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

Fioralba Cakoni (1) , David Colton (1) , Houssem Haddar (2)

1 Department of Mathematical Sciences
2 DeFI - Shape reconstruction and identification

We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under certain as- sumptions 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. Nu- merical examples are given showing the efficaciousness of our estimates.

Domaines: Equations aux dérivées partielles [math.AP]

Fioralba Cakoni, David Colton, Houssem Haddar. The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data. Journal of Integral Equations and Applications, 2009, 21, pp.203--227. ⟨10.1216/JIE-2009-21-2-203⟩. ⟨hal-00743819⟩