The geometry of the structure

The unit-cell structure is a modification of our previous work [Reference Sarin, Vinesh, Manoj, Aanandan, Mohanan and Vasudevan16], and the main difference is that it is devoid of the enclosed metallic cylindrical target, as shown in Fig. 1. All the other parameters remain the same. Eight dogbone metallic elements, printed on a substrate of dielectric constant 4.4 and height 1.6 mm, are arranged in a coaxial fashion, as depicted in Fig. 1(a). Figure 1(b) shows the top view of the structure. The inner diameter d is selected to be 14.5 mm. Figure 1(c) illustrates the unit-cell dimensions. We have used photolithographic etching techniques for fabrication, and the engraved copper thickness is 35 μm. The final full design used for measurement utilizes five such unit cells arranged vertically, as shown in Fig. 1(d).

Fig. 1. Description of the structure under study. (a) Formation of the unit cell, (b) top view, (c) geometrical specifications (L ₁ = 18 mm, L ₂ = 12 mm, W ₁ = 4 mm, W ₂ = 2 mm, d = 14.5 mm), and (d) photograph of the fabricated structure.

Simulation and measurement studies

We have used CST Microwave Studio for full-wave simulation studies of the structure. For that, a plane wave with polarization along y-axis is incident on the full structure shown in Fig. 1(d). Reflectance from the design is measured using a monostatic scattering measurement setup for normal incidence. For that, two ultra wideband antennas, with an azimuth offset of 5°, are mounted on a turntable assembly. We placed a metallic cylinder at the turntable assembly center for performing a THRU calibration. To avoid possible multipath clutters, proper time gating is applied to receive reflections only from the target. Replacing the reference target with the studied structure gives the design's reflectance, as depicted in Fig. 2, and is well matched. The observed resonance is around 2 GHz, and it indicates strong backscattering suppression at resonance.

Fig. 2. Reflection coefficient of the proposed structure.

The far-field scattering characteristics are studied using full-wave simulations and shown in Fig. 3. The scattering cross-section thus obtained for the structure compared with a metallic plane target is shown in Fig. 3(a). Around resonance, the design shows tremendous enhancement in scattered power as that of the bare metallic cylinder. Figures 3(b) and 3(c) compare the 3D scattering characteristics of both these structures. The cylindrical reference target shows omni-directional scattering, whereas the proposed structure scatters more power along the forward direction. Figures 3(d) and 3(e) represent the scattering patterns along the azimuth and elevation planes. It shows coherent forward scattering in both these planes. The 3 dB beamwidth is 57.6° and 111°, respectively, in these planes.

Fig. 3. Results of scattering studies performed. (a) Scattering cross-sections, (b) 3D scattering pattern of a bare metallic cylinder, (c) 3D scattering pattern of the proposed dogbone array, (d) azimuth plane RCS patterns, and (e) elevation plane RCS patterns.

Multipole scattering theory helps to study the scattering contribution from different multipoles [Reference Kaelberer, Fedotov, Papasimakis, Tsai and Zheludev9]. The power scattered from different multipoles is found by extracting the surface current distributions from the structure and then performing spatial integration as

(1)$$P = \displaystyle{1 \over {i\omega }}\int {Jd^3r} , \;$$

(2)$$M = \displaystyle{1 \over {2c}}\int {(\vec{r}XJ)} d^3r,$$

(3)$$T = \displaystyle{1 \over {10c}}\int {[ ( \vec{r}.J) -2r^2J] } d^3r.$$

The results of these computations give scattered power from different multipoles. In the above equations, P and M represent the lower order electric, magnetic dipole moments, T represents the higher-order Toroidal dipole moment, c is the velocity of light in vacuum, $\vec{r}$ is the displacement vector from the origin, ω is the angular frequency, and J is the surface current density.

Figure 4 illustrates the radiated power contribution from the P_y (electric), M_x (magnetic), and T_y (toroidal) moments. One could see here that power released from the magnetic dipole moment (black line) exceeds that from electric dipole moment P_y (redline) throughout the entire bandwidth under consideration. The power radiated from the magnetic moment M_x is 7000 times higher than that from the electric moment P_y at resonance. The radiated power contribution from the toroidal moment T_y is also indicated in the figure using a solid blueline. We could observe that power radiated from the toroidal moment is significantly high from this structure compared to our previous design [Reference Sarin, Vinesh, Manoj, Aanandan, Mohanan and Vasudevan16]. The excitation of toroidal mode is responsible for coherent forward scattering from it at normal incidence.

Fig. 4. Radiation contribution from different multipoles.

The cross-sectional magnetic field distributions are useful in studying the excitation of toroidal moments on the structure. Figure 5 shows the resonant surface current and the cross-sectional magnetic fields excited on the cell. Figure 5(a) confirms that the surface currents excited on the structure's input entrance and output faces are out of phase. These antiparallel current distributions create out-of-phase magnetic moments, creating strong in-phase magnetic field distribution at the center of the structure, causing toroidal moments T_y, as depicted in Fig. 5(b). The out-of-phase circulation of surface currents on the structure's input and output faces cancels the contribution of electric dipole moment P_y on far-field radiation. The unit-cell system will act as an efficient dielectric sensor because the enhanced magnetic energy density at the center of the structure enhances the sensor's sensitivity due to toroidal excitation. Figure 5(c) illustrates the computed cross-sectional electric field distribution at resonance. The electric field is concentrated on the top and bottom boundaries of the dogbone particle and is found minimum at the center where the magnetic field is maximum.

Fig. 5. Resonant field distributions on the structure. (a) Computed current distribution, (b) cross-sectional view of the magnetic field, and (c) electric field distributions.

To study the effect of the inner diameter on reflection coefficient, we performed a detailed parametric analysis because this inner diameter significantly affects the coupling between dogbone metal strips. Figure 6 illustrates the effect of variation on reflection coefficient for normal incidence. An increase in the diameter of the cell redshifts the resonant frequency. The inner diameter increases the magnetic resonant patch length due to the significant increase in displacement current channel. Moreover, this change causes an increase in reflection from the structure, and the system becomes more inductive due to the enhancement in the mutual inductance between consecutive dogbone elements.

Fig. 6. Effect of inner diameter on reflection coefficient for normal incidence.

We performed the scattering measurements inside an anechoic chamber, and Fig. 7 illustrates these results. For that, the same methodology adopted for cloaking measurements is used [Reference Sarin, Jayakrishnan, Vinesh, Aanandan, Mohanan and Vasudevan21]. Figure 7(a) shows the monostatic backscattered power from the structure for normal incidence. In this measurement, we rotated the design in the azimuth plane and recorded the received power. Measurements show that more than −20 dB reduction in backscattered power is observed for all the azimuth angles at resonance. The polar plot of monostatic backscattered power at resonance shown in Fig. 7(b) verifies this observation. Figure 7(c) illustrates the measured bistatic radar cross section (RCS). A significant reduction in backscattered power better than −7.1 dB is observed in comparison with the reference cylinder.

Fig. 7. Results of RCS measurements. (a) Monostatic measurements, (b) polar plot of monostatic backscattered power, and (c) bistatic measurements.