A new technique for the simulation of periodic structures including EBGs and Metamaterials

Because the EBGs and Metamaterial structures that exhibit interesting characteristics are almost always strictly periodic in nature and because there is an increasing interest in synthesizing new versions of these structures, we need access to both techniques-and computer codes developed on the basis of these techniques-to accomplish our own design goals. Some of the design objectives of Metamaterials are: (i) achieving close to isotropic scattering characteristics from an MTM slab; (ii) obtaining wider bandwidths and less dispersive behaviors; (iii) realizing low-loss characteristics; (iv) reducing the dependence on incident angle and polarization of the incident wave. The purpose of this paper is to describe a new and general-purpose technique capable of handling EBGS and MTMs, comprising of elements with arbitrary geometrical shapes and material properties, as shown schematically in Fig:1. The formulation is based on a combination of the Dipole Moment (DM) method, introduced recently, and the Characteristic Basis Function Method (CBFM), which serves to reduce the size of the matrix equation to be solved via the use macro-basis functions that are physics-based and tailored for the geometry being analyzed. We show that combining the above two methods leads to a relatively small matrix, often only 2x2 or 3x3 in size for many typical elements such as split rings, dipoles and spirals and hence, renders the method numerically very efficient. A number of numerical examples will be included in the paper to illustrate the computational efficiency as well as versatility of the proposed approach. In addition, benchmarking results for the performance of a code based on the DM/CBFM approach will be included, together with a comparison of the time and memory requirements of the proposed algorithm vis-a-vis other existing methods for analyzing similar periodic structures. Some initial results for wire dipole and loop elements are shown in Fig.2, where they are also compared wit- - h cells generated by using an existing code, called FSS, but for a strip type of structures (the FSS code cannot handle wire-type elements), which explains a slight difference between the two sets of results.