Generalized effective impedance boundary conditions for an imhomogeneous thin layer in electromagnetic scattering

Generalized effective impedance boundary conditions for an inhomogeneous thin layer coated on a perfectly conducting plane are considered. The first order and second order approximate impedance boundary conditions are derived first for a two-dimensional thin layer with TE plane wave incidence through an asymptotic expansion in power series of the thickness. Numerical results show that the second order boundary condition gives a sufficient accuracy for all incident angles. A rigorous derivation for the case of Maxwell's equations for a three-dimensional inhomogeneous thin layer is also given.