The paper focuses on a problem that describes propagation of transverse-electric (TE) waves in a plane dielectric waveguide filled with nonlinear medium. The nonlinearity is characterized by the power term [Formula: see text], where [Formula: see text], [Formula: see text] are constants and [Formula: see text] is the electric term of the guided electromagnetic field. The layer is located between two half-spaces filled with linear media having constant permittivities. It is proved that the nonlinear problem has infinitely many propagation constants (PCs), whereas the corresponding linear problem has only a finite number of them. The nonlinearity leads to the occurrence of infinitely many nonperturbative solutions of the nonlinear problem. Results of the paper show that the power nonlinearity (for any [Formula: see text]) and Kerr nonlinearity (for [Formula: see text]) produce qualitatively similar outcomes. In addition, the found results allow one to study very important cases of quintic, septimal, etc. nonlinear permittivities in the focusing regime.
