Generalized Boundary Conditions in Surface Electromagnetics: Fundamental Theorems and Surface Characterizations

Generalized boundary conditions (GBCs) for electromagnetic surfaces are investigated in this paper, which can be used to analytically characterize field discontinuities across two-dimensional surfaces. First, five representative features are described to categorize various surface problems which require proper GBC-based characterization procedures. Next, the generalized boundary conditions are discussed in details, in association with impedance boundary conditions, generalized sheet transition conditions, and surface scattering coefficients. Then an extraction method for surface susceptibilities, the characteristic parameters of surfaces in GBCs, are proposed and validated. Finally, to illustrate the applications of GBCs, two representative surface problems are demonstrated, namely, isolated-aperture surface analysis and surface-wave mode characterization. For the isolated-aperture surface, a characterization procedure is derived based on GBCs and Babinet’s principle, and the accuracy is validated through comparison with full-wave simulations. For surface wave analysis, a characterization procedure is also developed from GBCs, and the feasibility is verified by numerical examples as well.