A new formulation of multiscale method based on modal integral operators

Multiscale (MS) method is of great interest in electromagnetic modeling, especially when applied to complex patterns that contain fine details in large structure. Its principal advantage is the important reduction of the problem’s high aspect ratio since fine details are studied independently of the larger structure. Unlike full-wave methods that found their limitations when employed to model complex structures, the MS method has less limitations since it requires less processing time and memory storage. However, the accuracy of the MS method is linked to the exact formulation of modal operators of diffraction Γ^$ \widehat{\Gamma } $ and surface impedance Z^s$ \widehat{Z}_s $, mainly based on active modes. In fact, the parameters to optimize in this study are the needed number of active modes to well approximate Γ^$ \widehat{\Gamma } $ and Z^s$ \widehat{Z}_s $ and their criterion of selection in order to separate them from passive ones. We are interested in this paper particularly in studying these parameters against the sub-structure’s dimensions and the distances separating them. Moreover, we present a new criterion to select active modes arbitrarily chosen previously. The obtained results based on a good approximation of operators Γ^$ \widehat{\Gamma } $ and Z^s$ \widehat{Z}_s $ (that represent the sub-structures) are in agreement with those obtained by the MoM method. Considerable gain in computational time and memory storage is achieved.