Stationary Solutions of the Electromagnetic TE Waves Propagating along a   Single Interface between the Two Kerr-Type Nonlinear Media
  Propagation of the TE electromagnetic waves in self-focusing medium is governed by the nonlinear Schroedinger equation. In this paper the stationary solutions of this equation have been systematically presented. The phase-plane method, qualitative analysis, and mechanical interpretation of the differential equations are widely used. It is well known that TE waves can be guided by the single interface between two semi-infinite media, providing that one of the media has a self-focusing (Kerr type) nonlinearity. This special solution is called a spatial soliton. In this paper our interests are not restricted to the soliton solutions. In the context of the nonlinear substrate and cladding we have found solutions which could be useful to describe also the incident light in nonlinear medium. This result is the main point of the paper. Some of the presented stationary solutions were already used in similar optical context in literature but we show a little wider class of solutions. In the last section we review and illustrate some results concerning the spatial soliton solution. 
Marian Wabia and Jaroslaw Zalesny