On uniqueness and linearization of an inverse electromagnetic scattering problem

Consider the electromagnetic scattering problem for transverse magnetic polarization (TM) wave from a cavity in a ground plane, which leads to a boundary value problem govern by the 2-D Helmholtz equation with non-local boundary condition. The domain derivative of near-field with respect to the cavity shape is derived and the uniqueness of linearized problem of the non-linear map from cavity shape to the near-field is proven. Then we consider the inverse problem of recovering cavity shape from the wave fields given in the aperture. We prove the uniqueness of this non-linear inverse problem and give an iteration inversion algorithm based on the domain derivative expression.