Spectral properties of the modes supported by plasmonic waveguides in planarly layered media are studied by the method of Multiple MultiPoles (MMP). It is shown that the most important entities in the mode analysis are the wavenumbers of the upper and lowermost layers and the wavenumbers of the guided waves supported by the layered medium. These wavenumbers introduce branch points and associated branch cuts on the complex plane where the out-of-plane wavenumbers of the modes are searched. These branch points and associated cuts make the mode analysis in layered media more demanding than the mode analysis in homogeneous media, where there is only one branch point and associated branch cut related to the wavenumber of the homogeneous medium. Several numerical examples are given to address the differences introduced by the layered media in the mode analysis and guidelines that can be used in any well-known computational electromagnetics method are provided.

通过多多极点 (MMP) 方法研究了平面分层介质中等离子体波导支持的模式的光谱特性。结果表明，模态分析中最重要的实体是上、下层的波数和层状介质所支持的导波的波数。这些波数在复平面上引入分支点和相关的分支切口，在该复平面上搜索模式的平面外波数。这些分支点和相关的切割使得分层介质中的模式分析比均质介质中的模式分析要求更高，其中只有一个分支点和相关的分支切割与均匀介质的波数相关。