Scholarlink

Abstract <p>The paper considers the problem of propagation of two directed monochromatic TE-polarized electromagnetic waves in a planar optical waveguide placed between two isotropic homogeneous half-spaces. The permittivity of the medium in the layer is a diagonal tensor whose elements depend on the spatial coordinate and the squared magnitude of the electric field strength. From a mathematical point of view, this problem is a nonlinear two-parameter eigenvalue problem for a system of two nonautonomous nonlinear one-dimensional Helmholtz equations with boundary conditions of the third kind and an additional local condition. The problem is studied with a nonstandard perturbation method using a simpler nonlinear problem as the unperturbed problem. The main result of the work is a theorem establishing the existence of a finite number of solutions to the problem under consideration, including nonlinearizable ones. Some numerical results are also presented.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Perturbation Method and Existence of Nonlinearizable Solutions in the Problem of Propagation of a Nonlinear Coupled TE–TE Wave in a Planar Optical Waveguide with Spatial Inhomogeneity of the Medium

  • 期刊论文

  • 发表日期：

    2026年2月1日

查看全文
  • D. V. Valovik,
  • A. A. Dyundyaeva,
  • S. V. Tikhov

摘要

Abstract

The paper considers the problem of propagation of two directed monochromatic TE-polarized electromagnetic waves in a planar optical waveguide placed between two isotropic homogeneous half-spaces. The permittivity of the medium in the layer is a diagonal tensor whose elements depend on the spatial coordinate and the squared magnitude of the electric field strength. From a mathematical point of view, this problem is a nonlinear two-parameter eigenvalue problem for a system of two nonautonomous nonlinear one-dimensional Helmholtz equations with boundary conditions of the third kind and an additional local condition. The problem is studied with a nonstandard perturbation method using a simpler nonlinear problem as the unperturbed problem. The main result of the work is a theorem establishing the existence of a finite number of solutions to the problem under consideration, including nonlinearizable ones. Some numerical results are also presented.