Natural Mode Series Expansion of Transient Transmission Field Through an N-Layer Structure

Abstract

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.