Higher-order impedance boundary conditions for complex layered planar coatings

The widespread use of complex materials (e.g., bianisotropic, nonreciprocal), in the form of thin coatings on conducting bodies, e.g., in shielding and backscattering reduction/enhancement applications, demands more efficient CAD tools based on effective models. Approximate impedance boundary conditions (IBCs), whenever applicable, can be very helpful in reducing the computational cost of numerical methods. Hoppe and Rahmat-Samii (1995) devised a spectral domain approach for systematically deriving higher-order IBCs (HOIBCs) for piecewise homogeneous coatings with arbitrary constitutive properties on planar and as well as curved metallic boundaries. This approach turns out to be very well suited for CAD implementations, on account of its wide applicability and high accuracy. In this article, we extend the aforementioned method by studying the problem of scattering by an isotropic, longitudinally inhomogeneous, dielectric coating on a general (i.e., polarization-rotating) impedance planar boundary. Such an extension allows an easy handling of multilayer coatings consisting of arbitrarily stacked homogeneous bianisotropic and inhomogeneous dielectric layers.