  This work is concerned with an inverse electromagnetic scattering problem in
two dimensions. We prove that in the TE polarization case, the knowledge of the
electric far-field pattern incited by a single incoming wave is sufficient to
uniquely determine the shape of a penetrable scatterer of rectangular type. As
a by-product, the uniqueness is also confirmed to inverse transmission problems
modelled by scalar Helmholtz equations with discontinuous normal derivatives at
the scattering interface.
  Keywords: Uniqueness, inverse medium scattering, Maxwell equations, one
incoming wave, shape identification, right corners
