Green’s functions for high-impedance surfaces: A comparison between homogenized models and full-wave results

Among the variety of artificial periodic impedance surfaces proposed and studied in the last decade, Artificial Magnetic Conductors (AMC) or High-Impedance Surfaces (HIS) are of particular interest for antenna applications, as they allow for the realization of thin substrates for low-profile radiators (e.g., of printed type) with improved matching and radiation characteristics. The problem of calculating the electromagnetic field produced by an antenna in the presence of such artificial periodic impedance surface, usually placed on a grounded dielectric slab or more generally on a planar multilayer substrate, is a complex one, because of the necessity to model the interaction of aperiodic sources with a periodic environment. In order to develop fast but accurate design procedures for these antennas it would be extremely useful to have reliable analytical models for homogenized periodic surfaces. Homogenization allows for representing the effect of the artificial boundary through a suitable surface or transition (sheet) impedance; this, in turn, translates into an equivalent admittance in a transverse equivalent network representation of the structure in the spectral domain. The calculation of the field produced by a finite source is then reduced to the standard determination of a spectral-domain Green’s function and the subsequent numerical evaluation of Sommerfeld-type integrals in order to obtain the field in the spatial domain. In this work, we examine spectral representations of homogenized HIS with an electric line-source excitation, with the aim of determining their accuracy for both the near and far-field calculations. The HIS structures considered here are formed by a 2D array of frequency-selective surface elements (patches, Jerusalem crosses, etc.) printed on a grounded dielectric slab, with an electric line source directed parallel to one of the two axes of periodicity. Then, the excitation problem turns to the determination of the 2D electric-type Green’s function of the homogenized HIS structures. Results for the near field, which is the most critical issue, are compared with full-wave results obtained with the method of moments, in which the presence of an aperiodic source in a periodic environment has been taken into account via the Array Scanning Method. Numerical results for several HIS configurations are presented and discussed.