Controlling static magnetic fields with positive and negative permeability metamaterials

Abstract

Magnetism is present in our daily life – it is found at the basis of technologies such as electric generators and transformers, data storage systems, sensors, and biomedical equipment – and it is usually controlled by ferromagnetic materials. Recently, the introduction of magnetic metamaterials and the transformation optics technique has enabled the development of a wide range of devices for controlling magnetic fields, offering possibilities beyond those of conventional magnetic materials. In this thesis, we apply these concepts to propose different strategies for controlling static magnetic fields in novel ways. First, we review and study in detail the interaction of static magnetic fields with conventional materials with extremely large (ferromagnets) and extremely low (perfect diamagnets) magnetic permeability. Results show that there are some properties of materials with permeability close to zero that remain yet to be exploited, such as the possibility of overlapping the field created by wires located in different positions as if they had all been placed at the same point. Then, we explore the properties of different metamaterials with positive permeability, which consist of arrangements of ferromagnetic or perfect diamagnetic materials or combinations of both. We demonstrate that extremely anisotropic two-dimensional and three-dimensional shells with extremely large radial permeability and extremely low angular permeability can achieve strong magnetic field concentrations inside their holes without distorting externally applied magnetic fields. This could be used to enhance the sensitivity of magnetic sensors. For the case of a spherical concentrator, results are confirmed experimentally. These shells are also shown to expel towards their exterior the magnetic field generated inside their hole. Interestingly, these properties can be applied to effectively enlarge magnetic materials; a magnetic material surrounded by a concentrating shell responds to the applied magnetic field as if it was a larger material. Finally, we present a different metamaterial device which can make a magnetic sensor undetectable. In this way, the sensor would detect the applied field without being detected, which is interesting for applications requiring non-invasive sensing. In the last part of the thesis, we introduce the concept of negative permeability for static magnetic fields. We theoretically and experimentally demonstrate that, even though materials with negative permeability do not naturally occur, they can be emulated in practice by suitably tailored arrangements of currents, which constitute an active metamaterial. We propose two applications of negative permeability in magnetostatics: magnetic illusion and perfect magnetic lensing. On the one hand, we show that negative permeability enables the transformation of the magnetic signature of an object into that of another one. The experimental transformation of a ferromagnetic sphere into a perfect diamagnetic sphere confirms the theoretical ideas. On the other hand, we demonstrate that a cylindrical shell with permeability -1 behaves as the analogous of a perfect lens for static magnetic fields and can be used to create images of magnetic sources. Since the images may appear in empty space, this shell could enable the creation and cancellation of magnetic sources remotely, something unachievable with positive permeability. To sum up, in this thesis we propose different strategies for shaping, controlling and even for creating static magnetic fields based on positive and negative permeability metamaterials.