Study of Sierpinski Carpet fractal Structure Diffraction Using MS-MGEC Method
Ben Salah, T.; Aguili, T.
Enit, Labo syscom

In this paper we use a new EM Analysis method named MS-MGEC which stands for Multi Scale Method of Generalized Equivalent Circuit for studying the fractal Sierpinski Carpet structure placed in an infinite waveguide.

The proposed method is an extension of the MGEC method (a MoM based method) in which we introduce a new formulation using a Surface Impedance Operator for bypassing conventional 'scalar' surface impedance limitations. Indeed, the study of electromagnetic waves' diffraction by an obstacle with fractal geometry is a difficult problem because of the underlying multi-scale properties of such structures. This difficulty is mainly imposed by multiple length scales (self-similarity) characteristics of fractal structures that makes their design and analysis using classical methods require huge amount of resources (both memory and execution time). Existing Recursive methods iterate on EM characteristics so that they consider only one length scale per iteration. Usually, the input impedance of iteration is used as surface impedance in the next one. But such surface impedances luck in precision since they handle information only about a single mode (input impedance seen by the fundamental mode). In our work we generalize this approach to divide - automatically - a multi scale structure into smaller domains. Each domain - considered as a mono scale domain - is studied separately maintaining the boundary conditions. Then, it is replaced in the next iteration as a multi modal source which insures a better precision.