A 2-D differential surface admittance operator for combined magnetic and dielectric contrast

In this paper, we present a novel technique to accurately model scattering phenomena at two-dimensional circular and rectangular structures consisting of arbitrary homogeneous materials, including magnetic media in particular. The proposed formalism utilizes a differential surface admittance operator, which invokes a single source equivalence theorem to replace the inside material by its surrounding medium, while introducing an equivalent surface current density. The arbitrary magnetic contrast can be combined with an arbitrary electrical conductivity. As such, the skin effect is rigorously taken into account, making our method ideally suited for broadband modeling of good conductors as well. It is demonstrated that an appropriate choice of the basis functions for the discretized problem is critical to obtain a convergent result when magnetic contrast is introduced. The method is analytically validated for the case of a circular cylinder and additional numerical results illustrate the correctness of the technique for (combinations of) rectangular cylinders, through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.