Efficient Evaluation of Far-Field Asymptotic Series

Asymptotic far-field series are used for evaluating the free-space back propagation of a coherent, monochromatic electromagnetic field, starting from the knowledge of the angular spectrum, given in terms of the field distribution in the far-field zone (Fraunhofer approximation). The closed form of the complete asymptotic series is provided both for scalar and for vectorial fields, in 2D and 3D geometries. The diverging character of such series is then analyzed by suitable nonlinear resummation schemes, which also provide efficient computational tools for their evaluation in the near-zone.