Three-Dimensional Field Intensity Shaping: The Scalar Case

Due to the plethora of possible applicative fallouts, in the recent years several efforts have been made to develop three-dimensional (3-D) field intensity shaping methods. While many approaches able to focus a wave-field into a target point are available, few strategies have been instead developed to generate a field having a given intensity spatial distribution. This is probably due to the higher challenging nature of such a problem. In this letter, with reference to scalar fields, we present an innovative 3-D shaping procedure, which casts the problem as the solution of a finite number of convex programming problems. An example of the performance of the proposed procedure in a 3-D inhomogeneous scenario is given to show the capability of ensuring uniform field intensity within a target area while keeping it arbitrarily bounded elsewhere.