MoM-oriented array Green’s function for the analysis of large finite arrays

The application of the method of moment (MoM) to predict the behavior of periodic arrays and scattering from periodic surfaces printed in stratified dielectrics, often leads to large, dense, and poorly-conditioned matrices. On the other hand, the infinite-size approximation fails in predicting the behavior of the elements near the edges of the array. In order to overcome the intrinsic difficulties of the problem, the Floquet wave (FW)-based solution for the infinite array can be extended to large finite arrays; this leads to a drastic computational gain [1, 2, 3]. The methods are applicable to arrays or surfaces which exhibit periodicity or quasi-periodicity (in the sense of weak variations) of geometry and excitation. The above methods can be considered as modifications, more or less sophisticated, of the windowing of the radiating element currents introduced in [1][2]. Here, the windowing is performed on the Greenpsilas function more than on the element currents, thus allowing, inside the MoM solution, a higher degree of accuracy and the possibility to use sub-domain basis functions for improving the generality of the algorithm. In the windowing approach, although the number of unknowns does not decrease, the treatment of each element is attributed to the solution of an independent integral equation. This equation has, however, the complexity of the MoM system related to an isolated element, thus reducing the complex problem to the inversion of a large number (equal to the number of elements) of small size problems that can be efficiently computed collectively in terms of FWs.