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.

中文翻译：

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具有功率非线性的层中的电磁波传播

本文重点研究了一个问题，该问题描述了横向电 (TE) 波在填充有非线性介质的平面电介质波导中的传播。非线性的特征是幂项[公式：见正文]，其中[公式：见正文]，[公式：见正文]是常数，[公式：见正文]是引导电磁场的电项。该层位于填充有具有恒定介电常数的线性介质的两个半空间之间。证明了非线性问题具有无限多的传播常数（PC），而相应的线性问题只有有限数量的传播常数。非线性导致非线性问题的无限多非微扰解的出现。论文的结果表明，功率非线性（对于任何 [公式：见文本]）和克尔非线性（对于[公式：见文本]）产生质量相似的结果。此外，所发现的结果允许人们研究聚焦机制中非常重要的五次、七次等非线性介电常数情况。