Effective impedance boundary conditions for an inhomogeneous thin layer on a curved metallic surface

Effective impedance boundary conditions for an inhomogeneous thin layer coated on a perfectly conducting object are considered. The permittivity of the thin layer is inhomogeneous along both the normal and tangential directions. Explicit forms of the first- and second-order approximate impedance boundary conditions are derived first for a two-dimensional (2D) thin layer for the TE and TM cases. Numerical results are presented. The case of Maxwell´s equations for a three-dimensional inhomogeneous thin layer is also considered