The authors present generalized surface impedance conditions that improve medium characterization. One of the most common conditions that is often used to simulate a dielectric coating is the standard impedance boundary condition, and the improved boundary condition discussed can be viewed as a generalization of this, distinguished by the presence of higher-order derivatives of the field. By virtue of the derivatives, the conditions are less local in character, and the additional degrees of freedom can be used to better simulate the material properties of a surface. Following a review of the standard impedance condition, the new conditions are introduced. Several forms are presented, each with coefficients which are functions of the geometry and material properties of the surface. The applications of these to a variety of scattering problems are then discussed.>

The problem considered is that of a plane wave incident on a perfectly conducting half-plane with a thin dielectric coating on its upper face. The solution is accomplished by introducing a higher order boundary condition to simulate the effect of the dielectric, thereby allowing the structure to be treated as an infinitesimally thin half-plane. Two types of boundary conditions are developed, one applicable to a low-contrast dielectric and the other to a high-contrast one. The problem is then solved using a generalized version of the Maliuzhinets method in which certain additional constants are introduced to assure the correct behavior of the field at the edge. Although these constants play no role in the final solution, they are needed to cancel out inadmissible singularities in the solution of the homogeneous difference equation. The final solution is expressed in a uniform manner and some numerical results are presented.>