Constrained power focusing of vector fields: an innovative globally optimal strategy

Abstract

This paper introduces and discusses an innovative approach to focus the electromagnetic power carried by a vector field into a target point, while keeping the field level bounded elsewhere. To overcome the complexity of the underlying NP-hard problem, we introduce a multi-objective optimization framework based on convex programming sub-problems. Notably, such a strategy has the unique capability of achieving the globally optimal solution by means of local search algorithms. A numerical analysis is reported to assess the methods’ performance, including a comparison with previous contributions. The proposed approach is herein presented in the case of 2D vector fields (transverse electric polarization) but it can be easily extended to the general 3D case.

Keywords:

• array synthesis
• electromagnetic focusing
• convex programming
• multi-objective optimization

Notes

No potential conflict of interest was reported by the authors.

1 In particular, one can enforce that has to be larger than a value that guarantees an improvement of with respect to the current optimal solution. In the 2D TE case above, the condition would be where is the current optimal value for the objective function of problem (1). By so doing, a number of CP problems would become unfeasible, and one would not need to compute solutions that do not improve the final result.