Exploring the limits of magnetic field focusing: Simple planar geometries

Abstract This work explores the possibility to arbitrarily shape in space low-frequency magnetic fields using a recently introduced synthesization technique (Choi et al., 2016). We investigate the ability to focus a magnetic field on a two-dimensional region using magnetic field sources distributed on a parallel plane. In agreement with the recent work, arbitrarily tight focusing is demonstrated possible. However, our results indicate that this comes at the cost of exponentially large power requirements and also leads to exponentially large fields in the region between the source and target planes. This imposes strict limitations on the application of the technique. In addition, we also demonstrate that arbitrary steering of the magnetic field focus within the target region is possible, without any additional cost in terms of power requirement. In exploring the potential for magnetic field synthesis, our findings highlight limits to be considered for practical applications, as well as promising capabilities not identified before.