The pole-zero matching method for the analysis of metamaterial surfaces

Much interest has been devoted to the study of the dispersion properties of planar structures realized by frequency selective surfaces (FSS) on a grounded dielectric slab. An approximate model of an FSS may be given in terns of a quasistatic LC impedance placed in a TE or TM equivalent transmission line. This simple circuital representation contains the essential physics able to describe the basic concepts of the AMC properties qualitatively. However, the lack of description of important aspects such as the wavenumber dependence of the equivalent circuit or the coupling between TE and TM polarizations, imposes a more rigorous generalization of the model. Recently, we introduced a method, based on the application of Foster's reactance theorem, for the efficient synthesis of the FSS admittance matrix for the study of dispersion properties (Maci, S. et al., IEEE Trans. Antennas Propag., vol.53, no.1, p.70-81, 2005). This theorem implies that FSS admittance functions of frequency satisfy the pole-zero analytical properties of the driving point LC admittance functions. The paper generalizes the method in order to deal with a wide class of FSS-based artificial surfaces. A new derivation of the FSS admittance matrix is proposed and some general properties of this kind of structure are pointed out.