Calculation of the Transient Plane-Wave Reflection From an $N$-Layer Medium by the Method of Subregions

The transient reflected-field response of an arbitrarily incident plane wave from planarly-layered, dispersive materials is investigated. The reflection coefficient for the layered media is first determined in the frequency domain as a ratio of functions and a series solution is derived. Each partial sum of this series represents the reflection coefficient for a layered material consisting of a subregion of the problem of interest. It is shown that the transient reflected field may be written as a sequence of events, each of which is the late-time response of a subregion. This result can be used in time-domain methods to determine the properties of layered materials.