engleski

Green's Functions of Soft and Hard Surfaces Derived by Asymptotic Boundary Conditions and Homogenization Method

The concept of soft and hard surfaces has been introduced in electromagnetic theory to help engineers in designing antennas and electromagnetic structures (P.-S. Kildal, IEEE Trans. Antennas Propagat., 1990, pp. 1537-1544). In principal, the power density along the soft or hard surface has respectively a null or a maximum. The two most common realizations are the corrugated surface and the strip-loaded grounded dielectric slab. We have performed the rigorous analysis of open soft and hard surfaces using Floquet-mode expansion/moment method approach. If the source excites a full spectrum of plane waves, such as a dipole, the rigorous analysis is a laborious process. A simpler approach is to use approximate boundary conditions. We have used two types of approximate boundary conditions: the asymptotic boundary conditions for strips and corrugations (ASBC and ACBC, respectively), and boundary conditions obtained by the homogenization method (BCHM), i.e. by averaging the fields of the fundamental Floquet mode. ASBC and ACBC can be directly applied for analyzing curved surfaces, and in the BCHM case we have used a local planar approximation, that means we supposed that the surface where the strips are located is locally a plane surface. The purpose of the present paper is to give derivation the Green's functions for soft and hard surfaces, and by that to analyze different realizations of soft and hard surfaces. Strips and corrugations are analyzed using approximate boundary conditions (part of the work is given in Z. Sipus, H. Merkel, P.-S. Kildal, IEE Proceedings - part H, 1997, pp. 321-328). Furthermore, we have modified the algorithm G1DMULT that calculates Green's functions of planar, circular cylindrical and spherical general multilayer structure. By this one can analyze general multilayer structures with strips or corrugations as one layer. We have studied the fulfillment of the soft and hard boundary conditions in the near and far field regions. Special attention is given to the properties of surface waves that obstruct the fulfillment of these boundary conditions. The results show that the both approximate boundary conditions give good results when the period of the strips is small compared to the wavelength. However, BCHM gives more accurate results, and practically there is no difference between the moment method results and the results obtained by BCHM method if the periodicity is small enough. Numerical results are also compared to measurements showing a very good agreement.

boundary conditions; bounadry-value problems; approximation theory; soft and hard surfaces

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