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 nonvanishing incident field. The incoming wave is allowed to be an 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 hyperplane. 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.