We propose a tunable strategy for the ultrathin mantle cloak via metasurface. The tunable cloak is implemented by loading varactor diodes between two neighboring horizontal metallic strips which constitute the metasurface. We demonstrate that the varactor diodes enable the capacitive reactance of the metasurface to be tunable from −157 Ω to −3 Ω when the DC bias voltage is properly changed. The active metasurface is then explored to cloak conformally a conducting cylinder. Both numerical and experiment results show that the cloaking frequency can be continuously controlled from 2.3 GHz to 3.7 GHz by appropriately adjusting the bias voltage. The flexible tunability and good cloaking performance are further examined by the measured field distributions. The advanced features of tunability, low profile, and conformal ability of the ultrathin cloak pave the way for practical applications of cloaking devices.
© 2014 Optical Society of America
Over the last decade, with the fast developments and growing applications of metamaterials, cloaking has been one of the most fascinating topics in physics and material science [1–18]. Numerous techniques have been proposed to suppress or divert the scattering of objects in the frequency range from the microwave [5, 6, 8, 10, 11, 13, 19] to optical and terahertz regimes [20–27] to reach the cloaking effects. One of the most successful approaches is the transformation optics (TO) proposed by Pendry et al.  and Leonhardt , which is implemented by utilizing volumetric metamaterials with specific inhomogeneous and anisotropic material parameters. In this frame, the TO-based cloak enables the electromagnetic (EM) waves propagate around the object smoothly. However, due to the challenging in realizing the bulk metamaterials based on the currently available technologies, it is hard to realize the required anisotropic and inhomogeneous profiles precisely for the TO-based cloaking techniques. In addition, the cloak in this scenario also requires an overall thickness that is comparable with or larger than the size of target to be cloaked, which further limits its popularization in the real applications [28, 29].
Recently, to reduce the limitation of cloaks based on bulk metamaterials, an alternative approach to realize EM cloaking has emerged . The ultrathin mantle cloaking, proposed by Alù in 2009, is a scattering cancellation technique based on the “anti-phase” scattering fields radiated by an ultrathin metasurface. The so-called anti-phase response will cancel out the scattering fields radiated by the object to be cloaked and the outer cloak, and thus make the cloak as a destructive interference. By carefully synthesizing the effective surface impedance of the metasurface with proper metallic patterns, mantle cloaks with small thickness and moderate bandwidth were realized [31–33]. More recently, another ultrathin cloaking strategy has been reported based on the concept of single-layered microwave network which can be engineered with desirable cloaking performances for an electrically large conducting cylinder (greater than one wavelength in free space) . Although the cloak works in a narrow bandwidth, the ultrathin profile further simplifies the manufacture process, and thus enables competitive candidate for the conformal cloaking technique. These ultrathin cloaking techniques are different from the ideal TO-based cloaking, in which the region to be cloaked is completely isolated from outside. Instead, the EM wave can penetrate the mantle cloaks [35, 36]. Under this circumstance, a sensor placed inside the cloak may be able to detect the impinging signal without disturbing the environment outside, opening the possibility to noninvasive probing and low-interference communication. However, all such cloaks can only work in single frequency band and the cloaking effects cannot be tuned. To the best of our knowledge, tunable invisibility cloaks (either TO-based or mantle) have not been reported.
In this work, we present the first design and experimental realization of frequency- tunable ultrathin cloak for a conducting cylinder. By employing varactor diodes to a single-layered ultrathin metasurface formed by horizontally capacitive metallic strips, a wide range of tunability can be achieved. Then the required average surface reactance is generally determined from the theoretical analysis and optimized by numerical simulations of a real 3D model. Both the scattering cancellation and the frequency-tunable characteristics are numerically examined and experimentally verified from 2 to 4 GHz by far-field bistatic scattering measurements with a pair of double-ridge horn antennas. To further show the cloaking performance, the restoration of the incident wavefront around the cloak is examined by the near-field measurements.
2. The cloak design and fabrication
We focus our design on reducing the total scattering cross section (SCS) of a conducting cylinder with length L = 186 mm and radius a = 10 mm from 2 GHz to 4 GHz, as shown Fig. 1. Based on the previous studies on mantle cloaks , we know that a cylindrical cover with capacitive reactance may be tailored to suppress the scattering term significantly, which is the dominant term of an electrically small conducting cylinder. Even though the mantle cloak could be arbitrarily thin, there must be a gap between the cloak and the conducting cylinder to avoid any electrical connection. In the current design, a moderate cloak radius of ac = 1.25a (corresponding to a gap of 2.5 mm) is chosen by taking into account the tolerances during fabrication and assemble processes.
Figure 1 depicts the topology of the cloaking system consisting of a conducting cylinder with radius in the free space and an ultrathin metasurface illuminated by a monochromatic transverse-magnetic (TM) plane wave under the time convention. Since the transverse scale of the object is in deep sub-wavelength, it can be modeled as an isotropic and homogenous averaged surface impedance , which associates the averaged tangential electric field at the surface with the averaged induced surface current as: , where is induced by the discontinuity of tangential magnetic fields at the metasurface. For simplicity, the metascreen is assumed to be lossless and dispersionless. Therefore, the equivalent surface impedance of the metasurface reduces to a purely reactive quantity .
For the geometry given above, the incident and scattered electric fields can be represented by Mie expansions in the cylindrical harmonics Eqs. (5) and (6), and are the wave number and wave impedance outside the cloak, whereas and are in the region between the cloak and the conducting cylinder. The derivatives in Eqs. (5) and (6) are with respect to the arguments of and .
For an electrically small conducting cylinder, the higher-order terms (n>0) are much smaller than and thus can be neglected in the cloak design. Let , we can nullify the dominant scattering at the desired frequency. For the configuration of the cloak shown in Fig. 1, the required surface reactance can be analytically calculated by equaling Eq. (8) to zero, which is between −22 Ω and −113 Ω from 1 GHz to 5 GHz. Although these analytically calculated surface reactances of the unit cell deviate slightly from those required by the ideal scattering reduction of the entire cloaking model, they unambiguously function as initial guidance for the following numerical simulations and can be further adjusted for an exact design.
The detailed geometrical parameters of the unit cell are shown in Fig. 1(c), in which the width (w), height (h) and gap (g) of the capacitive strips are 15.7 mm, 12.5 mm, and 1.5 mm, respectively. The thickness of the copper layer and substrate layer (dielectric constant ε = 3.4 and loss tangent δ = 0.002) is 70 μm and 25 μm, respectively. The horizontal cross section of the designed cloak in the azimuthal plane consists of five unit cells which wrap around the cylinder conformally. This structure appears to be capacitive when it is illuminated by a TM-polarized plane wave at the normal incidence. The variable capacitive reactance of the metallic metasurface can be realized by inserting a varactor diode in the gap. Thereby, the surface reactance is able to be tuned within a desired range by controlling the capacitance of the varactor diode. The surface impedance of the unit cell can be analytically calculated from the S-parameters obtained by the full-wave simulation software, the CST Microwave Studio, with the following formula 
Figure 2 shows the extracted surface reactance for different capacitances of the varactor diode. We clearly see that the surface reactance grows gradually with both of the frequency and capacitance of the varactor diode. The surface reactance ranges from −157 Ω to −3 Ω when the frequency changes from 1 GHz to 5GHz, which completely covers the required range calculated by letting Eq. (3) be zero, and thus sufficiently fulfills the cloaking requirement. Since the real parts of the impedance are much smaller (less than 0.5 Ω) than the imaginary parts, they can be neglected in the design of mantle cloak and are not shown here for brevity of contents. It should be noted that the actual curved surface impedance may not be exactly the same as that extracted from the planar configuration. However, since the unit cells in our design are in deep sub-wavelength and there is no curvature along the polarization direction, the analytical expression in Eq. (3) may still hold with good accuracy.
The corresponding cylindrical mantle cloak were manufactured using the standard printed circuit board (PCB) fabrication process on a three-layer flexible copper-clad laminate (FCCL), which is composed of a single layer of polyimide and an electrolytic copper-clad sheet connected with the epoxy adhesive. The thicknesses of polyimide, adhesive, and copper foil layers are 25, 12.5, and 70 μm, respectively, and thus the total film thickness is 107.5 μm. The fabricated sample is wrapped around a cylinder with diameter of 25 mm. The value range of capacitance corresponds to 0.31–1.24 pF, which is the typical tuning range of a SMV-1430 varactor diode from Skyworks Technologies. The varactor diodes are carefully soldered onto the corresponding position on the cloak, as shown in Fig. 3(a). We remark that the capacitance is inversely proportional to the applied DC bias voltage on the varactor diode. As will be demonstrated in the experiments, the increase of voltage will result in the decrease of the surface reactance, which finally leads to the shift of scattering dip towards the higher frequencies. The fabricated sample is ultrathin (the left panel) and flexible (the right panel) compared with the plasmonic and TO-based cloaks. As a consequence, they can be wrapped around curved surfaces (the middle panel), and thus be suited for the realization of conformal ultrathin cloaks for any object with arbitrary curvature.
Figures 3(b) and 3(c) show the spice model model of this this varactor diode and its effective LCR series resonant circuit (see Fig. 3(c)), respectively. By adjusting the voltage of the DC bias in the commercial software Advanced Design System 2008, we show in Table 1 the extracted effective circuit parameters of this varactor diode with different reverse bias voltages. It can be estimated from Table 1 that the losses (real parts) only account for a small proportion (from 0.83% to 5.7%) of its surface reactances (imaginary parts), which can be reasonably neglected in the following full wave simulations for simplicity.
3. Full-wave simulations of the cloak
To predict the performance of the proposed cloak, we perform full-wave simulations using the transient solver in CST for the realistic geometry as shown in Fig. 1(a). To be consistent with experiments, we set the thicknesses of the polyimide and copper layers to be 25 μm and 70 μm, respectively. Extensive numerical simulations indicate that the thin polyimide layer has little effect on the surface impedance. Therefore, the previous formulas are still valid in the impedance prediction of the metasurface in case of cloaking an electrically small cylinder. Open boundary conditions and a broadband far-field monitor with 10−4 accuracy are selected for the exact evaluation of the bistatic SCSs for the object with and without cloak. The TM-polarized (the electric vector is parallel to the cylinder axis) plane waves are incident along the x direction, as shown in Fig. 1(a).
By integrating the bi-static SCSs over all visible angles φ in the azimuthal plane, we obtain the simulated results of total SCSs for the uncloaked and cloaked objects. In order to characterize the invisibility of the tunable cloak directly, here we simply show the scattering gain, which is defined as the total SCS of the cloaked object normalized by that of the uncloaked object at the same frequency.
Figure 4(a) illustrates the variation of the total scattering gain with respect to the frequency at different bias voltages ranging from 0.5 to 23 V, which corresponds to different values of capacitance of the varactor diodes (see Table 1). We clearly observe that scattering suppressions from −3.8 dB and −6.8 dB are achieved over a moderate bandwidth. We also notice that the curve of the surface impedance required to nullify the term has negative dispersion with frequency, which implies that the required surface impedance decreases with respect to the increasement of frequency. Therefore, the scattering dip in Fig. 4 shifts towards higher frequencies when the capacitance of the varactor diode decreases (i.e. voltage increases), which is in terms of decreasing the surface reactance. We remark that the scattering dip at 23 V (corresponding to 0.367 pF) is broadened and is not as deep as those for lower voltages (i.e. larger capacitances). This may be due to the higher-order multipoles which contribute to the residual scattering. Simple theoretical simulations show that the first and second scattering terms takes dominate part (the third scattering terms is only 6% of the first one) of the SCSs of a conducting cylinder with diameter of 20 mm at 3.75 GHz and can be suppressed to about 39.8%, 70% of their original value by the designed metasuface with around −40 ohm surface reactance, respectively. Thus, it is estimated that the total SCSs can be lower to about 52% of that of the bare cylinder, which agrees with the simulated data of −3.8 dB (64%) at 3.75 GHz read from Fig. 4(a). This implies that the single-layer metasurface with horizontal metallic strips may be only valid for cloaking cylinders with small diameters. We believe that through the theoretical analyses and numerical optimizations for a multi-layer mantle cloak, it may be possible to suppress most higher-order multiploes for electrically large objects.
Figures 4(b)–4(e) further report the simulated results of the bistatic scattering gains at different bias voltages for different angles in the azimuthal plane at (b) θ = 30°, (c) θ = 90°, (d) θ = 150° and (e) θ = 180°, respectively. Similar with the total SCSs gain curves, all the scattering dips in Figs. 4(b)–4(d) also increase with the increasing of DC voltages, which is in terms of decreasing the surface reactance. It is interesting to note that the frequency of the bistatic scattering dips for a specific direction does not match with those observed in the total scattering dips in Fig. 4(a). This phenomenon can be more appropriate attribute to the non-ideal cloaking characteristic of this technique, which is not designed to suppress all the scattering multipoles of a conducting cylinder at a single frequency point. Therefore, the scattering dips for different directions will not simply appear at the same frequency point but around a certain frequency after integrating all of them over 360 degrees in the azimuthal plane.
To further visualize the cloaking effect, Fig. 5 depicts the simulated electric-field distributions in the azimuthal plane for the cylinders with and without cloak, respectively. These results are taken at the cloaking frequencies corresponding to the scattering dips shown in Fig. 4. The objects are illuminated by a plane wave traveling along the x-direction with electric field parallel to the z-axis for the three test scenarios given in Figs. 5(a)–5(c). In the presence of the cloak, as illustrated in Fig. 5(c), the phase fronts around the cylinder are nearly the same as those in free space (without cloak). In contrast, as shown in Fig. 5(b), strong scattering occurs for a bare conducting cylinder without cloak. Figures 5(d)–5(f) further demonstrate the electric-field distributions of the cylinder covered by the designed cloak with different capacitance values. As expected, good cloaking effects are achieved at the corresponding frequencies when the capacitance ranges from 0.367 pF to 1.284 pF. The near-field distributions prove that the proposed cloak has good performance within its tunable frequency range.
4. Measurement setup and analysis
We adopt the same bistatic-scattering measurement setup as that presented in . A pair of double-ridge broadband horn antennas with the voltage-standing-wave ratio (VSWR) less than 2 over a wide frequency range from 1 to 18 GHz to measure the electric fields scattered by the uncloaked and cloaked objects from various directions in the azimuthal plane. As shown in Fig. 6, the distances between the transmitting and receiving antennas to the object are maintained the same (R = 70 cm), while the angle between them is scanned from =30° to =180° in the azimuthal plane. The reflection () and transmission () coefficients are recorded through a vector network analyzer (Agilent E5230C) in the band of 2-4GHz with 201 frequency points. To minimize the background noise, all measurements are conducted in a microwave chamber using the time-gating technique provided by E5230C.
The bistatic SCSs can be calculated from S-parameters using the radar range equation 
Figure 7 illustrates the measured scattering gains under different DC voltages for four different angles between the transmitting and receiving antennas in the azimuthal plane. We clearly observe that strong scattering suppressions occur in all cases at the corresponding frequencies. The reduction of scattering gain ranges from −6 dB to −11 dB for such four angles, indicating that the dominant scattering term of the conducting cylinder is suppressed significantly by the proposed ultrathin cloak in a wide range of angles. As expected, the frequency for the minimum scattering gain shown in Fig. 7 shifts upwards from 2.3 GHz to 3.7 GHz when the DC voltage increases from 0.5 V to 23 V, which corresponds to decreased capacitance from 1.284 pF to 0.367 pF. This tuning effect of measured scattering dips as a function of DC voltage has good agreement to the simulations. However, some deviations are observed in the strength of the scattering dips between the simulated and measured results. This discrepancy is probably introduced by the copper wires around and on the cloak to provide the DC bias, which interact with the cloak and are not considered in simulations. Larger loss and assembly error during experiments may also contribute to the relatively weaker scattering dips in Figs. 7(a)–7(d). Nevertheless, the tunablility of the cloak is unambiguously demonstrated.
We remark that the bistatic scattering gain for a specific direction shown in Fig. 7 is not the same as the total scattering gain depicted in Fig. 4(a). This is because the scattering dips for all directions may not coincide at the same frequency point. Therefore, the total scattering dip integrated over 360 degrees in the azimuthal plane is usually larger than that for a specific direction. This fact gives rise to two aspects indicated in Fig. 7. First, the scattering dip splits into several new dips for higher voltages in both cases of φ = 90° and φ = 150° at high frequencies, resulting in a moderate scattering reduction over a broad bandwidth. Second, the scattering dips at the same frequency for higher voltages deviate considerably from each other in all cases. These two phenomena may be due to the contribution of higher-order multipoles to the residual scattering at higher frequencies. Therefore, the scattering dips at different directions should be designed and optimized as close as possible to get a minimum total scattering gain, which intuitively affords us a general guideline in the cloak design.
To further validate the tunable cloaking performances of the proposed cloak, near-field measurements are conducted at different frequencies by scanning the TM-polarized electric field (Ez) in the azimuthal plane under different DC voltages. A mapping system is set up to measure the near electric fields, as shown in Fig. 8, in which a probe is connected with a low-loss cable and functions as excitation. To achieve measurement results with sufficient resolution, a square area of 200mm × 100mm is automatically scanned along the x and y directions in steps of 2 mm. A double-ridge horn antenna is placed at 38 cm away from the object under test. In this case, a nearly Gaussian beam with the electric field polarized along the z-axis is formed on the object. Although the mapping system is only able to scan a rectangular area in the positive direction of the y-axis due to the blockage of the object, the results are still sufficient for a clear view of the field distribution since the electric field in the negative y axis is exactly the mirror of that in the positive y axis.
Figure 9 shows the measured TM-polarized electric field (Ez) distribution under the DC voltages of 2V and 23V, at which the measured cloaking frequency is experimentally obtained as 2.78 GHz and 3.75 GHz, respectively. Three cases are considered for comparisons: the free space, the object without cloak, and the object with cloak. The Ez distributions for such three cases are plotted from the left to the right panels, respectively. From Fig. 9, we observe significant perturbations around the cylinder for the uncloaked cases (see the middle panel) with respect to the free space (the left panel) and the cloaked cylinder (the right panel). Although the incident wave is not an ideal plane wave since the cloak is placed close to the antenna, the field is well restored with the existence of cloak. In the case of DC voltage of 2 V, excellent cloaking effect occurs at 2.78 GHz. The phase fronts around the cloaked object are nearly indistinguishable from those measured in free space. In the case of higher DC voltage (23 V), good cloaking effect appears at 3.85 GHz. The deteriorative cloaking performances in the later case can be interpreted by the contribution of higher-order multipoles at the high frequencies. The agreements between the near-field measurements and the bistatic scattering measurements demonstrate the tunable cloaking performances at the desired frequencies.
We have investigated an ultrathin tunable mantle cloak numerically and experimentally for a conducting cylinder in the microwave frequency ranging from 2.3 to 3.7 GHz. Our design is inspired from the scattering cancellation of mantle cloaking technique. In addition to the very low profile and simple configuration, numerical and experimental results indicate that the proposed varactor-diode-assisted metasurface is able to reduce the total scattering gain of a conducting cylinder by about 68-79% with good tunability. Although small imperfections in fabrication and assembly process inevitably degrade the cloaking performance, experimental results still have good agreements to numerical simulations. The excellent cloaking effect in the tunable bandwidth is further demonstrated by the measurement of near-field distributions. To the authors’ best knowledge, this is the first time to employ varactor diodes to implement ultrathin frequency-tunable mantle cloak. Based on this exploration, we expect to use other lumped elements (e.g. chip capacitors and inductors) to achieve the desired surface impedance for any arbitrarily-shaped unit cell, thus providing another degree of freedom in engineering the required metasurface of mantle cloak. This work will pave a way for wideband mantle cloaks with the use of non-Foster active elements, through which the bandwidth can be dramatically broadened by carefully tailoring the negative dispersion curve of the surface impedance.
This work was supported by the National High Tech (863) Projects (2012AA030402 a 2011AA010202), the National Science Foundation of China (60990320, 60990324 and 61138001), the 111 Project (111-2-05), and the Joint Research Center on Terahertz Science.
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