Journal of Electromagnetic Analysis and Applications, 2012, 4, 118-128 doi:10.4236/jemaa.2012.43016 Published Online March 2012 (http://www.SciRP.org/journal/jemaa) Periodic Planar Multilayered Substrates Analysis Using Wave Concept Iterative Process El Amjed Hajlaoui 1 , Hichem Trabelsi 2 , Henri Baudrand 3 1 Laboratoire d’Electronique, Departement de Physique, Faculte des Sceinces de Tunis, Tunis, Tunisie; 2 Laboratoire d’Electronique, Departement de Physique, Faculte des Sceinces de Tunis, Tunis, Tunisie; 3 Laboratoire d’Electronique, Groupe Microonde ENSEEIHT, Toulouse, France. Email: hajlamjed@yahoo.fr Received January 1 st , 2012; revised February 5 th , 2012; accepted February 13 th , 2012 ABSTRACT Due to the practical importance and difficulties associated with their closed form solutions, the experimental and com- putational study of periodic planar multilayered structures, such as FSS in multilayered configuration and Multilayered Planar antennas array, are in complementary progress. During the past two decades, the widespread use of such meth- ods has allowed a broad range of important scattering problems involving non-standard shapes, boundary conditions and material composition to be solved. In this sense, an efficient iterative technique based on the concept of wave is presented for computing periodic substrates in multilayered configuration. This paper presents an extensible approach of the iterative method to study multilayered substrates (n layers in which n = 2, 20) with spatial periodicity in multi- layer configuration. Our new approach is performed in order to study 3 dimensional structures by the method called Wave Concept Iterative Process (WCIP). This method is adapted in its original form to study 2 dimensional structures. The third dimension is modulated by transmission line as an approximation for every mode in spectral domain. The utility of the new WCIP appears because of its fast convergence and little consumption in memory. Keywords: WCIP; Transmission Line Theory; Patch Antenna; Frequency Selective Surfaces (FSS) 1. Introduction Periodic structures have a variety of important applica- tions in electromagnetic engineering and modern techno- logies. Commonly used, periodic structures include fre- quency selective surfaces, optical gratings, phased array antennas and various metamaterials. Both applications can essentially be formulated as planar multilayered periodic arrays of metallic patches and/or slots. The use of periodic conditions to model the behavior of these arrays is justified by their large size (typically, 100 * 100 elements). As a result, the development of fast and efficient software tools, that can accurately predict the electrical behavior of the component being investigated, is of fundamental importance. For mechanical reasons, or the purposes of reducing the angular sensitivity [1], FSS structures are often mounted on dielectric substrates. Now more complex mediums have been used as the substrates: some works were reported on FSS structures with ferrite substrates [2] and with chiral substrates [3,4]. In this paper, to reduce the computational effort required for the analysis of arbitrary microwave components, we suggest an efficient method which can be incorporated in a circuit simulator. This theory is an extension of previous studies investigated with the MLC-WCIP [5], but here we introduce a new parameter characterized by the intro- duction of periodicity as a new approach in the studied structures (new boundaries conditions). The importance of periodicity, as a new investigation, appears in complex periodic multilayered structures characterized by infinite geometric dimension. A new approach is necessary to study the entire structure because of its infinite geometric dimensions. The idea is to extract and study one multi- layered cell to conclude about the entire structure with its infinite cells. This approach consists in introducing periodic walls for the analyzed substrate characterized by periodic elements and changing Fast Modal Transformation (FMT) of selected cells by new equivalent FMT taking account the presence of periodic lateral walls of the selected substrate. It offers high spatial resolution with low com- puting resources in time and memory, and makes the iterative method more effective in modeling arbitrarily- shaped structures. Here, we have achieved a factor of 4 in memory reduction and 7 - 11 in CPU speedup over other method (here is finite element method (F.E.M.) in case of typical meshing. Copyright © 2012 SciRes. JEMAA