Natural Mode Series Representation of the Transient Field Reflected From an N-Layer Lossy Medium

The conditions under which the plane-wave transient field reflected from a layered medium can be represented as a natural mode series are determined. It is shown that if each of the layers has frequency constant permittivity, permeability, and conductivity, then the late-time reflected field has a pure natural mode representation if the backing region is either lossless or a perfect electric conductor. This result, along with a decomposition of the temporal response into subregion responses, is used to determine periods of the early-time response which are also composed of pure natural mode series. Examples for structures with two and three layers are used to demonstrate the validity of the representation. The natural mode representation allows the use of existing techniques, such as the E-pulse method, to diagnose changes in the properties of the various material layers under the established conditions.