Layer stripping for time-harmonic Maxwell's equations with high frequency

Abstract

The inverse boundary value problem for Maxwell's equations is considered. The objective is to estimate the electric permittivity and conductivity as well as the magnetic permeability within a body from stationary high-frequency field measurements on the boundary of the body. A layer-stripping algorithm for estimating the parameters in the body can be described as follows. First, the unknown parameters are estimated at the boundary of the body by applying highly oscillating field excitations. Then the surface data are propagated through the estimated surface layer by an invariant embedding equation. Repeating the process, one 'peels off' the body layer by layer. The aim of this article is to show that the necessary tools for the algorithm applied to Maxwell's equations exist. A propagation equation for the boundary data is derived and it is shown that measurements with high spatial variations give an estimate for the unknown material parameters at the boundary. Due to the energy dissipation, the method is expected to work near the boundary of the body.