of how and why fractals originate in one of the simplest linear optical systems is addressed. The answer is related to the fact that unstabl... Read More about Diffractive origin of fractal resonator modes.

Non-paraxial beam propagation methods (2001)
Journal Article
Chamorro-Posada, P., Mcdonald, G., & New, G. (2001). Non-paraxial beam propagation methods. Optics Communications, 192(1-2), 1-12. https://doi.org/10.1016/S0030-4018%2801%2901171-3

Exact analytical results are employed in the testing of split-step and finite difference approaches to the numerical solution of the non-paraxial non-linear Schrodinger equation. It is shown that conventional split-step schemes can lead to spurious o... Read More about Non-paraxial beam propagation methods.

Transverse effects in multifrequency Raman generation (2000)
Journal Article
Syed, K., Mcdonald, G., & New, G. (2000). Transverse effects in multifrequency Raman generation. Journal of the Optical Society of America B, 17(8), 1366-1375. https://doi.org/10.1364/JOSAB.17.001366

The theory of ultrabroadband multifrequency Raman generation is extended, for the first time, to allow for beam-propagation effects in one and two transverse dimensions. We show that a complex transverse structure develops even when diffraction is ne... Read More about Transverse effects in multifrequency Raman generation.

Kaleidoscope laser (2000)
Journal Article
Mcdonald, G., Karman, G., New, G., & Woerdman, J. (2000). Kaleidoscope laser. Journal of the Optical Society of America B, 17(4), 524-529. https://doi.org/10.1364/JOSAB.17.000524

We report the first calculations of mode patterns of unstable-cavity lasers with truly two-dimensional transverse geometries. A detailed account of numerical techniques, incorporating a nonorthogonal beam-propagation method, and results for cavities... Read More about Kaleidoscope laser.