Stability of fundamental nonlinear guided waves

Abstract

We determine the stability of nonlinear guided waves, including solitons, nonlinear surface waves, and modes of nonlinear waveguides, by simply reading the familiar dispersion diagram without further calculation. The waveguide can be of arbitrary cross section and arbitrary profile shape and can be composed of arbitrary nonlinear materials distributed nonuniformly. This criterion is the first to our knowledge that is universal for the long-standing problem of stability of fundamental nonlinear guided waves, i.e., waves without nodes. We also show that the transverse stability of planar nonlinear guided fundamental waves demands that the material be self-defocusing in at least some portion of space, whereas planar black solitons are unstable in arbitrary self-defocusing material.