Constrained Power Focusing in Inhomogeneous Media as a Polarization Optimization

The problem of focusing a field into inhomogeneous media is a canonic open problem relevant in many engineering areas. Several approaches have been developed, for example, Time Reversal, Inverse Filter, and Eigenvalues approach, but they suffer from several drawbacks which are counteracted by Optimal Constrained Power Focusing (OCPF) technique. OCPF was first introduced to deal with scalar fields and, recently, it has been extended to tackle the problem of focusing vector fields. In particular, the proposed approach allows reducing the focusing problem, which is NP-hard in case of vector fields, to a series of convex programming (CP) ones. In this paper, an alternative OCPF formulation is presented, which consists in the research of the most suitable polarization of the field into the target point and relies on the convexity of the problem when fixing this polarization. Such a result allows the development of two different solution procedures: an enumerative one that can take advantage of parallel programming in order to explore all possible polarizations and hybrid one which relies on the exploitation of global search algorithm just to solve the nonconvex part of the problem at hand.