Near-Field Synthesis of Shaped Beams via Spectral Factorization and Warping Sampling

We extend to the near-field case the well-known spectral factorization method, which was applicable until today only to far field. This is done by restoring the bandlimitedness of the field through the adoption of a suitable warping variable. By so doing, it becomes possible, for the first time in the literature, to perform the mask-constrained power synthesis of 1-D shaped beams lying in arbitrary masks in the near field zone by just solving a linear programming problem followed by a polynomial factorization. It also becomes possible a-priori ascertaining whether the size of the source is sufficient to radiate a field lying in the assigned mask, and hence a-priori identifying the minimum feasible size of the source. Finally, the procedure identifies all the sources able to radiate the sought power pattern. An example concerning near field multi-focusing is provided.