On the use of Contour-FFT for the MBF-based analysis of arrays of antennas placed vertically above a multi-layered substrate

A method is proposed for the fast Macro Basis Functions (MBFs) characterization of arrays of antennas placed vertically above a multi-layered substrate by using the Contour-Fast Fourier Transform (Contour-FFT) method. The presented work aims at accelerating the evaluation of interactions between the MBFs defined on the elements corresponding to antennas extending vertically above the ground. We first write a complex-plane extension of the interaction between antennas via reflection by the ground. The calculation is then accelerated using the Contour-FFT. We exploit the Contour-FFT available for planar arrays to efficiently obtain the solution of the currents on the vertical antennas with the consideration of reflections from the semi-infinite ground. Results are presented and future perspectives are highlighted.