1. Introduction

Electromagnetically hiding an object from being detected by outside observers has garnered a substantial amount of research interest over the past decade [1, 2]. The primary approaches to achieve scattering signature reduction are based on transformation optics [3, 4], scattering cancellation [5, 6], and transmission line networks [7, 8]. The transformation optics method relies on an inhomogeneous medium, which sometimes requires anisotropy as well, to bend the incoming electromagnetic waves around the covered object [9]. It can be applied to objects with an almost arbitrary size and shape, but at the expense of the complicated material parameters that result and the bulky volume of the coating. The scattering cancellation coatings suppress the overall scattering signature by creating a local polarization vector that is in “anti-phase” with respect to that of the coated object. The coatings can be made of single- or multi-layer homogeneous materials [10, 11] or artificial media comprised by a collection of inclusions with custom designed electric and magnetic responses [12]. This approach provides a low profile, low loss, and effective solution for cloaking an object with a size usually smaller than the operational wavelength. The third venue of cloaking is based on rerouting the trajectory of waves using a mesh of transmission line networks, which is well-suited for low frequency applications but typically requires bulky structures that are sensitive to the polarization of the incident wave. Thus far, the various demonstrated cloak designs have mainly focused on the wave phenomena within a single operational band with either a narrow or a wide frequency window [13–21]. However, practical applications often necessitate more flexibility in the frequency bands of operation where multispectral cloaks are favorable. The designs and demonstrations of such multi-frequency cloaks have been rare in the literature. By incorporating a multilayer coating comprised of either natural materials, graphene, or impedance surfaces, dual-band cloaks for normally incident waves have been proposed and numerically validated [22–29].

Apart from hiding passive objects of various shapes and sizes from outside detection, another emerging application of cloaking technology relates to electromagnetic radiators. In [30] an approach was proposed that exploits cloaking coatings for restoring the electromagnetic performance of antennas operating in the receiving mode, i.e. similar to sensors. For radiators that operate in both the transmitting and receiving modes, however, a constant source impedance of 50 Ω should be enforced even when a cloaking coating is applied. It was first proposed and numerically demonstrated in [31] that, in the two-dimensional (2D) scenario, transformation optics based cloaks are capable of eliminating both the mutual coupling and mutual radiation blockage experienced when two 2D radiators are placed in close proximity to each other. However, for three-dimensional practical antennas, the required material parameters demand both inhomogeneity and extreme anisotropy, which are difficult to implement in practice. Alternatively, metasurface cloaks, which rely on scattering cancellation, have been numerically proposed for reducing the radiation blockage for single-band single- and dual-polarized wire antennas [32–35].

In this paper, we present the theory, design, and demonstration of multispectral and angle-tolerant metasurface cloaks for electromagnetic radiators, which enable simultaneous mutual coupling reduction and three-dimensional radiation pattern restoration. First, the scattering by a cylinder coated with multilayer metasurfaces under an obliquely incident plane wave excitation is analytically solved and used to determine the required surface electromagnetic properties of the coatings. The angular response of two dual-band cloak coating designs, each incorporating three metasurface layers, were analyzed and compared. Then, a set of discrete metasurfaces were designed to realize the desired surface electromagnetic properties. The dual-band cloaking effects of the infinitely-long structures are validated through full-wave simulations. Finally, the two coating designs were tailored for application to a practical finite-length monopole radiator. The performance metrics are compared both numerically and experimentally, revealing the impacts of the dispersive properties of the metasurfaces and radiator-to-radiator distance on the overall device behavior. A high-level overview of the basic results was briefly introduced in [35], but here we expand on that presentation to elaborate on the systematic design methodology and extensive numerical and experimental studies of the multispectral radiator cloak coatings.

2. Oblique incidence plane wave scattering by a cylinder coated with metasurfaces

The conceptual configuration of the cloaked monopole is illustrated in Fig. 1(a). A single-band monopole (Ant 1), operating at a frequency f₁, is located close to a dual-band monopole (Ant 2), operating at frequencies f₂ and f₃, assuming each of them is intended for a different system. Without the coating, the single-band monopole scatters the radiated wave from the dual-band monopole, thereby distorting the omnidirectional radiation pattern of the latter at f₂ and f₃. In addition, due to mutual coupling, currents can be induced on the single-band monopole at f₂ and f₃, thereby causing interference and crosstalk. When a properly designed coating is added surrounding the single-band monopole, the coated monopole can appear to be electromagnetically transparent to waves at f₂ and f₃, thereby restoring the desirable omnidirectional radiation pattern of the dual-band monopole. The coating should also possess a built-in filtering functionality to block signal transmission between the two antennas at f₂ and f₃. At the same time, the coating is expected not to have any adverse impact on the radiation of the coated monopole at f₁. For the proof-of-concept examples presented here, f₁, f₂, and f₃ are chosen to be 2.4, 3.5, and 5.2 GHz, which are widely used frequency bands.

 

Fig. 1 (a) Conceptual schematic of a monopole radiator (Ant 1), operating at frequency f₁, coated by a multilayer anisotropic metasurface that renders the enclosed monopole electromagnetically transparent (i.e. invisible) to waves radiated by a nearby dual-band radiator (Ant 2), which operates at frequencies f₂ and f₃. (b) Scattering by an infinitely-long cylinder coated with N layers of anisotropic metasurfaces under illumination by an obliquely incident TM_z polarized plane wave.

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To design the coating, we first consider the scattering of an infinitely-long cylinder coated with N layers of anisotropic metasurfaces under a plane wave excitation at an oblique incidence. As illustrated in Fig. 1(b), the metasurfaces are assumed to be separated by air spacers. Due to the fact that the magnetic field of the radiated wave from monopole antennas has a near-zero z-component, here only transverse magnetic to z (TM_z) polarization is considered. Without loss of generality, the incident plane wave (contained within the x-z plane with its H-field polarized in the y direction) is assumed to be incident at an angle ${\theta }_i=(0°<{\theta }_i\le 90°)$ with respect to the z axis. To keep this formulation general, the central cylinder is assigned an arbitrary relative permittivity denoted by ε_c. For the specific case where the cylinder is conducting, the same equations can be used by allowing the value of ε_c to approach –j∞. Since the metasurfaces have near-zero electrical thickness and are comprised of non-magnetic materials, their electromagnetic properties can be described by the surface electric and magnetic susceptibility tensors expressed as ${\overline{\overline{\chi }}}_m^E=diag[0,{\chi }_{m\phi }^E,{\chi }_{mz}^E]$ and ${\overline{\overline{\chi }}}_m^M=diag[{\chi }_{mr}^M,0,0]$ for the m^th layer located at a radius of r_m [36].

It should be noted that cross polarization coupling may occur due to the asymmetric structure as seen by an obliquely incident wave. Hence, the non-vanishing z-component of the magnetic field has to be taken into account. Assuming that the time dependence is exp(jωt), the z-component of the electric and magnetic fields in the region outside the multilayer metasurface coating (r ≥ r₁⁺) can be written as [37]

In order to solve the unknowns in a compact matrix form, we utilize the properties of Maxwell’s equations to establish a link between the fields in each region. By doing this, a total transfer matrix can be obtained which relates the tangential fields ($E_z^0$,$H_z^0$,$E_{\phi }^0$,$H_{\phi }^0$) in the region outside the coating and those ($E_z^{N+1}$, $H_z^{N+1}$, $E_{\phi }^{N+1}$, $H_{\phi }^{N+1}$) in the central cylinder. This reduces the number of linear equations from 2N + 2 down to only 4 no matter how many metasurface layers are considered. To obtain the total transfer matrix, two field relations are required – one relates the tangential fields at r_{m + 1}⁺ and r_m^– and the other relates the tangential fields at r_m^– and r_m⁺ across a metasurface, m = 1, 2, …, N.

For the first relation, Maxwell’s equations can be re-written by eliminating the radial component in cylindrical coordinates to arrive at

For the second relation, the second order boundary conditions must be considered at each metasurface layer. Specifically, the discontinuity in the tangential field components is due to the presence of a non-zero radial component of the magnetic susceptibility parameter. Hence, by utilizing the corresponding boundary conditions [38], the relationship between the tangential fields at r_m^– and r_m⁺ can be established as $\overline{V}(r_m^{+})={\overline{T}}_m\cdot \overline{V}(r_m^{-})$, where

In the final step, the total transfer matrix is obtained by iteratively applying these two relations. Hence, the tangential fields at r₁⁺ can be expressed in terms of those at r_{N + 1}^– such that

3. Dual-band cloak coating designs and their metasurface implementations

A. Analytical results for triple-layer cloak coatings

To achieve simultaneous dual-band cloaks with suppressed mutual coupling, multiple layers of metasurfaces are required. At the innermost layer, it is desired to place a filtering metasurface. This allows the waves to pass through at f₁ but blocks waves at f₂ and f₃, thereby suppressing these signals and preventing them from being transmitted onto the central conducting cylinder, i.e. the coated radiator. However, at the frequencies f₂ and f₃, the added filtering metasurface produces stronger scattered fields compared to those due to the radiator alone. In order to cloak the conducting cylinder coated by the filtering metasurface, at least a second metasurface layer is required. For a coated cylinder with an overall radius beyond the quasi-state limit, both the zeroth and the first order Mie scattering modes are active. In order to achieve a near-zero scattering width, both electric and magnetic resonators are required [39]. As a result, a solution containing only two metasurface layers would lead to greatly increased design complexity due to the simultaneous deployment of more than two kinds of resonators on one surface. To mitigate this issue, a triple-layer metasurface coating configuration is adopted. The innermost layer, with r₃ = 3.65 mm, has a near-zero value of ${\chi }_{3z}^E/{\lambda }_0$ at f₁ to enable a passband and its dispersive profile has a positive slope due to passivity [40], then a shunt parallel LC circuit model resonating at f₁ can be employed. Hence, the resulting values of ${\chi }_{3z}^E/{\lambda }_0$ at f₂ and f₃ are positive, which are assumed to be 5 and 17, respectively. Two additional metasurfaces are added, at a radius of r₂ = 6.35 mm and r₁ = 8.86 mm, respectively. Since the monopole has a finite length, the electric field of the emitted wave has components that are not exactly perpendicular to the ground plane. Hence, the scattering signature within a certain angular range ($70°\le {\theta }_i\le 90°$) was considered to ensure that the three-dimensional radiation pattern can be restored. Under these circumstances, four parameters – ${\chi }_{1z}^E/{\lambda }_0$, ${\chi }_{1r}^M/{\lambda }_0$, ${\chi }_{2z}^E/{\lambda }_0$, ${\chi }_{2r}^M/{\lambda }_0$ – need to be tuned in order to achieve the dual-band cloaking effect at f₂ and f₃. This leads to two different coating designs, denoted as C1 and C2, which are listed in Table 1. The SW of the conducting cylinder coated by C1 or C2 (normalized to that of the bare uncoated case) at f₂ and f₃ are shown in Figs. 2(a) and 2(b), respectively, as a function of the angle of incidence. It can be seen that, by properly choosing the electric and/or magnetic surface electromagnetic properties of each metasurface layer, a SW reduction of more than 10 dB can be achieved within the majority of the targeted angular range. Consequently, the coating is tolerant to the incident angle variation, which is in contrast to many of the previously demonstrated cloaks that only work in two dimensions [9, 13, 18], making it promising to restore the three-dimensional radiation pattern of a practical radiator.

Table 1. Surface properties of the triple-layer coating.

View Table

 

Fig. 2 (a) Scattering width of a conducting cylinder (a = 2 mm) coated by a triple-layer metasurface normalized to that of a bare conducting cylinder at (a) f₂ and (b) f₃.

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B. Realistic metasurface implementations

It has been shown in many previously demonstrated cloaking devices that the mutual coupling between the concentric layers containing different electric and/or magnetic resonators, implemented by periodic metallic patterns, are weak enough to be negligible [9, 13, 14, 18]. This indicates that each metasurface layer of the antenna coating considered here can be individually designed. In order to implement the required electric and magnetic surface susceptibilities at all three frequency bands, namely f₁, f₂, and f₃, different periodic metallic patterns are employed and designed for each layer to achieve the desired dispersion. During the unit cell design process, a finite element method solver, high frequency structure simulator (HFSS), was employed to perform the full-wave scattering calculations for a plane-wave illumination at different angles of incidence. The relevant effective surface susceptibility tensor parameters were then retrieved from the complex reflection and transmission coefficients [38]. Notably, due to the fact that the inner most metasurface layer is located in the vicinity of the metallic radiator, a special inversion algorithm was employed to take into account the effect of the metallic central radiator [41].

The metallic patterns of the unit cell of each metasurface layer of C1 are shown in Figs. 3(a)-3(c) along with their dispersive effective surface electric and/or magnetic susceptibility tensor parameters, i.e. ${\chi }_{mz}^{E,eff}/{\lambda }_0$ and/or ${\chi }_{mr}^{M,eff}/{\lambda }_0$ (m = 1, 2, 3), reported in Figs. 3(d)-3(g). The innermost layer is comprised of a meandered slot array to create the desired bandpass filtering functionality, which allows for signals to pass through at f₁ while blocking signals at the other frequencies. As seen from Fig. 3(g), its surface electric susceptibility has a near-zero value at around 2.4 GHz and large values in the 3.5 and 5.2 GHz bands. The unit cell of the middle layer consists of a meandered dipole [42], which provides a resonance at 4 GHz. By tuning the quality factor of its electric resonance, the surface electric susceptibility can meet the targeted values at bands centered around f₂ and f₃ for achieving the desired scattering suppression. The unit cell of the outermost metasurface layer contains two resonators – one is a capacitively coupled short dipole [43] and the other is a spiral magnetic resonator [44] – in order to provide the desired surface electric and magnetic properties at f₂ and f₃. It is noticed that all the metasurface layers have small surface electric and/or magnetic responses at around 2.4 GHz, indicating that a negligible impact will be imposed on the radiation and input impedance of the coated monopole over its intended operational band.

 

Fig. 3 Unit cell geometries of (a) the outermost, (b) the middle, and (c) the innermost metasurface layers of C1. The dimensions are p_φ11 = 9.28, p_φ12 = 6.65, p_φ13 = 3.82, p_z11 = 8, p_z12 = 8, p_z13 = 16, a₁ = 7.5, b₁ = 5.7, c₁ = 2.2, d₁₁ = 7.5, d₁₂ = 0.62, g₁ = 5.78, w₁₁ = 0.4, w₁₂ = 0.5, w₁₃ = 0.35, w₁₄ = 0.4, w₁₅ = 0.68, w₁₆ = 0.3, w₁₇ = 0.45, all in millimeters. The substrate thickness of all the layers is 100 μm. The substrate material is Rogers Ultralam 3850 (ε_r = 2.9, δ_tan = 0.0025). Retrieved effective surface electric and magnetic susceptibility tensor parameters for the metasurfaces of C1. (d) ${\chi }_{1z}^E/{\lambda }_0$ and (e) ${\chi }_{1r}^M/{\lambda }_0$ for the outermost layer, (f) ${\chi }_{2z}^E/{\lambda }_0$for the middle layer, (g) ${\chi }_{3z}^E/{\lambda }_0$ for the innermost layer.

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The metasurfaces of C2 are composed of different unit cells for the middle and outermost layers due to the alternative set of requirements on the surface electric and magnetic susceptibility parameters (see Table 1). Figures 4(a)-4(c) show the detailed geometry of the unit cells for each metasurface layer, while their dispersive effective surface electric and/or magnetic susceptibility tensor parameters are plotted in Figs. 4(d)-4(g). The innermost layer has the same dimensions and thus the same surface electromagnetic properties as that of the corresponding metasurface coating for C1. The unit cell for the middle layer of C2 is different from that of C1 such that it has one short dipole electric resonator and a spiral magnetic resonator, which is similar to the outermost layer of C1. It offers the desired dispersion for both the surface electric and magnetic susceptibility parameters (see Figs. 4(e) and 4(f)). For the unit cell of the outermost layer, two electric resonators are employed, including a meandered dipole and a capacitively coupled short dipole. The meandered dipole was designed to resonate at 4.4 GHz, while the short dipole provides another resonance at a higher frequency in order to jointly tailor the dispersive property of the surface electric response to satisfy the requirements at f₂ and f₃. Similar to the previous design, all three metasurfaces have small electric and/or magnetic responses at around 2.4 GHz, which ensures that the coating layers will have minimal effect on the operation of the enclosed monopole.

 

Fig. 4 Unit cell geometries of (a) the outermost, (b) the middle, and (c) the innermost metasurface layers of C2. The dimensions are p_φ21 = 9.28, p_φ22 = 6.65, p_φ23 = 3.82, p_z21 = 8, p_z22 = 8, p_z23 = 16, a₂₁ = 5.5, a₂₂ = 3.42, a₂₃ = 2, b₂ = 5.7, c₂ = 2.9, d₂₁ = 7.6, d₂₂ = 7.55, g₂ = 3.25, w₂₁ = 0.4, w₂₂ = 0.4, w₂₃ = 0.38, w₂₄ = 0.4, w₂₅ = 0.4, w₂₆ = 0.68, w₂₇ = 0.3, w₂₈ = 0.45, all in millimeters. The substrate thickness of all the layers is 100 μm. The substrate material is Rogers Ultralam 3850 (ε_r = 2.9, δ_tan = 0.0025). Retrieved effective surface electric and magnetic susceptibility tensor parameters for the metasurfaces of C1. (d)${\chi }_{1z}^E/{\lambda }_0$ for the outermost layer, (e)${\chi }_{2z}^E/{\lambda }_0$ and (f)${\chi }_{2r}^M/{\lambda }_0$for the middle layer, (g) ${\chi }_{3z}^E/{\lambda }_0$ for the innermost layer.

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The full-wave simulated scattering properties of the conducting cylinder with and without the realistic triple-layer metasurface coatings (C1 and C2) at both frequencies f₂ and f₃ were investigated. Two parallel perfect conducting plates were used in HFSS to mimic an infinitely long structure. A cylindrical wave source was placed at a distance of D away from the center of the conducting cylinder. As shown in Figs. 5(a) and 5(b), the bare conducting cylinder significantly scatters the wave, perturbing the original concentric wave pattern. With C1 or C2 present and a d value of 50 mm, at both frequencies f₂ and f₃, the scattering is minimized such that the cylindrical wave properties are well restored, as displayed in Figs. 5(c) and 5(d). For both C1 and C2, the scattering width is reduced by more than 30 dB. This dual-band cloaking effect is well maintained even when the separation D is reduced to only 20 mm, meaning that the distance between the cylindrical source and the outermost metasurface is only about λ₀/8 at f₂. This indicates that the triple-layer metasurface coatings are capable of cloaking an enclosed object (i.e., the radiator) at two pre-selected frequencies simultaneously even in the near-field.

 

Fig. 5 Snapshots of the full-wave simulated total electric field magnitude distribution for (a) the uncoated copper cylinder, and the same copper cylinder coated by the actual triple-layer metasurface cloaking structure (b) C1 and (c) C2 under a cylindrical wave excitation at a distance of D = 50 mm. The same set of plots for the copper cylinder coated by the metasurface cloaking structure (d) C1 and (e) C2 under a cylindrical wave excitation at a distance of only D = 20 mm.

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4. Radiator coated with integrated dual-band metasurface cloaks

Figures 6(a) and 6(b) illustrate the two designs when the multilayer metasurface coatings are integrated with the monopole radiator. The metasurface coatings have the same height as that of the 2.4 GHz monopole. Hence, in the z-direction, two unit cells are used for the innermost layer, while the middle and outermost layers both have 4 unit cells. A dual-band sleeve monopole is located at a distance D = 50 mm away from the center of the coated monopole. It has a 21.5 mm long central radiator and two 12 mm long parasitic elements positioned at a distance of 3.5 mm away from the central element. This configuration provides a dual-band operation at around 3.5 and 5.2 GHz. The coated monopole and the sleeve monopole are both fed by a 50 Ω SMA connector. To account for the truncation effect of the cloak coatings, the geometrical dimensions for both C1 and C2 were tuned. In particular, the size of the electric resonators, including the meandered slot, the meandered dipole, and the capacitively coupled short dipole, needs to be increased slightly, as reflected by the dimensions listed in the caption of Fig. 6.

 

Fig. 6 Configuration of the single-band monopole radiator (Ant 1) coated with multilayer metasurface (a) C1 and (b) C2 and a dual-band sleeve monopole radiator (Ant 2). The center-to-center distance between the two antennas is D = 50 mm. The ground plane size is 300 mm by 300 mm. Photographs of the fabricated prototype of the dual-band sleeve monopole (Ant 2) and the single-band monopole (Ant 1) surrounded by (c) C1 and (d) C2. For C1, the tuned parameters are w₁₇ = 0.4, d₁₂ = 0.52, g₁ = 5.78, and d₁₁ = 7.55, while for C2, the tuned parameters are w₂₈ = 0.4, d₂₁ = 7.7, g₂ = 3.25, and d₂₂ = 7.65, w₂₃ = 0.38, all in millimeters.

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The scattering parameters of the dual-band monopole and the 2.4 GHz monopole with and without the cloak are shown in Fig. 7. Both antennas have well-matched impedance in their own operational bands. When there is no coating, mutual coupling can be observed between the two radiators in the 3.5 and 5.2 GHz bands, manifested by a S₂₁ value of around −15 and −19 dB in the two bands, respectively. With the multilayer metasurface coating, the 2.4 GHz monopole maintains a dip at 2.4 GHz (see the S₁₁ plots in Figs. 7(b) and 7(c)), indicating that the added coating does not impair the input impedance of the enclosed antenna. Moreover, the two resonances of the dual-band radiator, at 3.5 and 5.2 GHz, are not affected by the added coating around the single-band monopole operating at 2.4 GHz (see the S₂₂ plots in Figs. 7(b) and 7(c)). Most importantly, a significant reduction in S₂₁ is observed, indicating that a high degree of mutual coupling suppression is achieved. For the case with C1, the S₂₁ at the 3.5 and 5.2 GHz bands is −23 dB and < −50 dB, respectively, whereas for the case with C2, the S₂₁ at the 3.5 and 5.2 GHz bands is −26 dB and < −50 dB. They both exhibit a > 30 dB drop at the 5.2 GHz band, since this frequency is located far away from the passband of the innermost layer of the coating around the 2.4 GHz monopole. At the 3.5 GHz band, C2 has a better performance than C1, due to the lack of a peak in the S₂₁, which is primarily caused by the electric resonance at 4 GHz of the middle layer of the coating that comprises C1.

 

Fig. 7 Simulated and measured scattering parameters of the single-band monopole radiator (Ant 1) and the dual-band sleeve monopole radiator (Ant 2) for the cases (a) without any coating, (b) with C1, and (c) with C2.

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To demonstrate the radiation blockage suppression effect that the coating enables, the radiation properties are examined in this sub-section. The gain variation (ΔGain), characterized by the difference between the maximum and minimum value of the gain in the x-y plane, at the 3.5 and 5.2 GHz bands is reported in Fig. 8 as a function of frequency. It can be seen from Fig. 8(a) that, without the coating, the radiation pattern in the H-plane of the dual-band antenna no longer preserves its original omnidirectional property. A simulated gain variation of more than 4 dB occurs, which represents a considerable performance degradation that deteriorates the signal coverage. As a reference, the gain variation is also plotted for the case where only the dual-band sleeve monopole is located at the center of the ground plane. The ΔGain value is on the order of 0.3 and 0.7 dB in the two bands, respectively. The non-zero value is attributed to the diffraction caused by the square shaped ground plane. The top rows of Figs. 9(a) and 9(c) show the normalized radiation patterns in the H-plane at 3.5 and 5.2 GHz, respectively. At 3.5 GHz, the radiation pattern becomes a quasi-elliptical shape, with weak radiation in the ± x directions, which is primarily due to the dipolar scattering mode of Ant 1. At 5.2 GHz, the radiation pattern has two dips at ~ ± 70° as measured from the + x direction with a level of −5 dB. The strongest radiation happens in the + x direction, which is about 4 dB higher than that in the –x direction. This distorted pattern is mainly caused by both the monopolar and dipolar scattering modes of Ant 1. In the orthogonal E-planes, i.e. the x-z and y-z planes, unequal main lobes can be observed, as presented in the top rows of Figs. 9(b) and 9(d). This indicates that the three-dimensional radiation patterns of the dual-band monopole radiator are significantly distorted compared to the original case where the radiator is operating alone.

 

Fig. 8 Simulated and measured gain variation (ΔGain) in the x-y plane versus frequency at the low (top) and high (bottom) operational frequency bands of the dual-band sleeve monopole radiator (Ant 2) for the cases (a) without any coating, (b) with C1, and (c) with C2.

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Fig. 9 Simulated and measured (a) H-plane and (b) E-plane radiation patterns at the low frequency band and (c) H-plane and (d) E-plane radiation patterns at the high frequency band for the cases without any coating (top row), with C1 (middle row), and with C2 (bottom row).

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With C1 surrounding the single band monopole, as displayed in Fig. 8(b), the ΔGain in the x-y plane is greatly reduced in the two targeted bands. Reduced gain variation is achieved over the frequency bands ranging from 3.39 to 3.55 GHz and from 4.5 to 5.4 GHz. The best performance occurs at 3.52 and 5.18 GHz, with a gain variation of only 0.9 and 1.6 dB, respectively. This indicates a drop in ΔGain of more than 3 dB. From the middle rows of Figs. 9(a) and 9(c), it can be seen that the radiation patterns in the H-plane of the dual-band radiator are recovered to be near-omnidirectional at both frequencies. Due to the fact that the coating can provide scattering suppression within a certain range of the incident angle, such pattern restoration effects can also be observed in the E-plane of the antenna. As presented in the middle rows of Figs. 9(b) and 9(d), the simulated normalized radiation patterns in the x-z and y-z planes show more symmetrical main lobes. The simulated gain values of the dual-band sleeve monopole are around 5.2 and 5.1 dBi at 3.52 and 5.18 GHz, respectively, which are very similar to the case where the dual-band radiator is operating alone. In addition, the radiation pattern and gain value of the coated monopole are also well maintained at around 2.4 GHz, with a gain drop of only about 0.5 dB, indicating that the coating is highly efficient, which corroborates previously reported results on metasurface coated monopoles [32, 33, 45].

With C2, as displayed in Fig. 8(c), the gain variation in the x-y plane is also greatly reduced in the targeted bands. From the simulated results, it is seen that the reduced gain variation is achieved in the frequency ranges from 3.29 to 3.64 GHz and from 4.82 to 5.47 GHz. Hence, the bandwidth for C2 at the low and high frequency bands is about 219% and 72% of that for the case with C1. At the frequencies where the best performance occurs, i.e. 3.55 and 5.22 GHz, the corresponding gain variation was determined to be 0.8 and 1.2 dB, respectively, which is slightly better than it was for the case with C1. The normalized H-plane radiation patterns at 3.55 and 5.22 GHz are shown in the bottom rows of Figs. 9(a) and 9(c). It is seen that near-omnidirectional radiation patterns are obtained at both frequencies. In addition, in the E-plane, symmetrical radiation patterns are also recovered in both bands by adding the coating, as displayed in the bottom rows of Figs. 9(b) and 9(d). With C2, the simulated gain values of the dual-band radiator are around 4.8 and 5.0 dBi at 3.55 and 5.22 GHz, respectively, which are very similar to those for the case where the dual-band radiator is operating alone. In addition, at around 2.4 GHz, the radiation pattern and gain of the coated monopole remain nearly the same, with a drop in gain of only about 0.6 dB. It should be noted that, the cloaking effect is not affected by the size of the finite ground plane.

5. Experimental comparison and discussions

The metasurface layers for both the C1 and C2 designs were fabricated using a standard printed circuit board etching process. Since the substrate is only 0.1 mm thick, they are extremely flexible. Thin plastic washers with properly chosen dimensions were employed as a frame to provide structural support for the coating and to ensure the correct diameters for each metasurface layer. The 2.4 GHz monopole and the dual-band sleeve monopole were also implemented. Finally, the multilayer metasurface coating was assembled and placed around the 2.4 GHz monopole. Photographs of the fabricated prototypes are displayed in Figs. 6(c) and 6(d) with the 2.4 GHz monopole shown surrounded by C1 and C2, respectively.

The scattering parameters, measured by an Agilent E8364B network analyzer, are reported in Fig. 7, for the following three cases: (a) without the coating, (b) with C1, and (c) with C2. For all three cases, very good agreement is achieved between the simulated and measured results, thus confirming the predicted performance in terms of the network parameters. The measured S₁₁ and S₂₂ show that the two fabricated radiators both achieve a good impedance matching within their operational frequencies. With a coating present (either C1 or C2), the S₁₁ remains well-matched, with a very slight frequency shift of less than 30 MHz. At the 3.5 GHz band, C1 provides a measured reduction in the mutual coupling S₂₁ of about 9 dB, while C2 yields a measured reduction of 13 dB. At the high frequency band around 5.2 GHz, for both coatings, the value of S₂₁ is reduced by more than 25 dB. The scattering parameters validate that the fabricated coating indeed suppresses the level of mutual coupling between the two antennas at both of the operational bands of the dual-band radiator.

The E- and H-plane radiation patterns were characterized in an anechoic chamber. The measured gain variations in the H-plane as a function of frequency for the cases where the 2.4 GHz monopole is uncoated, or surrounded by C1 and C2, are shown in Fig. 8. It can be seen that the coatings suppress the gain variation at both the 3.5 and 5.2 GHz bands, revealing greatly reduced scattering due to the 2.4 GHz monopole. For the case with C1, the frequencies with the minimal gain variation are 3.43 and 5.05 GHz, with a corresponding ΔGain value of 1.1 and 1.6 dB, respectively. At these two frequencies, the measured normalized radiation patterns in the H-plane exhibit a near-omnidirectional coverage (see middle rows of Figs. 9(a) and 9(c)), while the measured normalized radiation patterns in the E-plane display much improved symmetry in both the x-z and y-z planes (see middle rows of Figs. 9(b) and 9(d)). With C2 present, the best operational frequencies are at 3.68 and 5.04 GHz with a ΔGain value of 1.1 and 1.4 dB, respectively. At these two frequencies, the measured normalized radiation patterns in the H-plane possess a near-omnidirectional shape (see the bottom rows of Figs. 9(a) and 9(c)). At the same time, the measured normalized radiation patterns in both the x-z and y-z planes are much more symmetrical (see the bottom rows of Figs. 9(b) and 9(d)), in contrast to those without the coating. The measurements in both the H- and E-planes confirm that the three dimensional radiation patterns are restored by utilizing the metasurface coating prototypes. A slight frequency shift of less than 3.5% can be observed in Figs. 8(b) and 8(c) between the simulated and measured curves, which is primarily caused by fabrication imperfection and assembly inaccuracy. The measured gain values, which are within 1 dB difference of the simulated results, confirm the low-loss associated with the coating designs. In all, the measurements show that the metasurface coatings indeed provide the desired simultaneous mutual coupling and radiation blockage suppression. Compared to C1, C2 exhibits a better performance in terms of both mutual coupling reduction and radiation blockage suppression, as well as a more balanced bandwidth.

Finally, the impact of the distance between the dual-band radiator and the cloaked monopole is further investigated numerically. For three different values of the distance parameter D, the reflection coefficients of both antennas (S₁₁ and S₂₂), the mutual coupling reduction and the gain variation reduction are compared. As can be observed from Fig. 10(a) and 10(b), the input impedance of the single-band radiator remains nearly unchanged, i.e. with a single resonance at around 2.4 GHz. For the dual-band radiator, two resonances can be identified at around 3.5 and 5.2 GHz with slight frequency shifts due to the near-field coupling. Nevertheless, within the targeted frequency ranges, the port reflection coefficient magnitude remains below −15 dB, indicating near-perfect impedance matching is achieved even though the distance parameter D is greatly reduced. As shown in Fig. 10(c), it can be seen that when the distance between the two radiators is reduced from 50 mm to 20 mm, i.e. from 0.59λ₀ to 0.23λ₀ at f₂, the level of mutual coupling suppression is well maintained. Moreover, the reduction in the gain variation achieved with C1 and C2 at both bands is shown in Figs. 10(d) and 10(e). It can be seen that for different distances between the two radiators, the scattering reduction effect is achieved at both targeted bands. When the distance is reduced, a slight narrowing of the bandwidth can be observed, while the maximal value of gain variation reduction becomes higher as D decreases.

 

Fig. 10 Simulated S₁₁ and S₂₂ for the cases with (a) C1 and (b) C2. Simulated (c) mutual coupling (S₂₁) reduction and gain variation (ΔGain) in the x-y plane versus frequency at the (d) low and (e) high operational bands of the dual-band sleeve monopole radiator (Ant 2) for the cases with C1 (top) and C2 (bottom), where the distance D is varied.

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6. Conclusion

In summary, we have proposed a methodology to design compact multilayer metasurface coatings to suppress the mutual coupling and radiation blockage in multiple frequency bands caused by a monopole antenna when placed in close proximity to a source radiator. An analytical model of the scattering by a multilayer metasurface coated cylinder was developed for determining the electromagnetic properties of each metasurface layer required to achieve the desired scattering suppression effect. Two types of coatings, each containing three metasurface layers, were designed, implemented, and experimentally characterized. When either of these coatings were placed around a wire monopole antenna, greatly reduced mutual coupling and radiation blockage were demonstrated at the two operational bands of a nearby dual-band radiator, which are almost independent of the distance between the two radiators. Comparison between the performance metrics of the two different coatings provided guidance for obtaining an optimal design which exhibited a more balanced property over the multiple targeted bands. In all, through the demonstration of the compact and lightweight coatings for cloaking electromagnetic radiators, a new approach has been offered for mitigating the co-site interference among different radiators operating in multiple frequency bands, which can be extended for cloaking multi-spectral terahertz [46] as well as optical antennas [47–51].