The work below includes the first reports of bright (Helmholtz nonparaxial) Kerr solitons and their properties.
Nonlinear Helmholtz equation for focusing Kerr nonlinearity
Exact Helmholtz-Kerr bright soliton solution.
13. JM Christian, GS McDonald, (2004), Light Guiding Light Guiding Light: A New Angle, SPARC 2004 Conference, Research & Graduate Collge, University of Salford, Session B3, 2004.
Abstract. The propagation of spatial optical solitons (that is, non-diffracting beams) in a dielectric waveguide is routinely described by the Non-Linear Schroedinger (NLS) equation. This is a universal model for describing soliton phenomena, and occurs in many diverse branches of physics. However, NLS-based models suffer from potentially severe physical limitations in some regimes. For example, they cannot support multiple waves propagating at arbitrarily large angles with respect to the reference direction, or the interaction of these waves. Here, we present a brief overview of some aspects of Helmholtz soliton theory. This non-paraxial framework extends conventional soliton theory, and offers a full description of non-linear waves over the complete range of angular regimes. Consideration of angular aspects of the wave propagation problem gives rise to novel, non-trivial physical effects that have no counterpart in paraxial theory.
Amplitude vs. distance - launched paraxial solutions re-shape & converge to the expected Helmholtz solitons (shown by horizontal lines).
Beam area vs. distance - convergence to Helmholtz solitons.
12. P Chamorro-Posada, GS McDonald, (2004), Exact Analytical Helmholtz Bright And Dark Solitons , PROCEEDINGS OF SPIE (SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS) v5582, p154, 2004
11. P Chamorro-Posada, GS McDonald, (2003), Exact Analytical Helmholtz Bright And Dark Solitons, LASER AND FIBER-OPTICAL NETWORK MODELING, LFNM, ISBN 0-7803-7709-5, p3-11, 2003
10. P Chamorro-Posada, GS McDonald, (2003), Exact Analytical Helmholtz Bright and Dark Solitons [ Presentation ] , Intern Conf on Adv Optoelectronics & Lasers, Alushta, Crimea, Ukraine, Sept, 2003 [ Invited ]
9. P Chamorro-Posada, GS McDonald, GHC New (2002), Exact soliton solutions of the nonlinear Helmholtz equation , JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B v19, p1216, 2002
Abstract. Exact analytical soliton solutions of the nonlinear Helmholtz equation are reported. A lucid generalization of paraxial soliton theory that incorporates nonparaxial effects is found.
8. P Chamorro-Posada, GS McDonald and GHC New, Propagation Properties of Nonparaxial Spatial Solitons, J Mod Opt 47 (2000) 1877.
Abstract. We present an analysis and simulation of the non-paraxial nonlinear Schroedinger equation. Exact general relations describing energy flow conservation and transformation invariance are reported, and then explained on physical grounds. New instabilities of fundamental and higher-order paraxial solitons are discovered in regimes where exact analytical non-paraxial solitons are found to be robust attractors. Inverse-scattering theory and the known form of solutions are shown to enable the prediction of the characteristics of nonparaxial soliton formation. Finally, analysis of higher-order soliton break up due to non-paraxial effects reveals features that appear to be of a rather general nature.
7. P Chamorro-Posada, GS McDonald and GHC New, Exact Analytical Nonparaxial Solitons (Invited), Solitons Workshop, Fourteenth National Quantum Electronics Conference, Manchester, UK, Sept 6-9, 1999.
6. P Chamorro-Posada, GS McDonald, GHC New, J Noon and S Chavez-Cerda, Fundamental Properties of (1+1)D and (2+1)D Nonparaxial Optical Solitons, [ Presentation Extracts (unpublished): Fermion-Like Solitons, 2D+1 Soliton Space Quantisation ], Fourteenth National Quantum Electronics Conference, Manchester, UK, Sept 6-9, 1999.
Kerr solitons show fermion-like properties (unpublished).
Paraxial and non-paraxial modes have unexpected quantisation properties (unpublished).
5. P Chamorro-Posada, GS McDonald and GHC New, Nonparaxial Solitons, J Mod Opt 45 (1998) 1111.
Abstract. We derive a nonparaxial nonlinear Schroedinger equation and show that it has an exact non-paraxial soliton solution from which the paraxial soliton is recovered in the appropriate limit. The physical and mathematical geometry of the non-paraxial soliton is explored through the consideration of dispersion relations, rotational transformations and approximate solutions. We highlight some of the unphysical aspects of the paraxial limit and report modifications to the soliton width, the soliton area and the soliton (phase) period which result from the breakdown of the slowly varying envelope approximation.
4. P Chamorro-Posada, GS McDonald and GHC New, Exact Analytical Nonparaxial Optical Solitons, International Quantum Electronics Conference, San Francisco, USA, May 3-8, 1998.
3. P Chamorro-Posada, GS McDonald and GHC New, Nonparaxial Solitons, Thirteenth National Quantum Electronics Conference, Cardiff, UK, Sept 8-11, 1997.
2. S Chavez-Cerda, GS McDonald, GHC New and J Noon, Nonparaxial Eigenmodes in Nonlinear Beam propagation, Twelfth National Quantum Electronics Conference, Southampton, UK, Sept 4-8, 1995.
1. GS McDonald et al, 3D and 4D Structures in Paraxial and Nonparaxial Nonlinear Optics, Study Centre on Nonlinear Optics and Guided Waves, Edinburgh, UK, Aug. 1-20, 1994.