A class of exact and higher-order surface boundary conditions for layered structures

A class of exact and higher-order surface impedance boundary conditions (HOIBC's) is derived. Initially, exact impedance boundary conditions (IBC's) are derived first in the spectral and then in the coordinate domain. It is shown that in the coordinate domain they are expressed by a dyadic operator acting on the convolution product between the scalar Green's function, corresponding to the considered structure, and the tangential magnetic field. Next, it is demonstrated that the higher-order impedance boundary conditions in the spatial domain correspond to an appropriate expansion of the mentioned convolution product in the space domain. Finally, the accuracy of the HOIBC's is estimated by comparing the exact solution with that obtained through the HOIBC's for some typical canonical problems. The corresponding error curves presented refer to the worst error situation for each one of the chosen cases.