Optimizing Power Transmission in Given Target Areas in the Presence of Protection Requirements

We present a new approach to the synthesis of fields able to maximize the power radiated in an arbitrary portion of the visible space in the presence of protection requirements and constraints on the beam efficiency. As a by-product, beam efficiency can also be optimized if desired. The devised procedure works whether the target area has a linear, square, or circular footprint. The synthesis is stated in terms of a convex programming problem, with the related advantages in terms of both convergence speed and solutions optimality. The given theory is supported by numerical results including comparisons to state-of-the-art approaches.