HELMHOLTZ SOLITONS IN OPTICAL MATERIALS WITH A DUAL POWER-LAW REFRACTIVE INDEX

A nonlinear Helmholtz equation is proposed for modelling scalar optical beams in uniform planar waveguides whose refractive index exhibits a purely-focusing dual power-law dependence on the electric field amplitude. Two families of exact analytical solitons, describing forward-and backward-propagating beams, are derived. These solutions are physically and mathematically distinct from those recently discovered for related nonlinearities. The geometry of the new solitons is examined, conservation laws are reported, and classic paraxial predictions are recovered in a simultaneous multiple limit. Conventional semi-analytical techniques assist in studying the stability of these nonparaxial solitons, whose propagation properties are investigated through extensive simulations.