An Electromagnetic Cloaking Scheme Using Magnetic Dipole Based Scattering Cancellation

: This paper explores the possibility of creating a cylindrical electromagnetic cloaking scheme using resonant magnetic dipole excitation. Split-ring resonators are arranged around the cylindrical metal target to generate strong subwavelength resonant magnetic dipole moments to cancel far-field scattered power from the target. We used the multipole scattering theory to identify the actual reason behind scattering cancellation. The scattering from resonant circulating magnetic dipoles interferes destructively with that from the non-resonant electric dipole moments of the target resulting in a significant reduction in the Scattering Cross Section. The results are verified using full-wave simulation software and subsequently validated with backscattering measurements inside an anechoic chamber.


Introduction
The experimental realization of the electromagnetic invisibility cloaking scheme has attracted much research interest recently. The term cloaking refers to the significant reduction of scattering from reference metallic or dielectric targets. Mathematically, it refers to the effective reduction of the Scattering Cross Section (SCS) of the target, including the incident direction and all directions prone to scattering. The undetectability of the target finds applications in the area of sensors, Radars etc. It is a well-known fact that when the electric and magnetic dipoles induced on the sub-wavelength dielectric sphere oscillate out-of-phase, then the SCS of the composite will be significantly reduced [1]. This conclusion is known as Kerker's paradox, and a wide variety of studies are available on this particular research topic [2]. The problem with this scheme is the unavailability of natural magnetic materials used to create magnetic dipole moments at microwave frequencies. Artificial magnetic inclusions of circulating current loops are the right choice for obtaining magnetic polarizability in such a situation. However, such a closed metallic ring's diamagnetic susceptibility is too small to cause negative permeability [3].
The polarizability of the ring could be significantly enhanced by loading the loop with a capacitor [4]. Loading the capacitor creates resonance, and the modified polarizability could be written as It is clear from the equation that frequencies lying just above the resonant frequency exhibits negative permeability. In the microwave regime, the best option to implement the capacitive effect is to load a slit instead of using the lumped capacitor. Using this idea, J.B Pendry et al. showed that the Split-Ring Resonators (SRR) made of concentric metallic split rings could achieve artificial magnetism at microwave frequencies [5]. This invention is treated as a paradigm shift in electromagnetics because we could control the amplitude and phase of electric and magnetic moments individually to achieve unprecedented control over electromagnetic scattering.
J.B Proposed the practical demonstration of a cloaking scheme to make a copper cylinder invisible using single split-ring resonator metamaterials [6]. The combination of the target and the metamaterial creates an electromagnetic environment similar to space. Scattering cancellation-based cloaking is also implemented using plasmonic covers over dielectric objects [7]. The dielectric target's scattered field is canceled in plasmonic cloaking due to the anti-phase scattering from the negative permittivity outer layer. The mantle cloaking technique is used to cloak both the dielectric and metallic targets, and its basic idea relies on tuning the surface reactance of the FSS layer to cancel far-field scattering [8]. Recently, Fano resonance-based scattering cancellation techniques have attracted significant research interest [9]. Fano resonance arises due to the destructive interference between the bright resonant mode of the continuum and the dark asymmetric resonant mode. It is worth mentioning that the magnetic dipole transitions are approximated to be 10 5 times weaker than the corresponding electric dipole transition, and hence the optical frequency regime is said as a world of pure electric dipoles [10]. So the creation of Fano resonance is an excellent choice to excite strong magnetic dipole excitation in the visible regime [11]. The intense excitation of magnetic dipoles is used for electromagnetic cloaking in the microwave regime [12].
The authors proposed electromagnetic cloaking schemes using dogbone-shaped metallic particles [13][14]. Here, we propose another cylindrical cloaking scheme by arranging SRR particles around a cylindrical metallic target. The arrangement of SRR around the target excites the magnetic dipole resonance, and the scattering caused by them destructively interferes with that from the non-resonant electric dipole moment of the target to make the target invisible. We used the multipole scattering theory to validate the reason behind the scattering reduction.
Experiments are performed inside an anechoic using the Anritsu MS2027C Network analyzer to validate the full-wave simulation results.

Geometrical Description
For experimental and simulation studies, we constructed three prototypes. The first one, The dimensions of the SRR used are r = 6.7 mm, d = 2 mm, s = 0.8 mm, w = 1 mm, h = 1.6 mm, and p1 = p2 = 20 mm.

Simulation Results
We performed full-wave simulation studies on the three prototypes using CST Microwave Studio. The three structures are analyzed independently in the simulation by exciting the complete structure with a plane wave. The polarization of the plane wave is oriented along the Y-axis. The computed Scattering Cross Section (SCS) of the three structures are illustrated in fig. 2. The scattering dip for case 1 is observed at 2GHz, and it shows comparable scattering characteristics to the uncloaked metallic target. Case 2 reduces the SCS of the target significantly, and a well-defined resonant scattering reduction is observed. Case 2 shows a maximum scattering reduction at 1.9 GHz. Due to the increase in the mutual coupling between the SRR elements, a significant redshift is observed for case 3. The resonance is observed to be 5 at 1.6 GHz for this design and since this design shows the maximum scattering reduction, it is taken as the optmum design.

Fig.2 Scattering Cross Sections of the three prototypes
To understand the cloaking operation, the field distributions are studied for the cloaked and uncloaked target. Fig. 3 shows the simulated field distributions on the uncloaked target under consideration. One could observe from fig. 3(a) that the uncloaked cylinder blocks electromagnetic power flow, and a shadow is observed behind the target.

Fig. 3 Results of numerical simulation for the uncloaked target at 1.6 GHz a) Electric field distribution from the YZ plane and b) Pointing vector distribution from the XZ plane
The significant perturbation of electromagnetic power is also evident from the Pointing power distribution shown in fig. 3(b). excitation is responsible for this scattering mechanism, and hence the target is detectable from far-field scattering measurements. Fig. 5(b) shows the scattering pattern of the cloaked target (Case 3). A significant reduction in scattered power is observed at the far-field around the target.

Experimental Results
The scattering characteristics of the three prototypes are verified using backscattering measurements using a network analyzer. To measure backscattering, the uncloaked target is placed at the center of a turntable assembly. Two ultra-wideband antennas are utilized for the measurement. One antenna is configured in the transmission mode and the second one in the reception mode. A THRU calibration is performed by connecting the two RF cables, and Frequency Gated by Time (FGT) calibration is applied to notch out unwanted noise signals received from other directions. The resultant received power is taken as the reference, and finally, the cloaked target is placed instead of the bare metallic cylinder target. The backscattered power thus received is recorded using the interface computer. For bistatic measurements, the receiving horn antenna is rotated along the azimuth angle using the turntable assembly, and the corresponding backscattered powers are recorded for the three fabricated prototypes. Since the eight-layer structure (case 3) is showing a better reduction in backscattered power, it is taken as the optimum design. Fig. 5 shows the backscattered power from the fabricated designs.. Fig. 5(a) shows the backscattered power from the two-layer (Case1) design. It is evident that the design shows poor backscattering characteristics compared to the other two designs. For this case, the backscattered power is comparable in magnitude for most of the azimuth angle as that of the bare metallic target. It is interesting to note that as the number of SRR layers around the target increases, the backscattered power is decreased, as shown in fig. 5(b) and (c). Case 2 shows better backscattering characteristics compared to case 1. A significant reduction in backscattering is observed for the eight-layer design (Case 3) compared to the other two designs. A maximum backscattering reduction of the order of -16 dB is observed for this design. We have also performed the monostatic scattering measurements to compare the scattering performance of the three fabricated prototypes. In monostatic measurements, the power received from the uncloaked target located at the turntable assembly center is taken as the reference after performing the FGT calibration. The cloaked target is rotated along the azimuth plane while two UWB antennas are kept fixed. The received power thus obtained is plotted in fig. 6 for the three configurations under study. It is evident from the graph that the eight-layer configuration (case 3) gives a better backscattering reduction for all azimuth rotations of the target. It is also noted that the two-layer (case 1) and four-layer (case 2) structures also exhibit scattering reduction compared to a bare metallic target.

Discussions
To clarify the reason behind this peculiar scattering behavior, multipole scattering theory has been utilized to retrieve the structure's resonant mechanism [15]. The multipolar decomposition provides an in-depth description of the scattering properties of the composite due to the induced charge-current distributions. Scattered power from the induced multipoles could be calculated by integrating spatially distributed current distributions of the unit cell. The multipole amplitudes can be calculated as where P is the electric dipole moment, M is the magnetic dipole moment, T is the toroidal moment, c is the velocity of light in vacuum, → is the displacement vector from the origin, ⍵ is the angular frequency, and J is the surface current density retrieved from simulations. The total power radiated from different multipole moments can be formulated as scattering. The SCS of the composite is significantly higher than the uncloaked target at this frequency. At this frequency point, the toroidal moment shows a hike even though its magnitude is weak. It is noted that the scattering reduction from frequency lies at a lower spectral range of around 1.6 GHz in comparison with the magnetic resonance of the SRR. The specialty is that the power radiated from the toroidal and electric dipole moments at this frequency shows a significant dip, and the magnetic dipole moment is significantly higher. So it can be concluded that the scattering reduction arises from the destructive interference from the electric and magnetic dipole moments at the far-field.

Conclusions
The experimental realization of the cylindrical electromagnetic cloaking scheme using resonant magnetic dipole excitation in the microwave regime is studied and presented in this paper. The Split-Ring resonators arranged around the cylindrical metallic target excites strong magnetic dipole moments, and the scattering from these magnetic dipole moments destructively interferes at the far-field resulting in a reduction in the Scattering Cross Section of the target.
These results are verified using the multiple scattering theory and experimentally verified in the microwave regime inside an anechoic chamber.

Methods
The simulation studies of the proposed designs are performed in the frequency domain using the commercially available CST Microwave Studio. The complete structure is illuminated with a plane wave with polarization parallel to the axis of the metallic target to study the scattering characteristics. In order to increase the accuracy of computations, adaptive mesh refinement is used. Field monitors are used to extract the electrical currents excited on the composite, and mathematical computations are performed on these retrieved current distributions using the GNU Octave software to calculate the power radiated from different multipoles.