Analytical Evaluation of the Power Radiated by Sources Arbitrarily Distributed on a Surface

In this communication, an analytical expression for the fast evaluation of the power radiated by a set of electric and/or magnetic sources arbitrarily distributed on a quasi-planar surface (i.e., with orthogonal extension less than one wavelength) is presented. We proved that the computation of the radiated power with the proposed formula is convenient with respect to the classical numerical integration when the distance between the sources is larger than a ninth of the wavelength for a square source distribution. For oblong or sparse distributions, this threshold is even smaller. Therefore, the formula can be profitably used for the analysis and the optimization of sparse arrays, radial slot arrays, metasurfaces, transmitarray, reflectarray, and so on.