There has been a lot of recent activity on spatial solitons, including some very interesting work on soliton interactions. The latter work relies entirely upon the linear theory of rays in a graded index medium. This is a valuable viewpoint but since spatial solitons are solutions of the nonlinear Schrodinger equation NLSE they appear to lend themselves particularly well to a particle-like description. Indeed, quite a number of authors have adopted this fairly useful analogy with classical mechanics. It is an approach, however, that embodies a strong simplification arising from the use of the parabolic form of the Schrodinger equation. Namely, a paraxial approximation. The implication for the particleray approach is that, for a given direction, only a narrow cone of rays around it lie within the approximation zone. This is exactly what is required to consider the strong interaction case. If the chosen direction axis is along a real interface, for example, then only angles close to grazing instance can be permitted. This feature of the theory was anticipated a long time ago in a now famous paper by Kaplan.
This article is from 'OSA Proceedings of the Topical Meeting on Nonlinear Guided-Wave Phenomena Held in 2-4 September 1991. Cambridge, England United Kingdom. Volume 15', AD-A253 471, p388-390.