Transient electromagnetic scattering on anisotropic media

This dissertation treats the problem of transient scattering of obliquely incident electromagnetic plane waves on a stratified anisotropic dielectric slab. Scattering operators are derived for the reflective response of the medium. The internal fields are calculated. Wave splitting and invariant imbedding techniques are used. These techniques are first presented for fields normally incident on a stratified, isotropic dielectric medium. The techniques of wave splitting and invariant imbedding are applied to normally incident plane waves on an anisotropic medium. An integro-differential equation is derived for the reflective response and the direct and inverse scattering problems are discussed. These techniques are applied to the case of obliquely incident plane waves. The reflective response is derived and the direct and inverse problems discussed and compared to those for the normal incidence case. The internal fields are investigated for the oblique incidence via a Green\u27s function approach. A numerical scheme is presented to calculate the Green\u27s function. Finally, symmetry relations of the reflective response are discussed

Propagation of transient electromagnetic waves in time-varying media - Direct and inverse scattering problems

Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms

Resolution of inverse scattering problems for the full three-dimensional Maxwell-equations in inhomogeneous media using the approximate inverse

A new method is developed in this work to solve the inverse electromagnetic scattering problem in inhomogeneous media using near-field measurements. The modeling is based on the formulation as contrast source integral equations of the full three-dimensional time-harmonic Maxwell-model. This inverse problem is ill-posed and nonlinear. The known idea of using equivalent sources splits inverse scattering into two subproblems: the inverse source problem, which is linear and ill-posed, and the inverse medium problem, which is more stable but nonlinear. We introduce the concept of generalized induced source to recast the system of intertwined vector equations, describing the electromagnetic inverse source problem, into decoupled scalar scattering problems. We utilize the method of the approximate inverse to recover the induced source for each experiment. We consider in three-dimensional setting the spherical scattering operator introduced by Abbdullah and Louis [Abd98] for 2-D acoustic waves. We derive its singular-value decomposition and determine a basis for its null space. We further apply some results about error estimate from [Lou99] to the scalar problem in three-dimensions with spherical set-up. The nonlinear version of the algorithm of Kaczmarz is then adapted, using the generalized induced source, to derive an iterative scheme for the resolution of the inverse medium problem. Numerical simulations illustrate the efficiency and practical usefulness of the developed method

The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure

In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the structure is assumed to be homogenous and lossless with a positive dielectric coefficient. Below the structure is a perfect conductor partially coated with a dielectric. A periodic version of the linear sampling method is developed to reconstruct the doubly periodic structure using the near field data. In this case, the far field equation defined on the unit ball of R^3 is replaced by the near field equation which is a linear integral equation of the first kind defined on a plane above the periodic surface.Comment: 16 pages, Submitted for publicatio