An electromagnetic inverse problem for dispersive media

The dispersion of transient electromagnetic waves in a homogeneous medium can be characterized by expressing either the complex permittivity as a function of frequency or the susceptibility kernel as a function of time. In this paper, a time domain technique is used to derive a nonlinear integrodifferential equation which relates the susceptibility kernel for a one-dimensional homogeneous slab to the reflection operator for the medium. Thus, the susceptibility kernel (which is a function of time) can be determined from reflection data. A numerical implementation of this technique is shown. The more general case of a medium consisting of a stack of homogeneous dispersive layers is also addressed.