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Uniqueness of electromagnetic inversion by local surface measurements

Assume that a bounded body has been embedded in a homogeneous half-space. Our aim is to reconstruct the electromagnetic material parameters, namely the electric permittivity, conductivity and magnetic permeability, of the body from local field measurements on the surface of the half-space. All fields are supposed to be governed by time-harmonic Maxwell equations. We consider two kinds of initial data. The first data set consists of tangential electric and magnetic field vectors of a tangential magnetic dipole for all field and source points in an open subset of the surface. The second data set is one that we know locally on the surface - the admittance map - which, by definition, associates the tangential magnetic field with the tangential electric field. The purpose of this paper is to show that both of the data sets determine the material parameters uniquely.