On the essential dimensions of the scattering problems in planar layered structures

The efficient analysis of large printed planar arrays with elements of arbitrary shapes and locations is a challenging complex problem, as it requires large memory storage and long computational times. Therefore different techniques are being developed in order to reduce this cost. Aim of this paper is to determine the minimum number of unknowns required to get a given accuracy, i. e., the problem size. To this end, we exploit the concept of degrees of freedom of the radiated field and the well-known representations of the stratified Green´s functions. The obtained results can provide the basis for the development of computationally effective methods for the analysis of such kind of structures.