ELECTROMAGNETIC DIRECT AND INVERSE PROBLEMS FOR ABSORBING MEDIA (SCATTERING, REFLECTION, TRANSMISSION, DISSIPATIVE, DISPERSIVE)

This work addresses two time domain electromagnetic direct and inverse scattering problems for absorbing media. The problems differ from one another in the choice of the underlying wave propagation model. Equations are developed which relate the properties of the media to observable features of scattered fields. Some questions regarding existence, uniqueness and stability of solutions of these equations are examined. Also, several examples and a numerical implementation are presented. In the first chapter, the properties of a lossy medium are modeled by frequency independent permittivity and conductivity profiles. A point source is used to launch an incident field on a depth varying, finite or semi-infinite, inhomogeneous dissipative slab in order to produce two dimensional incident and reflected field data sets for simultaneous reconstruction of both the permittivity and conductivity functions. In order to solve the inverse problem, the data are Hankel transformed twice to produce two sets of one dimensional data. Wave splitting techniques are used to derive nonlinear integro- differential equations which relate the reflection kernels for the resulting one dimensional problems to the properties of the medium. The equations derived are also useful to study the direct problem, with permittivity and conductivity known. The second chapter presents a physically motivated model for the dispersion of transient electromagnetic waves via a new approach based on the underlying constitutive relation between the displace- ment field D(x,t) and the electric field E(x,t). In the simplest case, this is given by (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where G(t) is a time dependent susceptibility kernel. A time domain technique is used to derive a nonlinear integrodifferential equation which relates the susceptibility kernel for a one dimensional homo- geneous slab to the reflection operator of the medium. The more general case of a medium consisting of a stack of homogeneous dispersive layers is also addressed. Finally, incorporating ideas developed in Chapter 1, point source data is used in order to treat the problem of reconstructing the time and depth dependent susceptibility kernel for an inhomogeneous dispersive slab