Dimensional Crossover of Microscopic Magnetic Metasurfaces for Magnetic Field Amplification

TL;DR

This study explores how reducing the size of magnetic metasurfaces affects their ability to concentrate magnetic fields, revealing non-monotonic behavior and the roles of diamagnetic and paramagnetic components in low-dimensional structures.

Contribution

It provides the first detailed numerical and experimental analysis of magnetic field concentrators as their dimensions are scaled down, establishing design guidelines for low-dimensional magnetic devices.

Findings

Paramagnetic elements enhance magnetic channeling efficiency in thin structures.

Diamagnetic petals reduce stray fields and improve invisibility at certain thicknesses.

Experimental validation through superconductor-ferromagnet concentrators.

Abstract

Transformation optics applied to low frequency magnetic systems has been recently implemented to design magnetic field concentrators and cloaks with superior performance. Although this achievement has been amply demonstrated theoretically and experimentally in bulk 3D macrostructures, the performance of these devices at low dimensions remains an open question. In this work, we numerically investigate the non-monotonic evolution of the gain of a magnetic metamaterial field concentrator as the axial dimension is progressively shrunk. In particular, we show that in planar structures the role played by the diamagnetic components becomes negligible, whereas the paramagnetic elements increase their magnetic field channeling efficiency. This is further demonstrated experimentally by tracking the gain of superconductor-ferromagnet concentrators through the superconducting transition. Interestingly, for thicknesses where the diamagnetic petals play an important role for the concentration gain, they also help to reduce the stray field of the concentrator, thus limiting the perturbation of the external field (invisibility). Our findings establish a roadmap and set clear geometrical limits for designing low dimensional magnetic field concentrators.