Construction of Green´s Functions for Multilayered Media Using Signal-Flow Graphs [Education Column]

The utilization of signal-flow graphs is demonstrated as a simple and intuitive approach for constructing Green´s functions for multilayered media. The branches of the signal-flow graphs represent wave transmission or reflection coefficients in or between the different layers, while their nodes correspond to layer interfaces, the source and the observer points. First, the flow-graph derivation of the Green´s function is presented for the one-dimensional case of a plane wave produced by a uniform electric-current-sheet source normally incident on a two-layered medium. The derivation is next generalized to the case of multilayered media. The problem is solved for the case where both the excitation and the observation points are inside the first-layer medium. Finally, the one-dimensional case is then extended to higher dimensions.