Radiation conditions, limiting absorption principle, and general relations in open waveguide scattering
Radiation conditions, limiting absorption principle, and general relations in open waveguide scattering
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开放波导散射中的辐射条件、限制吸收原理和一般关系
DOI：
10.1163/156939394x00902
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发表时间：
1994
影响因子：
1.3
通讯作者：
A. Nosich
中科院分区：
文献类型：
--
作者：
A. Nosich
本文的目的是为与开波导有关的散射问题的严谨研究提供坚实的基础。在与他们相关的困难的核心，存在着无限但却可以穿透的界限。这就要求修正辐射的条件，并证明限制吸收原理的必要性。该分析是基于傅里叶变换方法和对变换函数关于参数的解析性质的研究。除了简单的二维几何外，还使用正则积分方程和算子理论定理。该结果不同于自由空间表达式，涉及到引导自然模谱。它还揭示了与每一特定模态相关联的潮流方向是需要考虑的。得到的表达式验证了直观清晰的能量守恒和互易方程。给出了一个数值算例，并讨论了对更复杂的开波导的推广。
The purpose of this paper is to give solid ground to rigorous studies of open-waveguide-related scattering problems. In the core of the difficulties associated with them there lies the presence of infinite but penetrable boundaries. This calls for a revision of the condition of radiation, and to the necessity of justifying the limiting absorption principle. The analysis is based on the Fourier-transform approach and study of the analytic properties of transform functions with respect to a parameter. Except for simple 2-D geometries, regularized integral equations and operator theory theorems are used. The result differs from the free-space expression and involves the guided natural modes spectrum. It reveals also that the direction of power flow associated with each particular mode is to be taken into account. The obtained expressions validate the intuitively clear equations of power conservation and reciprocity. A numerical example is given and extension to more complicated open waveguides is discussed.