Constrained focusing of vector fields intensity in near zone and/or complex scenarios as a low-dimensional global optimization

A hybrid effective approach is proposed to focus the intensity of a vector field generated by an arbitrary fixed-geometry array antenna into a target point and keep it bounded elsewhere. To overcome the complexity of the underlying non-convex problem involving a possibly large number of unknowns, we show how the space of possible polarizations can be regarded as a 5-sphere and introduce a nested procedure which jointly relies on an (external) global optimization of the field polarization on the target point plus an (internal) convex optimization of the array excitations. The approach can deal with both the cases of near-field (NF) and far-field (FF) focusing as well as with complex inhomogeneous 3-D media. The high-performance results achieved through full-wave simulations of realistic scenarios confirm the actual feasibility of tackling the problem as a low-dimensional global optimization, so that the best possible focusing can be hopefully realized.