Spatial solitons of the power-law nonlinearity

Abstract

Simple, exact analytical solutions of Maxwell's equations are given for the TE-type self-guided modes of a medium that has a power-law dependence on intensity I(q) for the continuum values of q. An analytical criterion shows that such spatial solitons are stable for q < 2 only. Our derivation is novel in that solitons are borrowed from the known modes of the sech(2) profile (linear) waveguide, rather than by solving the nonlinear wave equation. The results reveal the change in soliton propagation as the nonlinear medium itself changes.