The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data

Dedicated to Professor Dr. Rainer Kress on the occasion of his 65th birthday and the pleasure that knowing him has given to our lives! ABSTRACT. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under certain assumptions a lower bound on the norm of the (matrix) index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. Numerical examples are given showing the efficaciousness of our estimates. 1. Introduction. Anisotropic