Visibility and Invisibility

Abstract

The first part of this article concerns visibility, that is the question of determining the internal properties of a medium by making electromagnetic measurements at the boundary of the medium. We concentrate on the problem of Electrical Impedance Tomography (EIT) which consists in determining the electrical conductivity of a medium by making voltage and current measurements at the boundary. We describe the use of complex geometrical optics solutions in EIT. In the second part of this article we will review recent theoretical and experimental progress on making objects invisible to electromagnetic waves. This is joint work with A. Greenleaf, Y. Kurylev and M. Lassas. Maxwell’s equations have transformation laws that allow for design of electromagnetic parameters that would steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was hidden. The object would have no shadow. New advances in metamaterials have given some experimental evidence that this indeed can be made possible at certain frequencies. Mathematics Subject Classification (2000). Primary 35R30, 78A46 ; Secondary 58J05, 78A10 .