Abstract

The article deals with the problem of propagation of a two-frequency electromagnetic wave in a waveguide filled with a nonlinear medium. A two-frequency wave is the sum of two monochromatic TE waves with different frequencies. The permittivity of the waveguide is characterized by a very general nonlinearity function corresponding to self-action effects. It is shown that, under certain conditions, the two-frequency wave is an eigenmode of the waveguide. From a mathematical point of view, the problem reduces to a nonlinear two-parameter eigenvalue problem for the system of (nonlinear) Maxwell’s equations. The main result of the article is the proof of the existence of nonlinearizable solutions of the problem.

中文翻译：

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非线性波导中双频电磁波传播理论中的摄动方法I：TE-TE波

摘要

该文章处理了在填充非线性介质的波导中双频电磁波的传播问题。两频波是具有不同频率的两个单色TE波的总和。波导的介电常数的特征是与自作用效应相对应的非常通用的非线性函数。结果表明，在一定条件下，双频波是波导的本征模。从数学的角度来看，对于（非线性）麦克斯韦方程组，该问题简化为非线性两参数特征值问题。本文的主要结果是证明了该问题的非线性化解的存在。