Time-domain (early- and late-time) transmission response of an $N$ -layer composite structure has been analytically investigated using contour integration for uniform plane waves with perpendicular and parallel polarizations. It has been shown that whereas the late-time transmission response of an $N$ -layer structure is a sum of damped sinusoids provided that it is terminated in a lossless medium (e.g., air medium), its early-time response can be represented as the summation of individual subregional responses, which can be expressed by natural series if any subregion is surrounded by lossless media (assuming that the last layer is lossless). Numerical examples are presented to investigate the early- and late-time transmission responses, and thus validate the results obtained from contour integration, of transparent $N$ -layer composite structures for perpendicular and parallel polarization cases.

中文翻译：

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瞬态传输场的自然模式串联扩展 N-层结构

时域（早期和晚期）传输响应 $N$ 已经使用轮廓积分对具有垂直和平行极化的均匀平面波进行了分析研究 - 层复合结构。已经表明，虽然一个的延迟传输响应 $N$ -层结构是阻尼正弦曲线的总和，只要它终止于无损介质（例如，空气介质），其早期响应可以表示为各个子区域响应的总和，如果有的话，可以用自然级数表示子区域被无损媒体包围（假设最后一层是无损的）。给出了数值例子来研究早期和晚期传输响应，从而验证从轮廓积分获得的结果，透明的 $N$ 用于垂直和平行极化情况的层复合结构。