Shaping Intensities of Complex Scalar Fields in Inhomogeneous Scenarios via Linearly Combined Bricks

The ability to enforce a given behaviour on the electromagnetic field intensity distribution is relevant in a wide range of applications, including the particularly challenging case where shaping is required in heterogeneous media. In this respect, with reference to scalar fields, the paper proposes a new effective approach to design the optimal complex excitations feeding an antenna array able to ensure a shaped field intensity distribution within a specified region of interest while keeping under control the field intensity in other areas. To tackle the challenges and the curse of dimensionality of such a problem, the proposed strategy represents the unknown complex field as a combination of elementary (eventually focused) bricks. Then, the corresponding linear superposition coefficients are evaluated by using a semidefinite relaxation framework and by minimizing the nuclear norm of an auxiliary matrix. The approach is tested against 2D inhomogeneous lossless scenarios. Comparisons with respect to previous approaches are also provided.