Dark spatial solitons constructed from modes of linear waveguides

Abstract

Breaking with convention, we construct dark self-guided modes (spatial solitons) from known modal solutions of linear waveguides through a self-consistency procedure rather than by solving a nonlinear differential equation. This approach leads to a physical picture of dark spatial solitons and their analytical representation on the basis of reflectionless plane-wave scattering from a linear dielectric waveguide. The picture applies to solitons of arbitrary cross section propagating within a medium whose refractive index has an arbitrary dependence on intensity. Examples include the first reported dark spatial solitons of a threshold nonlinearity, revealing multiple- and higher-order solitons and a new simple expression for the field of a dark soliton in a Kerr medium.