Bright and dark surface waves at a nonlinear interface

Abstract

Stationary propagation of bright and dark surface waves at the nonlinear interface between a self-focusing medium and a self-defocusing medium is found possible within a certain range of the wave effective index ${\mathit{n}}_{\mathit{e}\mathit{f}\mathit{f}}$, depending on the linear refractive indices and nonlinear coefficients. In the low limits of the trapping region in terms of this ${\mathit{n}}_{\mathit{e}\mathit{f}\mathit{f}}$, each particular ${\mathit{n}}_{\mathit{e}\mathit{f}\mathit{f}}$ can be associated with two degenerate trapped mode patterns characterized by two different field profiles, whereas in the upper limits of the trapping region each ${\mathit{n}}_{\mathit{e}\mathit{f}\mathit{f}}$ corresponds to only one particular mode pattern. This contrasts with the bright or dark surface waves trapped at the interface between a linear medium and a nonlinear medium or between two self-focusing (self-defocusing) media where each particular ${\mathit{n}}_{\mathit{e}\mathit{f}\mathit{f}}$ pertains to only one mode pattern (for a nonlinear medium bounded by a linear medium) or two degenerate mode patterns (for two nonlinear media) over the whole trapping region.