1. Introduction

Metamaterial absorbers (MAs) are artificial composite structure capable of efficiently dissipating the electromagnetic energy into heat, resulting in the significant reduction of the reflected wave along the echo direction. Owing to the diversified absorption and flexible design, MAs have always been pursued for more extensive applications, including electromagnetic cloaking [1,2], stealth technique [3,4], thermal photovoltaic [5,6], sensing [7,8], and so on. Originally, the first MA based the configuration of metal-insulator-metal was proposed which can control its electric or magnetic resonance freely for near perfect absorption at any frequency [9]. Then, with the emerging surface subwavelength structure, a series of single-, dual-, and multi-band MAs were flexibly obtained, which exhibit the obvious advantages in thin thickness, high absorptive, and flexile expansibility [10–15]. However, driven by a wide range of applications, MAs with simultaneous broad operating bandwidth and high absorbing efficiency have always been persistently pursued in this topic. Aiming at this, more and more efforts are devoted to developing the broadband MA. One is based on multi-layered resonators with gradually varied period stacked together in vertical direction which can efficiently merge adjacent absorption peaks into continuous one in spectrum [16–20]. Based on this, the desired broadband absorption can be achieved at the sacrifice of thin thickness and light weight. On the other hand, deliberately controlling the dispersion and dissipation of the designed MA also provides another approach to broadband absorption, such as developing the subwavelength structure with low conductivity film [21–24], loading lumped resistor to metallic resonator [25–27], or replacing the dielectric substrate with magnetic materials [28–30].

Recently, with the aid of dispersion engineering, plasmonic structures have been demonstrated to afford more material options to the manipulation of electromagnetic waves by virtue of SSPP [31–34], in particular for broadband absorption [35,36]. For example, the straight wire array with gradually wire length adhered to the high-loss dielectric substrate can directly achieve the continuous and highly effective absorption, and the obtained absorption band can be customized by optimizing the length of straight wires [35]. Meanwhile, inspired by the reduced interval of adjacent resonances, PAS based on bent wire array is also proposed which can efficiently merge the fundamental and high-order absorption bands into ultra-wideband one [36]. However, the former design with the merging of multi-absorption bands can only extend the absorption band to the higher frequency, and the further enhancement of low frequency absorption is hard to be carried out with no increase of thickness. At the same time, limited by the length, the density and the structure of wire element, the contradiction between broad operating bandwidth and high absorbing efficiency in PAS has always been hard to be perfectly overcome.

In this paper, a comprehensive scheme of PAS is proposed which can integrate more multiple adjacent resonances for outstanding low-frequency absorption enhancement via multistage dispersion engineering. Our investigation shows that the multi-absorption peaks with the reduced intervals can be flexibly gained at the lower frequency by extending the bent wire to the 3D space. On such basis, PAS consisting of 3D bent wire array with gradually varied length is employed which assembles multiple adjacent absorptions in spectrum via dispersion engineering of SSPP. Then, to fill up the discontinuity of absorbing spectrum, combined 3D PAS based on spatial dispersion optimization is further proposed which combines multi-bent wire arrays with deliberately regulated period on the same plane, contributing to the enhancement of absorbing efficiency in the operating frequency band. Simulated result shows that the proposed combined 3D PAS can achieve extremely broadband absorption with the efficiency over 90% in the frequency band of 6.7-35.3GHz. At last, a sample of the proposed combined 3D PAS is fabricated, and the good agreement between simulation and measurement validates our design concept.

2. Theoretical analysis

As we know, the straight-wire-shaped MA has been demonstrated to excite multi-absorption peaks corresponding to fundamental and high-order resonances under the normal incidence, and their frequencies always follow: f_n = f₀·(2·n + 1), where f₀ is the frequency of fundamental resonance, f_n is the frequency of n-order resonance. When developing the straight wire into bent one, the multi-absorption peaks of the bent-wire-shaped MA in spectrum will be changed accordingly. As the schematic shown in Fig. 1(a), the three parallel wires are bent with 90° in the vertical plane of y-o-z, and then adhered to the side of the standing-up dielectric substrate periodically. As a simplified model, the vertical component has the same length with the horizontal component. Each unit cell is backed with squared metal backplane and the side length of squared one is p₁. For the thin dielectric substrate, the length, the thickness and the height are p₁, t₁ and d. For each bent wire, the length, the thickness, the width and the period are l₁, t_c, w and s. respectively. Numerical simulation is performed in the commercial software of CST Microwave Studio. The metal used in the model is copper with the electric conductivity of 5.8 × 10⁷S/m, and the permittivity of the dielectric substrate is 4.3(1-j·0.025). When giving the structural parameters of unit cell as follows: p₁ = 5.0mm, d = 5.0mm, t₁ = 0.8mm, t_c = 17.0μm, l₁ = 6.0mm, s = 0.1mm, and w = 0.2mm, the vertical bent-wire-shaped MA can achieve two absorption peaks at the frequency of 18.1 and 31.2GHz under the normal incidence of y-polarized wave in Fig. 1(b). With the increased length l₁ from 6.0 to 9.0mm, the two absorption peaks will move to the lower frequency accordingly, and the frequency ratio of the two absorption peaks always approximates to 1:2. Similarly, as the schematic shown in Fig. 1(d), the three parallel wires are bent with 90° in the horizontal plane of x-o-y, and a bent dielectric substrate with half thickness t₂ = 0.4mm are introduced on the squared metal backplane as substrate supporter. Here, the two components along x-axis and y-axis directions still have the same length, and the other structural parameters are consistent with the former model. Under the normal incidence, two absorption peaks are inspired by the horizontal bent-wire-shaped MA at the frequencies of 17.5 and 29.0GHz in Fig. 1(e). With the increased length l₂ from 6.0 to 9.0mm, the two absorption peaks will also move to the lower frequency accordingly. The frequency ratio of the two absorption peaks always approximates to 1:2. Based on this, it is obvious that the interval of adjacent absorption peaks can be reduced by bending the partial component of wire out of the electric direction. Based on the above discussion, when developing the bent wire structure to 3D space, multi-absorption of the lower frequency can be achieved with no increase of thickness. As the schematic shown in Fig. 1(g), the horizontal bent wires in Fig. 1(d) is attempted to be further extended to z-axis direction, and the total length l₃ of the 3D bent wire is twice as long as the original one. It is noted that the four components along x-axis, y-axis and z-axis directions have the same length. When giving the structural parameters as follows: p₃ = 5.0mm, d = 5.0mm, t₃ = 0.4mm, t_c = 17.0μm, l₃ = 12.0mm, s = 0.1mm and w = 0.2mm, simulated result shows that the 3D bent-wire-shaped MA can achieve three absorption peaks at the frequencies of 10.6, 21.6 and 35.1GHz in Fig. 1(h). With the increased length l₃ from 12.0 to 18.0mm, the three absorption peaks will move to the lower frequencies, and their frequency ratio is always approximates to 1:2:4.

 

Fig. 1 (a) Schematic of the vertical bent-wire-shaped MA and (b) simulated absorption spectra with different length l₁. (c) Calculated dispersion relationship of the vertical bent wire structure. (d) Schematic of the horizontal bent-wire-shaped MA and (e) simulated absorption spectra with different length l₂. (f) Calculated dispersion relationship of the horizontal bent wire structure. (g) Schematic of 3D bent-wire-shaped MA and (h) simulated absorption spectra with different length l₃. (i) Calculated dispersion relationship of the 3D bent wire structure.

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The dispersion relationships of the aforementioned three bent wire structures are also calculated by the eigenmode solver in CST Microwave Studio. In the calculation process, one unit of single bent wire adhered to the lossless dielectric substrate is employed here and the periodic boundary conditions are used along x, y, and z directions. As show in Fig. 1(c), for the different length l₁ of vertical bent wire, there are always two cut-off frequencies. With the increased frequency, the two dispersion curves will gradually drift away from the light line and then get cut-off at two certain frequencies. When the frequency is infinitely close to the cut-off, the maximum value of k-vector will produce the strongly localized surface wave, and the strongly localized surface wave always equipped with electric field enhancement. Then, the enhanced electric field and the enough dielectric loss work together, contributing to highly effective absorption close to the two cut-off frequencies. Thus, by comparing the frequencies of absorption peaks in Fig. 1(b) and the cut-off frequencies in Fig. 1(c), it is evident that the frequencies of the two absorption peaks are always infinitely close but always lower than the cut-off frequencies. Then, the dispersion relationships of the horizontal bent wire structure and the 3D bent wire structure are also discussed in Figs. 1(f) and 1(i), respectively. The obtained results are almost consistent with the former.

Notably, on top of the multi-absorption peaks can be achieved at the lower frequencies by developing the bent wire into 3D space, the obvious decrease of absorbing efficiency for the absorption peaks also attracts our attention. Aiming at this, the proposed 3D bent-wire-shaped MA based on different number of 3D bent wire are calculated in Figs. 2(a)-2(d), respectively. With the increased number of 3D bent wire, it is obvious that the frequencies of multi-absorption peaks are almost unchanged. For the MA based two 3D bent wires, simulated absorption spectra in Fig. 2(a) show that the absorbing efficiency is ranged from 11.0 to 37.0% with the 3D bent wires increase from 12.0 to 18.0mm. By contrast, for the MA based five 3D bent wires, simulated absorption spectra in Fig. 2(d) show that the absorption efficiency is obviously enhanced ranging from 56.0 to 72.0% with the 3D bent wires increase from 12.0 to 18.0mm. The former investigation shows that frequency of absorption peak is always low than the cut-off frequency, and thus the inspired surface wave can still propagate through the bent wire structure. When increasing the number of meandered wires, the propagation of surface wave will suffer from multiple power loss and the absorptivity value is bound to increase accordingly. Thus, it can be concluded that the optimized design of multiple wire in the proposed design can provide an effective way to achieve dispersion engineering of SSPP for diversified absorption performance.

 

Fig. 2 Simulated absorption spectra of the proposed MA based on (a) two 3D bent wires, (b) three 3D bent wires, (c) four 3D bent wires and (d) five 3D bent wires with different length l₃.

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Meanwhile, to get insight into the multi-absorption performance, the surface current distributions of the proposed 3D bent-wire-shaped MAs with different length l₃ are monitored at their absorption frequencies in Figs. 3(a)-3(d), respectively. As shown in Fig. 1(a), surface current on the 3D bent wire are always continuous and consistent at the first absorption peak frequency of 6.5GHz which is marked by the yellow line with the arrow. Meanwhile, the enhanced surface current almost concentrates on the entire bent wire. Then, for the second absorption peak frequency of 15.6GHz, there always have two isolated surface current oscillation on the 3D bent wires in the opposite direction which is marked by the orange line with the arrow. And the enhanced surface current of each oscillation on the 3D bent wire occupies almost half of the total length. Moreover, for the third absorption peak frequency of 27.8GHz, there have four isolated surface current oscillations on the 3D bent wires and the adjacent oscillations are always in the opposite direction, which is also marked by the blue line with the arrow. And the obviously enhanced surface current concentrates on the component along y-axis direction which occupies a quarter of total length. For the other three models of 3D bent-wire-shaped MA with the length l₃ = 16.0, 14.0 and 12.0mm, their corresponding surface current distributions in Figs. 3(b)-3(d) are almost consistent with the former one. According to the enhanced surface current distribution, the achieved frequencies of the three absorption peaks must follow the ratio of 1:2:4 which contribute to the reduced interval of multi-absorption peaks in spectrum compared to the original straight-wire-shaped MA.

 

Fig. 3 Surface current distributions of the 3D bent-wire-shaped MAs with the length of (a) l₃ = 18.0mm, (b) l₃ = 16.0mm, (c) l₃ = 14.0mm and (d) l₃ = 12.0mm at their corresponding absorption frequencies.

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3. Dispersion engineering of SSPP in 3D PAS

Inspired by the aforementioned discussion, the PAS consisting of 3D bent wires with the gradually varied length are proposed which attempts to assemble multiple adjacent absorptions in spectrum via dispersion engineering of SSPP. The schematic of the 3D PAS is shown in Figs. 4(a) and 4(b). To achieve polarization independent absorption, the dielectric substrate with the thickness t_f and height d are introduced here to construct squared grid. The side length of the squared dielectric grid as well as the squared metal backplane is p. For each unit cell, 3D bent wires with the gradually varied length ranging from l₁ to l₂ are assembled together, and then adhered to the bent surface of the dielectric grid periodically. Here, the thickness, the width and the period of the 3D bent wires are t_c, w and s, respectively. The structural parameters are given as follows: p = 5.0mm, d = 5.0mm, t_f = 0.8mm, l₁ = 1.1mm, l₂ = 17.6mm, t_c = 17.0μm, w = 0.1mm and s = 0.2mm. Under the normal incidence, simulated result in Fig. 4(c) shows that multiple adjacent absorptions inspired by our proposed 3D PAS can be assembled together in the frequency band of 7.0-40.0GHz. However, it is a pity that the adjacent absorption peaks are hard to be further overlapped for the achievement of broadband and highly effective absorption even if we adjust the side length p from 4.0 to 6.0mm.

 

Fig. 4 (a) Schematic of the 3D PAS unit cell. (b) Prospective view of the 3D PAS. (c) Simulated absorption spectra of the proposed 3D PAS with different period p. (d) Power loss distributions of the proposed 3D PAS at the highly effective absorption frequencies of 7.0, 13.0, 18.0 and 26.0GHz. (e) Power loss distributions of the proposed 3D PAS at the absorption frequencies of 11.0, 14.0, 15.0 and 16.0GHz.

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To better understand the dispersion engineering of SSPP, the power loss distributions of the proposed 3D PAS are monitored at the highly effective absorption frequencies of 7.0, 13.0, 18.0 and 26.0GHz in Fig. 4(d). For the low frequency around 7.0GHz, the fundamental resonance corresponding to the entire bent wire contributes to the highly effective absorption. For the frequency between 7.0 and 13.0GHz, there exist two kinds of resonances corresponding to the entire bent wire on the upper layer and the half bent wire on the lower layer, respectively. The two resonances work together contributing to highly effective absorption at certain frequencies. For the high frequencies from 13.0 to 18.0GHz, three resonances corresponding to their bent wire at different height are all inspired, contributing to highly effective absorption as well. Further, for the higher frequencies from 18.0 to 40.0GHz, more fundamental and higher-order resonances are simultaneously inspired, and multi-resonance work together contributing to near perfect absorption. Thus, 3D bent wire array with gradually varied length adhered to high-loss substrate can excite multiple resonances overlapped together in a wider frequency band by virtue of SSPP, contributing to the integration of multiple adjacent absorptions. Meanwhile, aiming at the relatively low absorbing efficiency, the power loss distributions of the proposed 3D PAS are also monitored at the frequencies of 11.0, 14.0, 15.0 and 16.0GHz in Fig. 4(e). From the power loss distributions, some bent wires on the middle or bottom layer take effect with less power loss enhancement due to their wire lengths not exactly match to the frequencies of resonances, and thus the proposed 3D PAS cannot provide enough absorbing efficiency at these frequencies. Moreover, compared with the former design in the literature [36], not only the length difference between the adjacent bent wires is increased to 0.8mm, but also the total number of 3D bent wires is always small with the existing bent wire density. Thus, the contradiction between expanding operating bandwidth and keeping high absorbing efficiency seems difficult to be perfectly overcome in our proposed 3D PAS.

4. Spatial dispersion optimization in combined 3D PAS

In order to fill up the discontinuity of absorbing spectrum, multi-bent wire arrays with deliberately regulated period are combined again on the same plane which attempts to further increase the multiple resonances in the operating frequency band via spatial dispersion optimization. The schematic of the combined 3D PAS unit cell is shown in Fig. 5(a), the dielectric substrate with the height d and thickness t_f are introduced here to construct a combined dielectric grid, including a small-sized squared enclosure, a large-sized squared enclosure and two rectangular enclosures. Here, the obtained unit cell of combined dielectric grid and the ground metal backplane is squared one with the side length p. For the combined dielectric grid, the side lengths of large-sized and small-sized squared enclosures are a₁ and a₂. Accordingly, the long side and short side of the two rectangular enclosures are also a₁ and a₂. On such basis, there have three kinds of bent surface in each unit cell of combined dielectric grid which can be seen as large-sized bent surface, small-sized bent surface and asymmetric bent surface. The insert I in Fig. 5(a) shows that the 3D bent wire array with the gradually varied length ranging from l₁ to l₂ is adhered to the each bent surface of large-sized enclosure. The insert II shows that another 3D bent wire array with the gradually varied length ranging from l₃ to l₄ is adhered to the each bent surface of small-sized enclosure. While the insert III shows that an asymmetric 3D bent wire with the gradually varied length ranging from l₅ to l₆ is adhered to the each asymmetric bent surface of rectangular enclosure. Herein, the width, the thickness, and the period of meandered wire are w, t_c and s, respectively. After optimization, the investigation shows that the bent wire arrays adhered on the two side of one dielectric substrate should be consistent in direction, while the meandered wire arrays on adjacent substrates should be an opposite direction, as shown in Fig. 5(b). When giving the structural parameters as follows: p = 13.9mm, d = 5.0mm, t_f = 0.8mm, a₁ = 7.6mm, a₂ = 6.3mm, l₁ = 3.4mm, l₁ = 22.8mm, l₃ = 0.8mm, l₄ = 20.2mm, l₅ = 5.6mm, l₆ = 21.5mm, t₁ = 17.0μm, w = 0.1mm and s = 0.2mm, simulated result in Fig. 7(c) shows that the proposed combined 3D PAS can achieve extremely broadband absorption with an efficiency of more than 90% in the frequency band of 6.7-35.3GHz. The averaged absorbing efficiency of our proposed combined 3D PAS during the operating frequency band of 6.7-35.3GHz is 97.2%, which exhibits an obvious enhancement of 12.8% compared with former 3D PAS in Fig. 4(a).

 

Fig. 5 (a) Schematic of the combined 3D PAS unit cell. (b) Overall view of the combined 3D PAS.

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To validate the spatial dispersion optimization, the power loss distributions of the combined 3D PAS are also monitored at the absorption frequencies of 6.7, 12.0, 16.0 and 26.0GHz in Fig. 6. From the power loss distributions, it is evident that combined 3D PAS can excite fundamental resonance of the entire meandered wire around the frequency of 6.7GHz, and the enhanced power loss concentrates on the bent wires of the four sub-arrays with similar length. For the middle frequencies from 6.7 to 12.0GHz, the resonances corresponding to the entire bent wire and half bent wires are inspired by the four sub-arrays, and enhanced power loss takes effect at different heights of the four sub-arrays. For the high frequencies around 16.0GHz, three kinds of resonances take effect simultaneously by the four sub-arrays at different height, respectively. Similarly, for the higher frequencies above 26.0GHz, more multi-resonances including fundamental and high-order ones are also inspired by the four sub-arrays at different height. Comprehensive analysis concludes that more multiple resonances can be inspired by our proposed combined 3D PAS with different spatial distributions via spatial dispersion optimization, and the increased resonances overlapped together in the operating frequency band, contributing to further enhancement of absorbing efficiency compared to the former 3D PAS. Meanwhile, our combined 3D PAS compared with the recent works is discussed in Table 1. The comprehensive evaluations of their absorption band can be carried out by the figure of merit (FOM). According to the Rozanov limit [37,38], 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 absorption band. Hereby, the smallest value of FOM is always expected for extremely broadband absorption, especially for low-frequency absorption enhancement. From the calculated results, it is obvious that our proposed combined 3D PAS gets an optimal choice with respect to the absorption band and thickness. To give an experimental demonstration, a sample of the proposed combined 3D PAS with the dimension of 194.6 × 194.6mm² is fabricated in Fig. 7(a). In the fabrication process, the rectangular dielectric strips are cut with periodical grooves by numerical control tool and then assembled together in combined grid method. Next, the planar bent wire array is printed on ultra-thin and flexible dielectric film and then bent with 90° as 3D bent wire array. With the aid of epoxy resin, 3D bent wire array is adhered to the combined dielectric grid periodically and then backed with metal backplane. The experimental measurement of the absorption properties is performed in an anechoic chamber. As the photograph shown in Fig. 7(b), the measurement system is based on an Agilent 8720ET network analyzer with five pairs of broadband antenna horns working in the frequency bands of 4-8, 8-12, 12-18, 18-26 and 26-40GHz, respectively. Finally, the measured absorption spectrum along with the simulated one are presented in Fig. 7(c), and the excellent agreement between them further validates our design concept.

 

Fig. 6 Power loss distributions of the combined 3D PAS at the absorption frequencies of 6.7, 12.0, 16.0 and 26.0GHz.

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Table 1. Simulated results of our combined 3D PAS and recent works.

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Fig. 7 (a) Fabricated sample of the combined 3D PAS. (b) Photograph of the test environment. (c) Simulated and measured absorption spectra of the combined 3D PAS.

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5. Conclusions

In summary, a comprehensive scheme of combined 3D PAS has been demonstrated to integrate more multiple adjacent resonances in a wider frequency band via multistage dispersion engineering, contributing to broadband absorption enhancement, especially for outstanding low-frequency absorption. The fundamental investigation shows that multi-absorption peaks with the reduced intervals can be flexibly gained at the lower frequency by extending the bent wire to the 3D space. Based on this, PAS consisting of 3D bent wire arrays with gradually varied length is proposed which can assemble multiple adjacent absorptions in spectrum via dispersion engineering of SSPP. Then, to fill up the discontinuity of absorbing spectrum in the 3D PAS, multi-bent wire arrays with deliberately regulated period are combined again on the same plane which makes full use of spatial dispersion optimization for further enhancement of absorbing efficiency. Owing to the multistage dispersion engineering, our proposed combined 3D PAS can achieve extremely broadband absorption with the efficiency more than 90% in the frequency band of 6.7-35.3GHz, contributing to low figure of merit compared to others. Our strategy provides an efficient and flexible design capable of enhancing the operating bandwidth and absorbing efficiency simultaneously in PAS, enabling a wide range of applications in radar stealth technology, electromagnetic shielding, energy harvesting, and so on.