Lagrangian formulation for inverse source problems: minimum energy and reactive power constraints

With the practical interest provided by the antenna synthesis problem and with the expectation of illuminating, from a new perspective, fundamental antenna limits connected to the reactive energy, we investigate the inverse source problem of deducing an unknown source from knowledge of its external field by means of a new Lagrangian formulation that encompasses different solution constraints, including important reactive power constraints. We arrive at a new minimum energy solution with the additional, antenna-motivated constraint of having a zero reactive power. Numerical results (shown at the conference), corresponding to a dipolar source, illustrate interesting properties of the solutions (such as their obeying a certain homogeneous wave equation) and of their fields and energy, and elucidate fundamental questions on antenna limits.