Calculation of the Free-Space Periodic Green's Function Using Equivalent Finite Array

We present a novel method for the calculation of the 2D and 3D free-space periodic Green's function (PGF), especially efficient when observation points are in the vicinity of the array plane, a case for which both spatial and spectral domain forms of PGF are known to be slowly convergent. The PGF is approximated by a truncation of the original array, and the assignment of new fictitious amplitudes to maintained sources. Both 2D and 3D numerical tests show that a highly accurate approximation of the PGF can be obtained with such an equivalent finite array composed of a few sources, making the method especially relevant for fast electromagnetic computation of periodic structures, with the method of moments (MoM) for example.