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Inverse time-harmonic electromagnetic scattering from coated polyhedral scatterers with a single far-field pattern

It is proved that a convex polyhedral scatterer of impedance type can be uniquely determined by the electric far-field pattern of a non-vanishing incident field. The incoming wave is allowed to bean electromagnetic plane wave, a vector Herglotz wave function or a point source wave incited by some magnetic dipole. Our proof relies on the reflection principle for Maxwell's equations with the impedance (or Leontovich) boundary condition enforcing on a hyper-plane. We prove that it is impossible to analytically extend the total field across any vertex of the scatterer. This leads to a data-driven inversion scheme for imaging an arbitrary convex polyhedron.