Helmholtz solitons: Maxwells equations, interfaces, bistability & counterpropagation

We give a brief overview of some new results in Helmholtz soliton theory. Firstly, fundamental considerations are made in terms of new contexts for Helmholtz solitons that arise directly from Maxwells equations. We then detail applications of Helmholtz solitons in material interface geometries: generalising Snells law to nonlinear beams and reporting new qualitative phenomena. Novel families of bistable soliton solutions to a cubic-quintic Helmholtz equation are also presented. Finally, an analysis of counterpropagating beams that includes new bidirectional solitons is summarized. This paper is dedicated to the late Dr. Valery E. Grikurov.