Electromagnetic study of planar pre-fractal structures using the scale changing technique

In this paper, the scale-changing method is used to compute the surface impedance of pre-fractal structures characterized by the coexistence of metallic patterns at multiple scale levels. The multi-scale nature of these structures is used to split them into sub-structures enclosed by appropriate boundaries. The calculation starts from the elementary substructure: N active modes excite the considered sub-structure in order to compute the corresponding surface impedance matrix useful for the transition from a scale toward another. The choice of active modes is important in order to ensure the coupling between two consecutive scales and to have a correct description of the electromagnetic state within discontinuities. Consequently, the local modal basis is divided into two parts: - Higher-order modes: localized modes essentially useful for the local electromagnetic description within discontinuities. - Lower-order modes or active modes: travelling modes useful for the coupling between sub-structures. When localized modes are used as active, we show that the electromagnetic description within discontinuities is not correct. The surface impedance obtained by the multi-scale method is compared to the surface impedance computed by the MoM method. The error variation with the number of active modes is presented. It converges with an error less than 0.3% when a sufficient Number of active modes are used.