Flexible and broadband microwave-absorbing structures have attracted significant attention in electromagnetic (EM) science. Although previous studies have demonstrated the potential of flexible microwave-absorbing structures using thin dielectric substrates or flexible materials, the need for broadband and flexible microwave-absorbing structures remains largely unmet, especially those that can be stretched to adapt to complex surfaces. In this article, a novel design concept of a stretchable meta-substrate comprising rigid pyramidal substrates and soft hinges is proposed, which operates as a dielectric substrate and a structural support for the metastructure. The proposed flexible and broadband microwave-absorbing metastructure is composed of a pyramidal microwave-absorbing unit and a stretchable meta-substrate, which exhibits a reflection coefficient lower than −20 dB from 2.2 to 20 GHz under normal incidence. By overcoming the mechanical and electromagnetic limitations of previous efforts with a soft material-based microwave-absorbing structure, the proposed metastructure can be stretched under 40% strain, while the −10 dB reflection coefficient spectrum only shifts by 1.1 GHz. Furthermore, the proposed metastructure exhibits stable absorption properties for EM wave irradiation with both transverse electric and transverse magnetic polarizations, even at an oblique incident angle of up to 70°. As a proof of concept, the proposed metastructure is conformally pasted on the unmanned aerial vehicle surface, and the maximum radar cross section reduction of the proposed metastructure is 30.5 dB larger than that of a conventional device. The fabricated sample can be readily applied for carrying and deployment, with potential applications in the fields of EM stealth as well as EM anti-interference.

The continuous development of electronic countermeasure technology and military informatization, coupled with the successive introduction of various new types of radar detectors, has led to a global focus on stealth technology for the concealment of weapons from detection. As a result, an ideal microwave-absorbing structure that can perfectly absorb electromagnetic (EM) waves has attracted extensive attention. Such periodic arrays of artificial units have offered immense potential for the manipulation of EM waves on deep subwavelength scales1–4 and, thus, can be deduced as an influential tool for absorbing the EM waves. An optimal microwave-absorbing structure ought to exhibit perfect absorption performance for all polarizations of incident waves in the thinnest possible structure, and the most efficient design, alongside excellent stability under oblique incidence. Nevertheless, microwave-absorbing structures, which rely on inherent resonance regimes, can merely absorb EM waves nearly perfectly in single frequency or multiband.5–8 For instance, a microwave-absorbing unit, consisting of electric and magnetic resonators, exhibits an absorption of more than 88% at 11.5 GHz.9 Hence, it is necessary to incorporate other mechanisms in addition to resonance to achieve a more significant absorption performance. Efforts to expand the absorption spectrum of microwave-absorbing structures have been researched extensively. This includes methods such as increasing losses, e.g., high-impedance surfaces (HISs),10–12 lumped resistors,13,14 and multilayered resonant cells.15 One important indicator of microwave-absorbing structures is their thickness. A sufficiently thick microwave-absorbing structure can absorb EM waves across a wide frequency range. There is a minimum thickness for broadband high-absorbing materials.16 Qu et al. designed a three-dimensional (3D) double-layer rectangular metal ring structure fabricated using PCB technology.17 The structure was filled with EM wave-absorbing foam in the middle, and the final sample achieved high-absorbing performance from 3 to 40 GHz with a thickness of 14 mm. Wen et al.18 proposed a fully dielectric 3D microwave-absorbing structure consisting of a resin shell and a brine structure to achieve more than 90% absorption from 0.9 to 40 GHz with a thickness of 38 mm, which is close to the theoretical limitation specified in the Planck–Rozanov limit. The fabrication of broadband microwave-absorbing structures using PCB technology is constrained by their tensile capacity, as they lack the necessary flexible properties. This significantly limits their applicability to deformable structures and complex large-scale weaponry. Therefore, the design of microwave-absorbing structures with high absorption performance is one of the objectives of this study.

To achieve the desired broadband, flexibility, and high absorption performance of the microwave-absorbing structure in such applications, a variety of approaches have been proposed. Microwave-absorbing structures have focused on utilizing more established polymer materials that offer greater flexibility.19–22 However, their material properties limit their suitability to bending structures as they do not exhibit flexible properties. Auxetic metamaterials, which are composed of periodic arrays of rotational squares and hinges, exhibit negative Poisson's ratio (v), and tend to expand in a direction perpendicular to the axial extension direction.23–26 A material that is not readily deformable can be deformed by an auxetic metamaterial strategy.27–29 Therefore, auxetic metamaterials are employed as the dielectric substrate of the microwave-absorbing metastructure to address these challenges, and a lossy meta-atom is placed on the rigid surface of this structure.30,31 Shen et al. demonstrated that 3D origami microwave-absorbing structures exhibit superior broadband and wide-angle stability performance compared to planar structures, particularly for TM-polarization.32 They combined planar and folded-angle HIS structures to achieve over 90% absorptivity at oblique incidence up to 75° from 3.6 to 11.4 GHz. The 3D origami structure represents a novel approach to achieving wide-angle absorption. However, absorption is nearly negligible under TE-polarized wave irradiation at large incident angles, and the fabrication process for 3D structures is complicated. Zhu et al. proposed a reconfigurable microwave-absorbing structure with wide-angle stability.33 This novel structure is based on origami and incorporates cross-shaped resistive sheets on the substrate for EM energy absorption. The folded structure can operate on multiple spectra, enabling its application in various scenarios. However, this origami-based MA is sensitive to polarizations, and it is only available at a specific folding angle, which is not conducive to the application of flexible structures in EM wave absorption. Furthermore, the enhancement of wide-angle absorption represents a persistent objective for broadband microwave-absorbing structures, particularly in the ongoing advancement in the detection capabilities of both ground-based and airborne radars. Consequently, the development of microwave-absorbing structures with flexible and high absorption performance under large oblique incident angles has become a pressing requirement for the development of EM stealth.

In this work, a novel approach was proposed for metastructures with flexible, broadband, and wide-angle stability properties inspired by the physical mechanism of auxetic metamaterials. The design principle demonstrated that the pyramidal microwave-absorbing (PMA) unit, comprising four lossy loop-shaped resonators (LLSRs), was affixed to the flexible meta-substrate. The flexible meta-substrate enables the proposed metastructure to be stretched and easily conformed to the desired shape. Furthermore, the PMA unit is strain insensitivity, maintaining their geometric dimension and material properties under strains. Full-wave simulation results indicated that the proposed metastructure exhibits the −20 dB reflection coefficient from 2.2 to 20 GHz under normal incidence. Furthermore, the proposed metastructure exhibits 90% absorption for both transverse electric (TE) and transverse magnetic (TM) polarizations at oblique incident angles from 0° to 70° in the frequency range of 3.4–20 GHz. The proposed metastructure is designed to be independent of material properties, allowing for high elastic deformations.

Figure 1(a) schematically illustrates the proposed metastructure, which can be stretched and bent arbitrarily by external mechanical action while maintaining wide-angle absorption. As illustrated in Fig. 1(b), the upper LLSR layer of the PMA unit is a hollow-out pyramidal indium tin oxide (ITO) pattern on a pyramidal substrate, while the lower part consists of a self-similar ITO pattern pasted on the meta-substrate to effectively dissipate the incident EM wave. RS1 = 150 Ω/sq and RS2 = 100 Ω/sq are obtained by optimizing the sheet resistance of the ITO patterns. The period length of the PMA unit amplifies with the increase of tensile strain due to the negative Poisson's ratio of the auxetic metamaterial.34 The hinges in the meta-substrate significantly increase the degrees of freedom for stretching of the metastructure. All ITO patterns are located on an ultra-thin polyethylene terephthalate (PET) film (with a thickness of 50 μm).35,36 Furthermore, a metal plate is affixed to the background of the metastructure to prevent the transmission of EM energy.

FIG. 1.

Schematic of the proposed metastructure. (a) Metastructure pasted on a complex surface. (b) Each layer of the PMA unit. (c) Geometrical parameters of the PMA unit. (d) Photograph of the fabricated metastructure exhibiting excellent flexibility properties. (e) Reflection coefficient spectrum of the PMA unit. (f) Effective normalized impedance of the PMA unit.

FIG. 1.

Schematic of the proposed metastructure. (a) Metastructure pasted on a complex surface. (b) Each layer of the PMA unit. (c) Geometrical parameters of the PMA unit. (d) Photograph of the fabricated metastructure exhibiting excellent flexibility properties. (e) Reflection coefficient spectrum of the PMA unit. (f) Effective normalized impedance of the PMA unit.

Close modal

The design of the broadband metastructure is the process of impedance matching to the free space.37 For a metal reflector-supported metastructure, the majority of EM waves incident to the metastructure are absorbed, with the remaining waves being reflected or refracted.38,39 The EM characteristics of the metastructure, including reflection R(ω) and absorption A(ω), can be determined by the reflection coefficient |S11|, i.e., the reflection R(ω) = |S11|2 and the absorption A(ω) = 1 − |S11|2. As shown in Fig. 1(e), according to the radar-specific frequency range assigned by the ITU, the proposed metastructure has been engineered to exhibit a |S11| ≤ −25 dB within the S–Ku band, exhibiting multiple absorption peaks. To achieve high absorption performance over a wide frequency range, the input impedance of the proposed metastructure Zeff and the characteristic impedance of free space Z0 should be identical over a specified spectrum. In our design, the dispersions are introduced to achieve high absorption performance, where the real part of Zeff is almost matched to Z0, while the imaginary part is close to zero [see the gray highlighted regime in Fig. 1(f)]. This approach demonstrates that the proposed metastructure can exhibit excellent absorption from 2.2 to 20 GHz.

As illustrated in Fig. 2(a), the fundamental component of the metastructure is a loop-shaped resonator (LSR), and every four LSR layers were pasted on the meta-substrate to form a unit. Each unit was connected to the four surrounding ones by soft hinges.40 The LSR is an ITO pattern with a small sheet resistance (ZLSR = 0.1 Ω/sq). The meta-substrate was designed with a periodic array of 3D pyramidal substrates linked by elongated hinges (3D printed from the TPU 95A), which serve to provide both structural support and dielectric substrate for the metastructure. Finite element analysis (FEA) was used to investigate the transformation mechanism of the meta-substrate under different strains.41  Figure 2(b) exhibits the strain distribution by stretching the flexible material and tends to contract in a direction perpendicular to the direction of stretching. Figure 2(c) shows the stress distribution of the meta-substrate under 20% strain, with significant deformation occurring at the hinges. The proposed meta-substrate can not only stretch but also keeps the aspect ratios constant during the stretching process. The ratio of transverse transformation (W/w) and longitudinal transformation (L/l) is defined as Poisson's ratio,
(1)
FIG. 2.

Design and spectral responses of the metastructure. (a) Schematics of the loop-shaped resonator, (b) stress distribution of the flexible material under 20% strain, (c) stress distribution of the unit under 20% strain, (d) maximum tensile strain of the unit under different stretching angles, and (e) reflection coefficient spectra of the unit under strains of 0%–40%.

FIG. 2.

Design and spectral responses of the metastructure. (a) Schematics of the loop-shaped resonator, (b) stress distribution of the flexible material under 20% strain, (c) stress distribution of the unit under 20% strain, (d) maximum tensile strain of the unit under different stretching angles, and (e) reflection coefficient spectra of the unit under strains of 0%–40%.

Close modal

The diagonal LSRs of the proposed meta-substrate rotate in the same direction as strain increases, while the neighboring LSRs rotate in the opposite direction at the same angle. The maximum tensile strain of the meta-substrate is determined by the degree of deformation of the hinges between the neighboring squares, as the stresses at these hinges accumulate during meta-substrate transformation. The results of the FEA simulation demonstrate that Poisson's ratio (v2) of the proposed meta-substrate is −1 in comparison to the flexible material with positive Poisson's ratio. As the tensile strain increases, the maximum stress of the meta-substrate also increases significantly, as shown in Fig. 2(d). It is worth noting that the magnitude of the reflection coefficient |S11| increases as the substrate is stretched at strains from 0% to 30%, as shown in Fig. 2(e). However, the EM responses of the metastructure exhibit minimal variation with an increase in tensile strain from 30% to 40%.

As illustrated in Fig. 3, we have obtained a spectrum of −20 dB reflection coefficient in the frequency band of 2.2–20 GHz by optimizing the scaling factor β. The simulated results indicate that if the optimal value of β is chosen to be 0.9, the internal layer of the PMA unit is relatively too large and the coupling between the internal and outer layers is too strong, which may result in lower absorption in the operating bands. Instead, if β = 0.1, the starting and ending absorption will drop rapidly, which can cause a dip in the absorption spectrum. Therefore, by considering the simulation results together, we choose β = 0.5 as the best value, just because the other parameters cannot cover the high and low frequency bands of the absorption spectrum. The geometrical parameters of the PMA unit are given in Table I.

FIG. 3.

Reflection coefficient spectra with different β.

FIG. 3.

Reflection coefficient spectra with different β.

Close modal
TABLE I.

Geometrical parameters of the PMA unit.

ParameterValue (mm)ParameterValue (mm)
w1 1.2 h2 15.0 
w2 0.3 h3 30.0 
w3 3.1 l1 15.4 
w4 1.4 l2 7.3 
w5 7.0 l3 30.8 
w6 2.4 l4 14.6 
w7 0.6 d1 0.8 
w8 6.2 d2 5.0 
w9 2.8 d3 23.6 
w10 13.9 r 0.5 
h1 1.3 P 14.3 
ParameterValue (mm)ParameterValue (mm)
w1 1.2 h2 15.0 
w2 0.3 h3 30.0 
w3 3.1 l1 15.4 
w4 1.4 l2 7.3 
w5 7.0 l3 30.8 
w6 2.4 l4 14.6 
w7 0.6 d1 0.8 
w8 6.2 d2 5.0 
w9 2.8 d3 23.6 
w10 13.9 r 0.5 
h1 1.3 P 14.3 

To investigate the EM invisibility capacity of the proposed metastructure under the interference of stretching, the absorption performance was simulated under strains of 0%–40%, as shown in Fig. 4. In the simulations, geometric modeling is feasible for a planar structure, but it becomes considerably complicated when the substrate is folded into a curved shape. To simplify the simulation process for the proposed metastructure, we only simulate the metastructure stretched in the horizontal plane and assume that the metastructure is uniformly stretched. In the zero strain state of the proposed metastructure, the spectrum of the −10 dB reflection coefficient covers the range of 1.7–20 GHz, while the −20 dB reflection coefficient covers the range from 2.2 to 20 GHz. In strain levels ranging from 0% to 40%, the fractional bandwidth (FBW) of the −10 dB reflection coefficient merely transfers the spectrum to a higher frequency. This is evidenced by a shift from 168.7% at 0% strain to 150.9% at 40% strain. This shift is presumably due to the introduction of an air gap in the meta-substrate during stretching, which leads to a mismatch between Zeff and Z0.

FIG. 4.

Reflection coefficient spectra under strains of 0%–40%.

FIG. 4.

Reflection coefficient spectra under strains of 0%–40%.

Close modal

To enhance the comprehension of the broadband absorption performance, we have provided a visual representation of the loss distribution at three frequencies, i.e., 2.7, 10.2, and 16.8 GHz, as shown in Fig. 5. The losses incurred by the proposed metastructure, viewed from the surface, are mainly attributable to the LLSR. At 2.7 GHz, it can be seen from the concentrated region of loss distribution that introducing a window into the LLSR can effectively increase the losses at lower frequencies, with power losses primarily concentrating at the bottom edge. Conversely, at higher frequencies of 10.2 and 16.8 GHz, there are substantial losses distributed at the top edge of the LLSR, and the overall maximum of the EM energy loss shifts to the edges and corners. The pyramidal structure is mainly responsible for the broadening of the absorption spectrum, whereas absorption in the low frequency range is facilitated by the window region of the LLSR surface. Likewise, the top opening contributes to the increased dissipation of EM energy in the high frequency range. As shown in Fig. 5(b), the distribution pattern of the power loss under 20% tensile strain is analogous to that observed under the original state. This result demonstrates that the proposed metastructure exhibits excellent absorption properties under tensile deformations. In general, a pyramidal structure can display λ/4 resonances within a specific frequency range to dissipate EM energy.42–44 The wave-absorbing properties are attributed to the specific geometrical structures and resistive loss materials.

FIG. 5.

Loss distribution at 2.7, 10.2, and 16.8 GHz.

FIG. 5.

Loss distribution at 2.7, 10.2, and 16.8 GHz.

Close modal
The structure of the metastructure is designed for the polarization insensitive performance under normal incidence. A strong absorption band is clearly revealed from 2.2 to 20 GHz, with a −20 dB reflection coefficient through polarization rotation angles ranging from 0° to 90°. Figure 6(a) illustrates this phenomenon where the absorption curve remains almost constant throughout the working range, regardless of the angle of polarization. This verifies the polarization insensitive performance of the metastructure, which is attributed to the symmetry of the metastructure. When a plane wave illuminates onto the metastructure at an oblique incident angle θ, we can determine the reflection coefficients R(ω)TE and R(ω)TM from the interface for TE-polarized and TM-polarized waves, respectively, using Fresnel's equations,45 
(2)
(3)
where ɛeff and μeff are the relative permittivity and relative permeability of the metastructure, respectively.
FIG. 6.

(a) Simulated absorptivity of the proposed metastructure at different polarization rotation angles under normal incident wave. Simulated absorptivity of the proposed metastructure at different incident angles, illuminated by (b) TE-polarized wave and (c) TM-polarized wave.

FIG. 6.

(a) Simulated absorptivity of the proposed metastructure at different polarization rotation angles under normal incident wave. Simulated absorptivity of the proposed metastructure at different incident angles, illuminated by (b) TE-polarized wave and (c) TM-polarized wave.

Close modal

Figures 6(b) and 6(c) illustrate the reflection coefficient spectra of the proposed metastructure at different oblique incident angles for both TE and TM polarizations. The reflection coefficient of the proposed metastructure for both TE and TM polarizations is below −20 dB at an oblique incident angle of 30°. Moreover, the proposed metastructure retains the reflection coefficients of less than −10 dB for both TE and TM polarizations when the oblique incident angle reaches 70°. It is evident that the proposed metastructure exhibits high absorption under large oblique incident angles for both TE and TM polarizations, which is a crucial attribute for metastructures.

Taking advantage of the excellent flexibility of the proposed meta-substrate, the metastructure could be conformally applied to a curved surface. As a proof of concept, the metastructure is applied to the surface of an unmanned aerial vehicle (UAV), as shown in Fig. 7(a). Figures 7(b)7(g) illustrate the monostatic RCS of the UAV and the UAV pasted with the proposed metastructure at 2.7 GHz. The roll and yaw monostatic RCS patterns under horizontal and vertical polarizations demonstrate that the monostatic RCS of the UAV pasted with the metastructure is considerably diminished in comparison to the UAV model, with the exception of the UAV head and tail positions. With regard to the pitch monostatic RCS pattern, the maximum RCS reduction of the UAV pasted with the metastructure is 30.5 dB, and it exhibits excellent microwave-invisibility capacity for incoming waves at all angles of incidence. To demonstrate the broadband RCS reduction performance of the metastructure, the fabricated sample is applied on both the planar and cylindrical surfaces, as shown in Fig. 7(h). The planar structure achieves a −20 dB RCS reduction from 2.3 to 20 GHz, compared with the cylindrical structure, which achieves a −15 dB RCS reduction from 2 to 20 GHz, as shown in Fig. 7(i).

FIG. 7.

Microwave-invisibility capacity of the metastructure. (a) UAV pasted with a flexible metastructure. (b)– (d) Monostatic RCS of the UAV and the UAV with the metastructure for the horizontal polarization at (b) roll, (c) pitch, and (d) yaw angles. (e)–(g) Monostatic RCS of the UAV and the UAV with the metastructure for the vertical polarization at (e) roll, (f) pitch, and (g) yaw angles. (h) Photographs and (i) monostatic RCS reduction curve of the metastructure conformally applied to a planar and a cylindrical surface.

FIG. 7.

Microwave-invisibility capacity of the metastructure. (a) UAV pasted with a flexible metastructure. (b)– (d) Monostatic RCS of the UAV and the UAV with the metastructure for the horizontal polarization at (b) roll, (c) pitch, and (d) yaw angles. (e)–(g) Monostatic RCS of the UAV and the UAV with the metastructure for the vertical polarization at (e) roll, (f) pitch, and (g) yaw angles. (h) Photographs and (i) monostatic RCS reduction curve of the metastructure conformally applied to a planar and a cylindrical surface.

Close modal

To experimentally validate the absorption performance of the proposed broadband and flexible metastructure, a fabricated sample containing 20 × 20 units with a total size of 290 × 290 mm2 was measured. The meta-substrate was 3D printed (using Raise 3D Pro3) under an unstretched condition from the TPU 95A material. All the ITO films were pasted on the meta-substrate to achieve the metastructure functional elements. For experimental characterization of the fabricated metastructure sample, we performed measurements of reflection coefficients across a frequency range of 1–18 GHz using an arch-method measurement setup, as shown in Fig. 8(a). In this experiment, we employed a pair of linearly polarized horn antennas, which were linked to a Ceyear 3674D vector network analyzer (VNA) via a 50 Ω coaxial cable. In this configuration, the antennas served the dual function of an emitter and a receiver, respectively. The processing of all measured scattering parameters allows the extraction of the reflection coefficients within the operating band.46,47

FIG. 8.

(a) Photographs of the measurement setup. Measured and simulated reflection coefficient spectra of the proposed metastructure for (b) TE-polarized wave and (c) TM-polarized wave. Measured and simulated reflection coefficient spectra of the proposed metastructure under (c) 20% strain and (d) 40% strain.

FIG. 8.

(a) Photographs of the measurement setup. Measured and simulated reflection coefficient spectra of the proposed metastructure for (b) TE-polarized wave and (c) TM-polarized wave. Measured and simulated reflection coefficient spectra of the proposed metastructure under (c) 20% strain and (d) 40% strain.

Close modal

The reflection coefficients of the proposed metastructure under TE and TM polarizations at different incident angles were measured, as shown in Figs. 8(b) and 8(c). The reflection coefficient was found to be less than −20 dB from 2.2 to 18 GHz under normal incidence, as evidenced by both the measured and simulated results. For a larger oblique incident angle of 70°, the proposed metastructure exhibited efficient performance with a reflection coefficient of less than −10 dB from 3.4 to 18 GHz. The measured reflection coefficients demonstrated a high degree of agreement with the simulated results.

As illustrated in Figs. 8(d) and 8(e), the reflection coefficients were measured in the stretching states under normal incidence. The proposed metastructure exhibits a −10 dB reflection coefficient spectrum from 2.1 to 18 GHz at 20% strain, with a frequency shift toward higher frequencies of 0.5 GHz at 40% strain. In summary, the proposed metastructure exhibits considerable stretchability and a reflection spectrum with a −10 dB bandwidth that is almost invariant. In practical situations, the varying shapes of the targets will benefit from our proposed metastructure.

We have introduced three indicators to estimate the thickness, bandwidth, and oblique incidence stability performance and to facilitate comparison with the previously reported works. A practical research on the metastructure has mainly concentrated on the broadband absorption performance in the thinnest possible structure, in which the actual thickness of the proposed metastructure h = 32.3 mm, and the Planck–Rozanov limit indicated a minimum thickness of the metastructure, which is given by
(4)
where λmax and λmin are the maximum wavelength and the minimum wavelength of the operating band, respectively. By plugging the measured reflection coefficient spectrum of the proposed metastructure into Eq. (4), we get hmin = 21.7 mm, and the causality ratio defined by hc = h/hmin = 1.44.
The second indicator is the relative bandwidth, defined by
(5)
where fmax and fmin are the maximum and minimum frequencies, respectively. In our work I, fmin = 2.2 GHz and fmax = 20 GHz with the reflection coefficient, |S11| < −20 dB, so FBW = 160.4%.

The third indicator is the oblique incident angle of θ; we will examine the impact of oblique incident waves for both TE-polarized and TM-polarized waves on reflection coefficients within the framework of Eqs. (2) and (3).

Based on these three indicators, we can comprehensively evaluate the overall performance of the proposed metastructure. Table II shows the performance comparison between our proposed metastructure and some reported typical works to better understand the performance of our metastructure. We noted that the FBW in Table II is the measured 90% absorptivity bandwidth under the condition of normal incidence. In the references, most of the microwave-absorbing structures only provide the simulation results of large angle absorption, so the angle absorption stability adopts the simulation results. The proposed metastructure offers several advantages, including polarization insensitivity, oblique incidence stability, high absorptivity, and flexible properties.

TABLE II.

Comparison with other works.

ReferenceOperating band (GHz)FBW (%)Thickness (mm)h/hmin|S11| (dB)Angle stability (TE/TM)
10 3.6–13.9 117.3 1.13 <−10 0° – 45°/0° – 45° 
14 5.9–35.9 143.5 1.21 <−10 0° – 40°/0° – 40° 
17 3.0–40.0 172.1 14.2 1.05 −19.4 0° – 45°/0° – 45° 
23 4.3–11.1 88.3 9.7 1.94 <−10 0° – 60°/0° – 60° 
31 1.5–4.5 100.0 22 1.41 <−10 0° – 45°/0° – 82° 
33 1.4–40.0 186.0 22.9 1.03 <−10 45° – 70°/0° – 70° 
This work 2.2–20.0 160.4 31.3 1.44 <−20 0° – 70°/0° – 70° 
ReferenceOperating band (GHz)FBW (%)Thickness (mm)h/hmin|S11| (dB)Angle stability (TE/TM)
10 3.6–13.9 117.3 1.13 <−10 0° – 45°/0° – 45° 
14 5.9–35.9 143.5 1.21 <−10 0° – 40°/0° – 40° 
17 3.0–40.0 172.1 14.2 1.05 −19.4 0° – 45°/0° – 45° 
23 4.3–11.1 88.3 9.7 1.94 <−10 0° – 60°/0° – 60° 
31 1.5–4.5 100.0 22 1.41 <−10 0° – 45°/0° – 82° 
33 1.4–40.0 186.0 22.9 1.03 <−10 45° – 70°/0° – 70° 
This work 2.2–20.0 160.4 31.3 1.44 <−20 0° – 70°/0° – 70° 

This article presents a proof of concept for the use of auxetic metamaterials as a flexible meta-substrate in broadband metastructures. The design strategy for the meta-substrate ensures isotropic expansion and contraction of the metastructure by transferring the deformations onto 3D pyramidal unit rotation and soft hinges stretching. The proposed metastructure, consisting of a PMA unit and a stretchable meta-substrate, demonstrates a high absorption spectrum spanning from 2.2 to 20 GHz, with oblique incidence stability performance for both TE and TM polarizations. Furthermore, the proposed metastructure exhibited strain insensitivity, with a mere 1.1 GHz shift in the −10 dB reflection spectrum observed under 40% tensile strain. It has also been demonstrated that the proposed metastructure could conformally wrap the UAV, indicating that our developed metastructure would provide the potential for conformal stealth designs for complex targets.

This work was supported by the Foundation of Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education (No. 2022ML0015).

The authors have no conflicts to disclose.

Feihong Lin and Yu Bai contributed equally to this work.

Feihong Lin: Conceptualization (equal); Software (equal); Writing – original draft (equal). Yu Bai: Conceptualization (equal); Methodology (equal). Jiawei Chen: Visualization (equal); Writing – review & editing (equal). Zhongming Yan: Conceptualization (equal); Funding acquisition (equal); Writing – review & editing (equal). Hongcheng Zhou: Data curation (equal); Validation (equal). Yu Wang: Methodology (equal); Supervision (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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