Electromagnetic Inverse Problems and Cloaking.

摘要

In this thesis, we study two aspects of inverse problems for electromagnetic waves: visibility and invisibility. The first part of the thesis concerns visibility, that is the question of determining the internal properties of a medium by making electromagnetic measurements at the boundary. In particular, we consider the problem of determining different types of obstacles embedded in an inhomogeneous electromagnetic background medium using the enclosure method. Two types of waves are used, complex plane waves to enclose the convex hull of the obstacle and complex spherical waves that has the advantage in recovering the non-convex part of the obstacle. The second part of this thesis focuses on invisibility, that is how to make objects invisible to detections by electromagnetic waves. Due to the singular transformations needed for the cloaking effects, the blueprint for the transformation optics based cloaking device involves degenerate singular electromagnetic parameters. In the construction of appropriate metamaterials, the singular electromagnetic parameters are approximated by non-singular ones. We make a thorough study of this approximation and its effect on cloaking.