Pursuing highly efficient broadband absorption performance has always been a central focus in the electromagnetic absorbing materials and devices community. Remarkably, metamaterials have provided unprecedented material options to achieve near-perfect absorption performance due to their optimization of impedance-matching characteristics, enabling extensive applications in the fields of stealth technique^[1-2], energy harvesting^[3-5], thermal emission control^[6-8], image sensing^[9-11], and so on. Early research indicated that an MA-based metal-insulator-metal configuration can flexibly control its electric or magnetic resonance to achieve near-perfect absorption^[12]. Then, with the development of subwavelength structure, a series of MAs with single-, dual-, and multi-band absorption were raised gradually, contributing to the continued boom in MA research^[13-21].

Achieving broadband absorption has long been an important goal in MA application. Remarkably, the scheme of overlapping multiple absorption peaks into continuous ones in a spectrum was first proposed to achieve broadband MA. The multiple resonators based on metal-insulator-metal configuration were assembled in the same plane^[22-25] or along the vertical direction^[26-29]; however, when they were adopted, they faced challenges in meeting both broadband absorption requirements and maintaining a lightweight design simultaneously. Meanwhile, it has been shown that dispersion engineering of multiple resonances by loading special material can also provide an efficient approach to broadband MA^[30-35]. For example, using the standing-up ohmic sheet as a subwavelength unit cell, no-planar resistive MA can excite absorption peaks with a smoother profile at adjacent frequencies in the extremely wide frequency band^[30-32]. Owing to its strong ohmic loss, resistive MA based on an ohmic sheet exhibits extreme broadband absorption while remaining lightweight. However, the broadband absorption of resistive MA is easily disturbed by the resistance value of the ohmic sheet. Meanwhile, through further research on dispersion engineering, a metallic PS based on gradually varied wire arrays adhered to the side of a loss dielectric substrate has been demonstrated to inspire spoof surface plasmon polaritons (SSPPs) in microwave frequency, contributing more diversified broadband and highly efficient absorption performance^[36-39]. By contrast, the proposed PAS offers clear advantages in optimizing broadband absorption performance comprehensively.

In this paper, we attempt to add the PS on the side of no-planar resistive MA to further improve the operating bandwidth, absorption efficiency, and performance stability. Our investigation shows that the multiple resonances with the enhanced electric field can be excited on the surface of the ohmic sheet. Therefore, more ohmic loss takes effect in resistive PAS by the efforts from the enhanced electric field and ohmic sheet, contributing to stability enhancement in broadband absorption. At last, two samples were fabricated according to the simulated models, and the agreement between simulation and measurement validated our comprehensive scheme. With the aid of two absorbing mechanisms, our strategy provides an efficient way to enhance the compositive absorption performance, enabling a wide range of applications in radar stealth technology, electromagnetic shielding, energy harvesting, and so on.

As mentioned above, resistive MA based on an ohmic sheet exhibits extreme broadband absorption and is lightweight. Here, we will first discuss no-planar resistive MA. As the schematic shows in Fig. 1(color online), the dielectric substrate with the thickness t_f and height d was employed to achieve a squared grid. The side length of each grid unit cell is p. Then, four trapezoid ohmic sheets were printed on the inside of the grid along the clockwise direction, and one side of each trapezoid ohmic sheet was always close to the side of the dielectric substrate. Each trapezoid ohmic sheet had the upper edge length a₁, the bottom edge length a₂, the height d, and the resistance value f_z. The square metal plate was employed as a backplane on the bottom. The metal used was copper with an electric conductivity of 5.8×10⁷ S/m, and the permittivity of the dielectric substrate was 4.3(1−j·0.025). When giving the aforementioned parameters as follows: p=6.0 mm, d=5.0 mm, t_f=0.8 mm, a₁=2.6 mm, a₂=17.6 mm, and f_z=250 Ω/sq. The simulated result shows that the proposed no-planar MA achieves broadband absorption at an efficiency of more than 90% in the frequency band from 10.6 to 40.0 GHz under the normal incidence. Notably, the broadband absorption performance of the proposed resistive MA is easily affected by the resistance value of the ohmic sheet. As shown in Fig. 1(c), with the increased f_z from 100 to 250 Ω/sq, the absorption bandwidth concentrating on lower frequency was accordingly decreased. Meanwhile, significant improvement of absorption efficiency was observed during the middle-frequency band around 16.1−23.4 GHz. Moreover, accurately controlling the resistance value of the ohmic sheet in scale manufacturing is difficult, making it hard to achieve stable and efficient broadband absorption by relying solely on the resistive MA method.

Meanwhile, Fig. 2(a) (color online) shows the schematic of the bent-wire-shaped structure made of metal wire and a dielectric substrate. The unit cell of the bent-wire-shaped structure was obtained by bending the straight wire 90° at the center point; thus, the two components had the same length along horizontal and vertical directions. The bent wire with the total length l, width w, and thickness t_c was adhered to the dielectric substrate with the length a and height d. Then, the structural parameters were given as follows: a=6.0 mm, d=5.0 mm, t_f=0.4 mm, t_c=17.0 μm, w=0.1 mm. The dispersion relationship of the bent-wire-shaped structure with a different length l can be simulated by the eigenmode solver in CST Microwave Studio. In the modeling process, the metal was a perfect electric conductor, and the substrate had a relative dielectric constant of 4.3. To achieve an equivalent electromagnetic medium consisting of the bent-wire-shaped unit cell, the periodic boundary conditions were used along x and y while the plane wave with k-vector was incident along z direction. As the simulated results shown in Fig. 2(b) (color online), the ordinate represents the frequency change, while the horizontal coordinate represents the normalized k-vector change. Under the excitation of x-polarized waves, there are always two cut-off frequencies during the frequency of 0−30.0 GHz. All of the dispersion curves drift away from the light line and then approach their cut-off frequency as the k-vectors increase. Moreover, as shown in Tab. 1, with the increase in metal wire length from 7.0 mm to 10.0 mm, the first cut-off frequencies gradually decrease from 14.5 to 10.6 GHz, while the second cut-off frequencies gradually decrease from 24.9 to 20.4 GHz. This conclusively demonstrates that by adjusting the length of the metal wire, the cut-off frequency can be flexibly controlled in the bent-wire-shaped structure.

On illumination, multiple bent wires with gradually varied lengths as well as fixed spacing were adhered to each side of the dielectric grid. Fig. 3(a) (color online) shows the longest bent wire had the length l₂=9.9 mm, comprised of a vertical section of 4.9 mm and a horizontal section of 5.0 mm. The following twenty-four bent wires with the same reduced length of 0.4 mm were also adhered to the dielectric substrate. For each bent wire array, the width, the period, and the thickness of the meandered wire were w=0.1 mm, s=0.2 mm, and t_c=17.0 μm, respectively. The period of the adjacent bent wire was always s=0.2 mm. Then, the achieved metal-dielectric combinations were rolled up as squared unit cells. The side length of the squared one was p=9.2 mm. The dielectric substrate was t_f=0.8 mm thick and d=10.0 mm tall. The backplane of bent-wire-shaped PS was air and the S-parameter spectra were calculated by the commercial software of CST Microwave Studio. As shown in Fig. 3(b) (color online), there was broadband suppression of more than 5 dB in the reflection spectrum from 9.5 GHz to 40.0 GHz and transmission spectrum from 17.0 GHz to 40.0 GHz under the normal incidence. Accordingly, the absorption spectrum of bent-wire-shaped PS can be obtained based on A(ω) = 1−R(ω)−T(ω) = 1−|S₂₁|²−|S₁₁|², where A(ω), |S₁₁|², and |S₂₁|² are the absorbance, reflectivity, and transmissivity, respectively. As shown in Fig. 3(c), the results demonstrate that bent-wire-shaped PS can achieve almost continuous absorption with an efficiency of more than 80% in the frequency band from 10.3 to 40.0 GHz.

Owing to the enhancement of the electric field inspired by dispersion engineering, bent-wire-shaped PS was loaded into no-planar resistive MA to further improve the operating bandwidth, absorption efficiency, and stable absorption profile. As shown in Fig. 4 (color online), the trapezoid ohmic sheet was printed on each side of the dielectric grid, then the bent wire array was also printed on each ohmic sheet. For each unit cell, there were four ohmic sheets and four bent wire arrays which were always arranged clockwise. The side length of each unit cell was P. The thickness and the height of the dielectric substrate were t_f and d. For the trapezoid ohmic sheet, the upper edge length, the bottom edge length, the height, the thickness, and the resistance value are a₁, a₂, d, and f_z, respectively. For the bent wire array, the width, the period, and the thickness of the meandered wire are w, s, and t_c. Each array has twenty-five bent wires with lengths ranging from l₁ to l₂. When giving the aforementioned parameters as follows: p=6.0 mm, t_f=0.8 mm, d=5.0 mm, a₁=2.6 mm, a₂=17.6 mm, f_z=250 Ω/sq, w=0.1 mm, s=0.2 mm, t_c=17.0 μm l₁=0.2 mm and l₂=9.9 mm, the simulated result shows that the proposed resistive PAS can achieve broadband absorption with an efficiency of more than 90% during the frequency band from 7.8 GHz to 40.0 GHz, which is a significant improvement of lower-frequency absorption as compared with resistive MA. Here, the comprehensive evaluations of their broadband absorption can be carried out by the figure of merit (FOM). According to the Rozanov limit^[40-41], the FOM is calculated following the relation FOM=d/(λ_L−λ_H), where d is the sample thickness, λ_L and λ_H are the lower-bound wavelength and high-bound wavelength of the absorption band. Hereby, the smallest value of FOM is always expected for desired broadband absorption. Calculated results show that the FOM values of resistive MA and resistive PAS are 0.24 and 0.16. The resistive PAS proposed in this paper exhibits outstanding improvement in broadband absorption, especially for low-frequency absorption. Furthermore, the simulated absorption spectra in Fig. 5(a) (color online) show that the absorption bandwidth remains almost constant as the resistance value f_z decreases from 250 Ω/sq to 100 Ω/sq.

To better understand its absorption principle, the electric field E_y distributions of bent-wire-shaped PS were monitored at the frequencies of 10.0, 15.0, 20.0, and 25.0 GHz in Fig. 5(b) (color online). For the lower frequency of 10.0 GHz, one resonance corresponding to several adjacent bent wires was obtained, which contributed to the clear enhancement of the local electric field. The enhanced electric field on the metal-dielectric interface took effect with the loss from the dielectric substrate, and highly effective absorption was achieved following the relation P_abs=1/2(ωε″+σ)|E|², where ω was the angular frequency, ε″ was the imaginary part of permittivity, r was the conductivity, and E was the total electric field. For the higher frequencies of 15.0 GHz, 20.0 GHz, and 25.0 GHz, there were always two kinds of resonances corresponding to the entire wire on the top layer and the remaining half wire on the bottom layer. The two resonances worked together to contribute highly efficient absorption at each frequency. Each resonant frequency was always consistent with the former cut-off frequency. Also, the electric field E_y distributions of resistive PAS were also monitored at the frequencies of 10.0, 15.0, 20.0, and 25.0 GHz, as shown in Fig. 5(a). Owing to the dispersion engineering of bent-wire-shaped PS, the inspired localized surface-wave-like electromagnetic oscillation took effect at those frequency points on the loss substrate of the ohmic sheet, and thus broadband and highly efficient absorption performance was achieved. Therefore, it can be concluded that the resistive PMA proposed in this paper achieves optimal performance with comprehensive consideration of the operating bandwidth, absorption efficiency, and stable absorption profile.

To validate the proposed resistive PAS, two samples with the ohmic sheet of f_z=100 Ω/sq and f_z=250 Ω/sq were fabricated, and the other structure parameters remained exactly the same. As shown in Fig. 6, one sample with the ohmic sheet f_z=100 Ω/sq had the dimension of 140.0 mm×140.0 mm, including of 196 unit cells. In the fabrication process, the rectangular dielectric strips were cut with periodical grooves by a numerical control tool and then assembled on the copper plane through a squared grid method. On each side of the dielectric substrate, the metallic bent wire arrays were printed at regular intervals by circuit board printing technology. Meanwhile, the ohmic sheets with the resistance values of f_z=100 Ω/sq and f_z=250 Ω/sq were printed on the ultra-thin dielectric films respectively by screen printing technology and then adhered to the metal-dielectric grid at regular intervals by epoxy resin. The experimental measurements of the two models were performed in an anechoic chamber. The measurement system was based on an Agilent 8720ET network analyzer with five pairs of broadband antenna horns working in the frequency bands of 5−8, 8−12, 12−18, 18−26, and 26−40 GHz. Figs. 7(a) and 7(b) (color online) present the measured absorption spectra along with their simulated results. The strong agreement between simulation and measurement further validates the design concept outlined in this paper.

In summary, we describe the achievement of resistive PAS based on a comprehensive scheme that provided an efficient path to absorption performance optimization, contributing more potential applications. The proposed resistive PAS was obtained based on the integration of no-planar resistive MA and plasmonic structure. The theoretical investigation demonstrated that multi-resonance can be excited based on spatial dispersion engineering of PS, causing the localized electric field to take effect on the surface of the resistive ohmic sheet. The proposed approach counters the defect of the broadband absorption performance being easily affected by its constituent ohmic sheet in resistive MA. As proof, two samples were fabricated according to the simulated models. The strong agreement between simulations and experimental measurements demonstrates that resistive PAS can always achieve broadband and highly efficient absorption performance during the frequency band from 8.0 to 40.0 GHz with the ohmic sheet ranging from 100 to 250 Ω/sq.