Simultaneous identification of a two-layered medium and the embedded obstacle with Maxwell's coefficients

Consider the inverse scattering of electromagnetic waves in a two-layered medium containing an inhomogeneous scatterer coated with a thin, highly conductive layer. We focus on the inverse problem of establishing the global uniqueness for the simultaneous recovery of the unbounded interface of the layered medium, the buried scatterer D along with its Maxwell’s coefficients (ε, σ), and the surface conductivity η. This is achieved using near-field data measured only in the upper half-space, without any a priori knowledge of the conductive scatterer D or Maxwell’s coefficients. The recovery of the unbounded interface is established via a novel mixed reciprocity relation that connects different electric fields and a new derivation of a priori estimates for magnetic fields. The identification of Maxwell’s coefficients relies on constructing auxiliary modified Maxwell’s transmission problems within sufficiently small subdomains. The key technique for recovering the surface conductivity involves the design of Dirichlet Maxwell’s systems.