Scattering by two concentric spheres using the impedance boundary conditions on the inner surface

The concept of impedance boundary conditions has proven to be a useful tool for obtaining solutions to certain electromagnetic scattering or propagation problems. It is normally defined on the surface of an imperfectly conducting or coated object located in free space. The authors examine the validity of the concept when the impedance surface is inside a lossy medium. The model chosen for this study is a lossy sphere coated with a lossy shell. The plane wave scattering problem is formulated in two ways: first, by an exact analytic method using appropriate potential functions for the interior sphere, its lossy coating and the exterior region; and second, by replacing the interior sphere with an impedance surface. The results show that the impedance boundary conditions can be applied and accurate solutions can be obtained with relatively simple formulations.