Long-Distance Transfer and Routing of Static Magnetic Fields

We show how the static magnetic field of a finite source can be transferred and routed to arbitrary long distances. This is achieved by using transformation optics, which results in a device made of a material with a highly anisotropic magnetic permeability. We show that a simplified version of the device, made by a superconducting-ferromagnet hybrid, also leads to an excellent transfer of the magnetic field. The latter is demonstrated with a proof-of-principle experiment where a ferromagnet tube coated with a superconductor improves the transfer of static magnetic fields with respect to conventional methods by a 400% factor over distances of 14 cm.

Figure 1

The maximum field at a distance $d$ of the top surface $B_z(z=2d+L)$, normalized to the maximum field of the isolated dipole at a distance $2d$, $B_z^{\mathrm{DIP}}(z=2d)$, is plotted for an ideal FM cylinder (middle green line), an ideal SC tube (lower blue line), and a bilayer magnetic hose (upper red line), when a dipolar source is placed at a distance $d$ below them as a function of the cylinder lengths $L$. In the inset, sketches of the three cases are shown, with the FM in orange and the SC in gray. In all these calculations the radius of the FM cylinder is $r=0.8d$ and the thickness of the SC tube $w=0.5d$.

Figure 2

The field of a magnetic source, e.g., a point dipole (a) (field lines in white and vertical field $B_z$ in colors), is exactly transferred to an arbitrary distance, (b), through an infinite slab of ideal material (shaded region) having ${\mu }_{\parallel }=\infty$ along the thickness and ${\mu }_{\perp }=0$ along the width. (c) Maximum vertical field at a distance $d$ above a magnetic hose made of the ideal material, when a vertical dipole is placed at a distance $d$ below the hose, as a function of the radius $R$. The field is normalized to the maximum field created by an isolated dipole at a vertical distance $2d$, $B_z^{\mathrm{DIP}}(z=2d)$. Different hoses of length $L=2d$, $4d$ and $10d$ are plotted (from top to bottom).

Figure 3

Maximum field transferred by hoses discretized into different number of layers $n$. A point dipole is placed at a distance $d$ below the bottom end and the field is calculated at a distance $d$ above the top. SC and FM layers have all the same thickness, as shown in the insets (FM in light orange and SC in gray). The field transferred by an ideal hose with the same geometry is plotted with a blue dashed line. The total radius of the hose is $R=2d$ and its length $L=4d$.

Figure 4

Vertical field component $B_z$ (in color scale) in the middle plane of different 3D geometries. The field source is a point dipole (sketched in white) placed at a vertical distance $d$ from the hoses. The FM cylindrical core (light orange) has a radius $r=0.5d$ and the surrounding SC (gray) a thickness $w=0.75d$. In each simulation the average output field ${\overline{B}}_z$ is calculated as the quotient between the flux that exits each hose end and the area of the ferromagnetic section and normalized to the maximum vertical field created by an isolated dipole at a distance $d$, $B_z^{\mathrm{DIP}}(z=d)$. Analytical and numerical values of ${\overline{B}}_z$ fully agree for the closed hose (b). Case (c) shows a hose divided into two branches; when one of its ends is closed with the SC, (d), we recover the case of a hose with a single branch (a). See Sec. VI of the Supplemental Material [21] for further discussions of the results.

Figure 5

Pictures of the construction of the experimental devices (of length 60 mm): (a) the FM cylinder, (b) the SC shell wrapped around a plastic former, and (c) the $\mathrm{SC}+\mathrm{FM}$ bilayer magnetic hose. (d) Measured transferred magnetic field at one end of cylinders of length 60 and 140 mm. At the other end the field source is a coil fed with 1 A direct current (see the sketches below). Three cases are measured: SC only, FM only, and the $\mathrm{SC}+\mathrm{FM}$ bilayer magnetic hose. Lines are calculated results for the field of the bare coil (purple curve) and that transferred by the FM only (green).