Static Magnetic Cloak without a Superconductor

Similar to its electromagnetic counterpart, magnetic cloaking also has very important technological applications. However, the traditional method to build a static magnetic cloak requires the use of superconducting materials as the diamagnetic component, which seriously limits the practical potential because of the cryogenic condition. We show that a diamagnetic active current boundary combined with a high-permeability magnetic inner shell (MIS) can be designed to solve this problem, rendering an ideal magnetic cloaking effect at zero frequency. We first theoretically prove that a current boundary could magnetically behave as a superconductor to external observers. Based on this phenomena, we introduce a high-permeability MIS made of magnetically ultrasoft metallic sheets (permeability $\mu >{10}^3$) and experimentally prove that the bilayer combination can exactly balance out the disturbance to the external probing field and, meanwhile, have a large invisible inner space. We also show that the active boundary currents can be accordingly configured to overcome the permeability and frequency band limits, leading to a robust cloak over the entire quasistatic frequency region. Our work creates an efficient way to circumvent the traditional limits of metamaterials to build magnetic cloaks for ultralow frequencies. The active-passive hybrid approach could be generally extended to yield other artificial magnetic devices or systems as well.

Figure 1

Active diamagnetic response. (a) Schematic of the SC (left image) and ACB (right image) models. The black dashed circle of radius $R_2$ denotes the boundary where we solve Eq. (2). (b),(c) The magnetic-field distribution scattered by the SC cylinder and generated by the ACB, respectively. The external field ${\mathbf{H}}_0$ is assumed along the $x$-axis direction. (d) The relative magnitude $\eta$ calculated along the dashed straight line in (b) and (c). (Inset) The ACB’s current values in the first quadrant. The rest can be obtained using structural symmetry.

Figure 2

Active static magnetic cloak. (a) Schematic of the sample model, consisting of a cylindrical high-$\mu$ MIS and a surrounding ACB. (b),(c) The magnetic-field distribution scattered by the MIS ($\mu =3000$) and generated by the ACB, respectively. In the former case, only the external field ${\mathbf{H}}_{\mathrm{ext}}$ is excited, while only the active current ${\mathbf{H}}_{\mathrm{cur}}$ is turned on in the latter case. (d) The total magnetic-field distribution when both ${\mathbf{H}}_{\mathrm{ext}}$ and ${\mathbf{H}}_{\mathrm{cur}}$ are turned on.

Figure 3

Pictures of the (a) sample and (b) measurement setup. For the sample, we roll the commercial magnetic tape around the Teflon cylinder with a radius of 19.1 mm and a length of 120 mm. The current copper wires are uniformly distributed around the cylindrical surface with the help of Kapton tape. The $x$ component of the magnetic field is scanned along one straight line at $x=-R_2$ in the $y\text{−}z$ plane, which is 5 mm above the sample. High reproducibility of the measurement data is guaranteed by utilizing a programmed step motor to move the probe.

Figure 4

Measured field disturbance dependent on the applied field strength. The relative magnitude $\eta$ at the point ($R_2$, 0) is measured when only the external field (the red squares), only the active current (the blue dots), and both sources (the black triangles) are turned on. The green rhombuses give the penetrated field strength $|{\mathbf{H}}_x|$ measured at the center point (0, 0). The horizontal axis is the magnitude of the external field ${\mathbf{H}}_0$, whose value is finally limited by the maximum active currents we can experimentally apply. The field measurement error is $\pm 0.02\mathrm{Oe}$.

Figure 5

Spatial field disturbance. The relative magnitude along the line $x=R_2$ is (a) measured and (b) simulated for the three different cases described in Fig. 4. (Insets) Enlarged expressions for the curve (${\mathbf{H}}_{\mathrm{ext}}$ and ${\mathbf{H}}_{\mathrm{cur}}$) with both sources excited. The field measurement error is $\pm 0.02\mathrm{Oe}$.

Figure 6

Active magnetic cloaking for imperfect MIS or dynamic frequencies. (a) The relative magnitude is scanned along the line $x=R_2$ for samples composed of an infinite (the red line), and a 500-permeability (blue line) MIS with the ACB obtained assuming a PMC inner shell (the original case) and also a 500-permeability MIS (circled black), but with an adjusted ACB. (b) The relative magnitude varies with the permeability value of a triangular inner object introduced in the cloaking region, as shown in the inset. The ACB currents in the first quadrant are plotted with a PMC (red) and a 500-permeability (blue) MIS. (c) The active current values in the first and fourth quadrants used in the dynamic cases are zero frequency (red), 100 Hz (blue), and 10 kHz (black). The MIS has a constant permeability, $\mu =2500$. (d) The magnetic-field distribution for the hybrid sample (left) without and (right) with the ACB applied at 10 kHz.