A hybrid spectral/spatial method to evaluate the active Green´s function of large planar rectangular arrays: a combined asymptotic/numerical algorithm

The article illustrates a formulation to evaluate the array Green´s function (AGF) of large finite planar phased array for observation points on the array plane, possibly close to the array contour. The procedure is based on the AGF representation in terms of a double spectral integral, whose integration paths are properly deformed to have an exponential attenuation of the integrand. The diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges. This latter comprises higher order contributions. Thanks to the convergence properties, the final algorithm is numerically accurate, stable and more efficient with respect to the individual element summation for large arrays. It also constitutes the basic step for the efficient evaluation of the AGF of a multilayer environment