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Ultra-broadband and wide-angle absorption based on 3D-printed pyramid
Optics and Laser Technology 124 (2020) 105972
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Ultra-broadband and wide-angle absorption based on 3D-printed pyramid ⁎
T
Xiqiao Chen, Zhuang Wu, Zilong Zhang, Yanhong Zou
Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education & Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics and Devices, School of Physics and Electronics, Hunan University, Changsha 410082, People’s Republic of China
H I GH L IG H T S
pyramidal absorber is directly fabricated with 3D printing technology. • The pyramid can excite more resonance mode to enhance absorption. • Constructing • The pyramidal absorber realized ultra-broadband and wide angle absorption.
A R T I C LE I N FO
A B S T R A C T
Keywords: Ultra-broadband Wide-angle Pyramidal absorber 3D printing Carbon-loaded ABS
This paper proposes a 3D-printed pyramidal absorber, which comprises of the printing filaments, carbon-loaded Acrylonitrile Butadiene Styrene (ABS). This ABS has certain absorption effects, and shows simple and rapid prototyping characteristics. Here, we experimentally demonstrated the directly printed pyramidal absorber showing the absorption more than 90% within the frequency range from 5.3 to 18 GHz. The incident energy at the low and high peak frequencies are mostly attenuated by λ/4 resonances, corresponding to the wavelength of λ/4 and 3λ/4 separately. Distinct from the flat absorber, the pyramidal structure and absorbent take synergistic effects for broadband absorption. Additionally, the pyramid maintained its absorption bandwidth within quite a wide incident angle, 50° for transverse electric (TE) polarization and 60° for transverse magnetic (TM) polarization. It is expected that the proposed pyramidal absorber has great potential for application in radar cross section reduction and electromagnetic shielding.
1. Introduction Electromagnetic absorber, with efficient attenuation ability of electromagnetic waves, has been widely applied for military and civil technologies, such as radar cross section reduction [1–3], energy harvesting [4,5], electromagnetic compatibility [6,7] and so on. Dielectric or magnetic slabs were initially proposed for microwave absorption [8], and various noncorrugated layer has also been validated to show perfect absorption [9,10]. Over the past few decades, electromagnetic metamaterial has been introduced for perfect absorption as its permittivity and permeability can be manipulated by designing artificial metallic structure [11–13]. Efforts about metamaterial absorber indicate that the metallic structure design indeed lead to near-unity absorption but also a narrow bandwidth inevitably as its high resonance dispersion [14]. By coupling the multiband resonance, metamaterial-based absorber can obtain a broader absorption band, but suffer from poor tunability as its complicated metallic structure [15,16]. Accordingly, all-dielectric absorber, with the electromagnetic properties
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manipulated by dielectric structure, is more desirable for broadband absorption [17–22]. Thus, dielectric materials have been widely applied for designing broadband absorber. By designing a fishnet-like absorber with magnetic absorbing material, Chen et al. [17] realized the ultra-broadband absorption within 4.8–20.7 GHz. Based on the absorptive dielectric material water, Xie et al. [20] proposed a microwave absorber with the absorption bandwidth within 12–29.6 GHz. By composing graphene composite into a multi-layer absorber, Yin et al. [21] realized its absorption bandwidth within 4.5–40 GHz. Efforts about all-dielectric absorber indicates the significance of attenuation ability from dielectric itself on the enhanced absorption. Structures based on highly absorptive materials are more conductive to the consumption of electromagnetic waves. Thus, applying highly absorptive dielectric materials are critical for effective absorption. Similarly, owing to the little absorption of printing filaments, dielectric-based absorbers were auxiliarily fabricated with the 3D printing technology [17,20–22], which simplified the fabrication process significantly. 3D printing technology, with the thermoplastic
Corresponding author. E-mail address: [email protected] (Y. Zou).
https://doi.org/10.1016/j.optlastec.2019.105972 Received 12 June 2019; Received in revised form 3 November 2019; Accepted 23 November 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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filaments extruded and printed layer by layer, shows the advantage of low cost, simple and fast prototyping, as well as high precision even for complicated models [23,24]. 3D printing has been widely applied for fabrication of plastic components, such as waveguides [25], antennas [26,27], and absorbers [28,29]. However, the conventional 3D printing filaments, like acrylonitrile butadiene styrene (ABS) and polylactic acid (PLA), generally have almost no attenuation ability on incident waves [17,22], so it is difficult for them to fabricate effective absorber directly. Here, loading conductive dielectrics into the printing filaments has great potential on tuning the electromagnetic properties [28,29], namely higher permittivity, which make it possible for the fast prototyping of absorber. In this paper, we proposed a pyramidal absorber using the conductive ABS, and fabricated the model with 3D-printer directly. The pyramidal absorber was theoretically and experimentally demonstrated to be ultra-broadband absorption within 5.3–18 GHz. The physical origin was specified for comprehending its broadband absorption, indicating the synergistic effects of absorbent itself and geometrical structure. Similarly, the angular performance of pyramidal absorber shows its wide tolerance of incident angle. Owing to these excellent performances, the pyramidal absorber may find applications in radar cross section reduction and electromagnetic shielding.
2.2. Structure and result To significantly broaden the absorption bandwidth of conductive ABS, the pyramidal structure with metal back was designed and presented in Fig. 2(a) and (b). Fig. 2(a) shows the perspective view of pyramidal absorber. In simulation, the incident wave is set as x-polarization, while the propagation direction is along with z-direction. Fig. 2(b) shows the cross section of the proposed structure. The unitstructure is stacked with five plate, each plate with a same thickness of t = 1.3 mm. The periodic of the bottom plate is largest, optimized with parameter p (p = 37.5 mm), while the periodic for these five stacked plates is gradiently decreased from bottom to top, and the periodic discrepancy between neighboring two plate is c (c = 1.8 mm) on each side. Generally, the absorption is calculated by A(ω) = 1 − T(ω) − R (ω), where T(ω) and R(ω) represent the reflectance and transmittance, which can be obtained with the complex S-parameters |S11|2 and |S21|2 [30]. With the presence of metal back, the transmittance equals to zero. So, the absorption can be directly obtained with A(ω) = 1 − R(ω). The simulated absorption of the pyramid is compared with that of the flat conductive ABS with a thickness of 6.5 mm, while the results are presented in Fig. 2(b). The flat conductive ABS owns two peak absorption, which are excited by the λ/4 resonance. Even so, its absorption bandwidth is still too narrow to achieve the standard for practical applications. By constructing pyramidal structure, the absorption bandwidth is significantly broadened to 5.3–18 GHz. By comparing the two spectra, it can be found that they both own peak absorption at about 5.0 GHz and 15.0 GHz, which is corresponding to the wavelength of λ/4 and 3λ/ 4. Obviously, the relating peak frequency for pyramidal absorber is relatively higher than that for flat conductive ABS. But the smaller filling ratio leads to the lower resonant wavelength for pyramidal absorber, as compared to flat conductive ABS. Thus, the peak absorption at 6.1 GHz and 17.4 GHz for pyramidal absorber is assumed to be excited by λ/4 resonance. Moreover, we also compared the absorption performance of the typical microwave absorption structures (multilayer structure [32,33], honeycomb structure [34,35], pyramidal structure [36,37]), as shown in Table 1. Here, we applied Wob/t = (λU − λL)/t to compare their comprehensive absorption performance [38], while λU and λL represent the upper and lower wavelength of the absorption bandwidth, t stands for the thickness. It is clear that our pyramidal structure shows comprehensive absorption performance in bandwidth and thickness, as its highest value of Wob/t. Traditional pyramidal absorbers are generally composed of multi-layers dielectric-metal combinations, but our pyramidal absorber comprises a lossy dielectric material. That is to say, except for the structural effects, the material itself also contribute to the high absorption performance [14]. Besides, the carbon-loaded ABS used in this work contribute to its relative simpler and faster fabrication process as compared to the traditional absorbent.
2. Simulation and experiment 2.1. Electromagnetic properties of conductive ABS The dielectric material for broadband absorber is a kind of conductive ABS, provided by Time 80s Technology Co., Ltd. (Shenzhen China). The commercial conductive ABS, with carbon loaded into ABS, has been extruded as printing filaments, showing a higher dielectric loss. To further comprehend the characteristics of conductive ABS, its electromagnetic parameters in the frequency range of 2–18 GHz are measured by the professional measurement system, vector network analyzer (AV3672B-S), while the measured results are shown in Fig. 1(a). The permeability on real part basically maintains its value of 1.0, while its imaginary part is about 0.0, within the entire frequency range, which indicates its non-magnetic property. For permittivity, its real part is around 6.0, and descended slowly with the increasing frequency, while its imaginary part maintains its value of 1.0, indicating its dielectric loss property. Based on the measured electromagnetic parameters, its absorption with several graded thicknesses are calculated and presented as shown in Fig. 1(b). The bandwidth with absorption higher than 90% does not exceed 3.0 GHz for the flat conductive ABS regardless of the thicknesses, which is resulted from the characteristics of dielectric loss and multiple reflection of λ/4 resonance model [30,31].
Fig. 1. The electromagnetic characteristics of conductive ABS: (a) permittivity and permeability; (b) absorption with different thicknesses. 2
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Fig. 2. Structure of pyramidal absorber: (a) perspective view, (b) front view; (c) absorption comparison between flat conductive ABS and conductive ABS-based pyramidal absorber.
circle. Based on the above-discussed field distributions by Eq. (3), the spatial separation between electric and magnetic fields indicates the existence of standing waves, showing a typical distribution of λ/4 resonance. The absorption mechanism at 6.1 GHz analyzed by field distribution is corresponding to the above-analysis based on the absorption comparison of flat absorbent and pyramidal absorber. Besides, the power loss is mainly focused on the top part of the pyramidal absorber, which is the location where electric field is concentrated on. Since the pyramidal absorber consists of the dielectric loss ABS, strong dielectric reactions are excited to electric field. Fig. 3(b) shows the field distributions at the second peak frequency 9.1 GHz. The electric field is confined on the right-angles of the upper three steps and the cavity between two neighbouring pyramids, while the magnetic field is focused on the central of the three electric field semi-circle. Power loss mainly occurs in the interior of right-angles. For the highest absorption peak 17.4 GHz, the electric field is mainly confined in the cavity of neighboring pyramid units as shown in Fig. 3(c), but certain electric field also takes place in the surfaces, edges and corners of the pyramid. Importantly, the relative weak spatial distribution of electric field and magnetic field can also be distinguished, and the thickness is relating to 3λ/4 approximately, indicating the λ/4 resonance. In this frequency, power loss is strengthened at the edge of bottom step. Based on the analysis of Fig. 3, λ/4 resonance takes great effects on dissipating electromagnetic wave energy of pyramidal structure. At the peak frequency 6.1 GHz and 17.4 GHz, typical characteristics of λ/4 resonance can both be found. Besides, from low frequency to high frequency, power loss moves gradually from the interior of the pyramid to its surfaces, edges and corners, because the relative wavelength gets smaller [39]. Since the applied absorbent shows certain dielectric loss, the power loss generally occurs in where electric field confined. Overall, pyramids can excite λ/4 resonance for energy dissipation over certain frequency range [31,39]. But by constructing geometrical structures, the resonance of electric field between neighboring units can also improve its absorption. So, the absorbent and its geometrical structure collaborate to promote the absorption performance.
Table 1 Performance summary with typical microwave absorption structure. Type
Bandwidth (GHz)
Thickness (mm)
Wob/t
References
Multilayer
3.7 (8.5–12.2) 2.4 (10.1–12.4)
2.0 1.7
5.4 3.2
[32] [33]
Honeycomb
13.1 (4.9–18.0) 4.0 (8.0–12.0)
8.0 7.6
5.0 1.6
[34] [35]
Pyramid
3.2 (7.9–9.8, 11.0–12.3) 6.9 (7.8–14.7) 12.7 (5.3–18.0)
5.5 5.0 6.5
1.9 3.6 6.1
[36] [37] This work
2.3. Absorption mechanism The above-mentioned λ/4 resonance indicates that the superposed reflected waves will lead to a destructive interference when the thickness of flat absorbent is about nλ/4. This resonance model can be clearly illustrated by the field distributions in flat absorbent, as the superposition of transmitted and multiple reflected waves will contribute to the formation of standing waves. For the field distributions in flat absorbent, the superposed waves show its propagation direction along with incident waves [31], while the electric and magnetic fields are supposed to be:
E1y (z , t ) = E0 cos(kz − ωt ),
B1x (z , t ) = B0 cos(kz − ωt ).
(1)
But for the superposed waves along with the anti-incident direction, their corresponding field expressions are
E2y (z , t ) = −E0 cos(kz + ωt ),
B2x (z , t ) = B0 cos(kz + ωt ).
(2)
Thus, the field of standing waves can be expressed by
Ey (z , t ) = 2E0 sin(kz ) sin(ωt ),
B y (z , t ) = 2B0 cos(kz ) cos(ωt ).
(3)
The expressions of electric and magnetic fields from Eq. (1) indicates that the traveling waves show a same filed distribution at the same position, namely the same phase condition. Known by the filed expressions from Eq. (3), the standing waves show a 90° phase difference between electric and magnetic fields, leading to the spatial separation of electric and magnetic field components. Here, the distinct fields characteristics of traveling and standing waves give great probability for the differentiation of these two waves. To understand the working mechanism of pyramidal absorber, we monitored and plotted its electric field, magnetic field and power loss at three absorption peak frequencies 6.1 GHz, 9.1 GHz and 17.4 GHz, while every distribution shows both perspective view and cross section on xoz plane, as shown in Fig. 3. As can be seen from Fig. 3(a), the electric field at 6.1 GHz is mainly concentrated on the top part of the pyramidal absorber, and a semi-circle is formed on its bottom part, while the magnetic field is mostly focused on the center of the semi-
2.4. Parameter choice Obviously, the broadband absorption is highly related to the geometry parameters. Fig. 4(a)–(c) distribute the absorption spectrum with the graded parameters p, c, and t. As discussed above, the λ/4 resonance contributes mostly to the effective absorption in the peak frequencies at 6.1 GHz and 17.4 GHz, while the λ/4 resonance is in positive correlation of the filling fraction. Here, decreased c, and increased t all increased the filling fraction of the conductive ABS, which is corresponding to the variation trade of the displayed spectrum at 6.1 GHz and 17.4 GHz. Besides, the absorption curve for the gradient parameter c in Fig. 4(b) shows a similar variation trade of the absorption spectrum 3
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Fig. 3. The distributions of electric field, magnetic field and power loss under normal incidence at (a) 6.1 GHz; (b) 9.1 GHz; (c) 17.4 GHz.
Fig. 4. Absorption spectra with gradient parameter configuration: (a) period of the unit-cell; (b) the period discrepancy of neighboring stacked plate on each side; (c) the thickness of each plate.
Fig. 5. Absorption contour with the variation of incident angles at: (a) TE polarization; (b) TM polarization.
from flat absorber to pyramidal absorber as can be seen in Fig. 1(b), which indicate the λ/4 resonance at 6.1 GHz and 17.4 GHz, as well as cavity mode at 9.1 GHz obviously. In addition, parameter p shows a little influence on the overall absorption, as the small discrepancy between the neighboring stacked plate lead to its approximately equivalent structure to the flat absorber with the thickness of 6.5 mm.
2.5. Angular tolerance As flat absorbents are usually polarization and incident angle dependent, it is worthy to learn the angular performance of the proposed pyramidal absorber. Its absorption spectrum with incident angles varies from 0° to 60° under transverse electric (TE) and transverse magnetic (TM) polarizations are displayed in Fig. 5(a) and (b). For both TE and 4
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Fig. 6. (a) Experimental setup schematic; (b) Measured absorption spectrum of the printed pyramidal absorber, with the prototype shown at the inset simultaneously.
TM polarizations, the absorption efficiency at 6.1 GHz decreased with the increasing of incident angles. It is due to that the λ/4 resonance contribute mostly to the high absorption at this frequency, and the increased incident angle is accompanied with decreased intensity of λ/4 resonance. As discussed above, the high absorption for 9.1 GHz is related to electric field related edge diffraction effects and strong magnetic confinement, so the absorption efficiency at 9.1 GHz both decreased for TE and TM polarization. Equally, the above mentioned λ/4 resonance at 17.4 GHz lead to the absorption decreasing for TE polarization but stable absorption for TM polarization as incident angle increased. Overall, the absorption bandwidth within 5.3–18 GHz is basically maintained with the incident angle less than 50° for TE polarization, and 60° for TM polarization.
polarization. Distinct from the traditional fabrication technology, the pyramidal absorber composed of conductive ABS (a kind of commercial printing filaments), can be directly fabricated by 3D printer, which greatly reduced the difficulty and cost for fabrication. Therefore, the proposed pyramidal absorber, with such an ultra-broadband and wideangle absorption, has great potential for application in radar cross section reduction and electromagnetic shielding.
2.6. Fabrication and measurement
Acknowledgments
To confirm the reliability of our simulation, the relevant experiment has been carried out. Based on the designed pyramid, the model with optimized parameter configuration was imported to the 3D printer. The detailed parameters are set as p = 37.5 mm, c = 1.8 mm and t = 1.3 mm. Finally, the conductive ABS-based model with a size of 300 × 300 mm2 (with 8 × 8 unit-cells) was directly printed with the prepared filaments. The reflection loss was measured by the vector network analyzer (AV3672B-S) with two horn antennas for transmitting and receiving electromagnetic waves, and the whole measurement was in microwave anechoic chambers, as can be seen from Fig. 6(a). Besides, the distance between pyramid and horn antennas is quite far as to ensure normal incidence. The measured curve is shown in Fig. 6(b), while the fabricated prototype is shown at its inset. The little inaccuracy of the fabricated pyramid may lead to the resonant frequency shift relating to λ/4 resonances, and the surface roughness may bring little diffuse reflection as well. Overall, the measured absorption is basically consistent with the simulated result, showing a similar absorption bandwidth within 5.3–18 GHz. Overall, the measured absorption is basically consistent with the simulated result, showing a similar absorption bandwidth within 5.3–18 GHz.
This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61378002) and the Key Research and Development Plan of Hunan Province (Grant No. 2017NK2121).
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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3. Conclusion In summary, a conductive ABS-based pyramidal absorber was demonstrated to be ultra-broadband absorption by simulation and experiment simultaneously. The broadband absorption bandwidth can be resulted from the absorbent itself and the synergistic effects of geometric structure. With the increase of frequency, power loss concentration moves gradually from the interior of pyramid to its exterior part. The simulated and measured absorption indicate that the pyramidal absorber achieved its absorption more than 90% within 5.3–18 GHz. The consistence between simulation and experiment demonstrates the reliability of the proposed absorber. Furthermore, the pyramid can basically maintain its absorption bandwidth with the incident angle less than 50° for TE polarization, and 60° for TM 5
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Ultra-broadband and wide-angle absorption based on 3D-printed pyramid ⁎
T
Xiqiao Chen, Zhuang Wu, Zilong Zhang, Yanhong Zou
Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education & Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics and Devices, School of Physics and Electronics, Hunan University, Changsha 410082, People’s Republic of China
H I GH L IG H T S
pyramidal absorber is directly fabricated with 3D printing technology. • The pyramid can excite more resonance mode to enhance absorption. • Constructing • The pyramidal absorber realized ultra-broadband and wide angle absorption.
A R T I C LE I N FO
A B S T R A C T
Keywords: Ultra-broadband Wide-angle Pyramidal absorber 3D printing Carbon-loaded ABS
This paper proposes a 3D-printed pyramidal absorber, which comprises of the printing filaments, carbon-loaded Acrylonitrile Butadiene Styrene (ABS). This ABS has certain absorption effects, and shows simple and rapid prototyping characteristics. Here, we experimentally demonstrated the directly printed pyramidal absorber showing the absorption more than 90% within the frequency range from 5.3 to 18 GHz. The incident energy at the low and high peak frequencies are mostly attenuated by λ/4 resonances, corresponding to the wavelength of λ/4 and 3λ/4 separately. Distinct from the flat absorber, the pyramidal structure and absorbent take synergistic effects for broadband absorption. Additionally, the pyramid maintained its absorption bandwidth within quite a wide incident angle, 50° for transverse electric (TE) polarization and 60° for transverse magnetic (TM) polarization. It is expected that the proposed pyramidal absorber has great potential for application in radar cross section reduction and electromagnetic shielding.
1. Introduction Electromagnetic absorber, with efficient attenuation ability of electromagnetic waves, has been widely applied for military and civil technologies, such as radar cross section reduction [1–3], energy harvesting [4,5], electromagnetic compatibility [6,7] and so on. Dielectric or magnetic slabs were initially proposed for microwave absorption [8], and various noncorrugated layer has also been validated to show perfect absorption [9,10]. Over the past few decades, electromagnetic metamaterial has been introduced for perfect absorption as its permittivity and permeability can be manipulated by designing artificial metallic structure [11–13]. Efforts about metamaterial absorber indicate that the metallic structure design indeed lead to near-unity absorption but also a narrow bandwidth inevitably as its high resonance dispersion [14]. By coupling the multiband resonance, metamaterial-based absorber can obtain a broader absorption band, but suffer from poor tunability as its complicated metallic structure [15,16]. Accordingly, all-dielectric absorber, with the electromagnetic properties
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manipulated by dielectric structure, is more desirable for broadband absorption [17–22]. Thus, dielectric materials have been widely applied for designing broadband absorber. By designing a fishnet-like absorber with magnetic absorbing material, Chen et al. [17] realized the ultra-broadband absorption within 4.8–20.7 GHz. Based on the absorptive dielectric material water, Xie et al. [20] proposed a microwave absorber with the absorption bandwidth within 12–29.6 GHz. By composing graphene composite into a multi-layer absorber, Yin et al. [21] realized its absorption bandwidth within 4.5–40 GHz. Efforts about all-dielectric absorber indicates the significance of attenuation ability from dielectric itself on the enhanced absorption. Structures based on highly absorptive materials are more conductive to the consumption of electromagnetic waves. Thus, applying highly absorptive dielectric materials are critical for effective absorption. Similarly, owing to the little absorption of printing filaments, dielectric-based absorbers were auxiliarily fabricated with the 3D printing technology [17,20–22], which simplified the fabrication process significantly. 3D printing technology, with the thermoplastic
Corresponding author. E-mail address: [email protected] (Y. Zou).
https://doi.org/10.1016/j.optlastec.2019.105972 Received 12 June 2019; Received in revised form 3 November 2019; Accepted 23 November 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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filaments extruded and printed layer by layer, shows the advantage of low cost, simple and fast prototyping, as well as high precision even for complicated models [23,24]. 3D printing has been widely applied for fabrication of plastic components, such as waveguides [25], antennas [26,27], and absorbers [28,29]. However, the conventional 3D printing filaments, like acrylonitrile butadiene styrene (ABS) and polylactic acid (PLA), generally have almost no attenuation ability on incident waves [17,22], so it is difficult for them to fabricate effective absorber directly. Here, loading conductive dielectrics into the printing filaments has great potential on tuning the electromagnetic properties [28,29], namely higher permittivity, which make it possible for the fast prototyping of absorber. In this paper, we proposed a pyramidal absorber using the conductive ABS, and fabricated the model with 3D-printer directly. The pyramidal absorber was theoretically and experimentally demonstrated to be ultra-broadband absorption within 5.3–18 GHz. The physical origin was specified for comprehending its broadband absorption, indicating the synergistic effects of absorbent itself and geometrical structure. Similarly, the angular performance of pyramidal absorber shows its wide tolerance of incident angle. Owing to these excellent performances, the pyramidal absorber may find applications in radar cross section reduction and electromagnetic shielding.
2.2. Structure and result To significantly broaden the absorption bandwidth of conductive ABS, the pyramidal structure with metal back was designed and presented in Fig. 2(a) and (b). Fig. 2(a) shows the perspective view of pyramidal absorber. In simulation, the incident wave is set as x-polarization, while the propagation direction is along with z-direction. Fig. 2(b) shows the cross section of the proposed structure. The unitstructure is stacked with five plate, each plate with a same thickness of t = 1.3 mm. The periodic of the bottom plate is largest, optimized with parameter p (p = 37.5 mm), while the periodic for these five stacked plates is gradiently decreased from bottom to top, and the periodic discrepancy between neighboring two plate is c (c = 1.8 mm) on each side. Generally, the absorption is calculated by A(ω) = 1 − T(ω) − R (ω), where T(ω) and R(ω) represent the reflectance and transmittance, which can be obtained with the complex S-parameters |S11|2 and |S21|2 [30]. With the presence of metal back, the transmittance equals to zero. So, the absorption can be directly obtained with A(ω) = 1 − R(ω). The simulated absorption of the pyramid is compared with that of the flat conductive ABS with a thickness of 6.5 mm, while the results are presented in Fig. 2(b). The flat conductive ABS owns two peak absorption, which are excited by the λ/4 resonance. Even so, its absorption bandwidth is still too narrow to achieve the standard for practical applications. By constructing pyramidal structure, the absorption bandwidth is significantly broadened to 5.3–18 GHz. By comparing the two spectra, it can be found that they both own peak absorption at about 5.0 GHz and 15.0 GHz, which is corresponding to the wavelength of λ/4 and 3λ/ 4. Obviously, the relating peak frequency for pyramidal absorber is relatively higher than that for flat conductive ABS. But the smaller filling ratio leads to the lower resonant wavelength for pyramidal absorber, as compared to flat conductive ABS. Thus, the peak absorption at 6.1 GHz and 17.4 GHz for pyramidal absorber is assumed to be excited by λ/4 resonance. Moreover, we also compared the absorption performance of the typical microwave absorption structures (multilayer structure [32,33], honeycomb structure [34,35], pyramidal structure [36,37]), as shown in Table 1. Here, we applied Wob/t = (λU − λL)/t to compare their comprehensive absorption performance [38], while λU and λL represent the upper and lower wavelength of the absorption bandwidth, t stands for the thickness. It is clear that our pyramidal structure shows comprehensive absorption performance in bandwidth and thickness, as its highest value of Wob/t. Traditional pyramidal absorbers are generally composed of multi-layers dielectric-metal combinations, but our pyramidal absorber comprises a lossy dielectric material. That is to say, except for the structural effects, the material itself also contribute to the high absorption performance [14]. Besides, the carbon-loaded ABS used in this work contribute to its relative simpler and faster fabrication process as compared to the traditional absorbent.
2. Simulation and experiment 2.1. Electromagnetic properties of conductive ABS The dielectric material for broadband absorber is a kind of conductive ABS, provided by Time 80s Technology Co., Ltd. (Shenzhen China). The commercial conductive ABS, with carbon loaded into ABS, has been extruded as printing filaments, showing a higher dielectric loss. To further comprehend the characteristics of conductive ABS, its electromagnetic parameters in the frequency range of 2–18 GHz are measured by the professional measurement system, vector network analyzer (AV3672B-S), while the measured results are shown in Fig. 1(a). The permeability on real part basically maintains its value of 1.0, while its imaginary part is about 0.0, within the entire frequency range, which indicates its non-magnetic property. For permittivity, its real part is around 6.0, and descended slowly with the increasing frequency, while its imaginary part maintains its value of 1.0, indicating its dielectric loss property. Based on the measured electromagnetic parameters, its absorption with several graded thicknesses are calculated and presented as shown in Fig. 1(b). The bandwidth with absorption higher than 90% does not exceed 3.0 GHz for the flat conductive ABS regardless of the thicknesses, which is resulted from the characteristics of dielectric loss and multiple reflection of λ/4 resonance model [30,31].
Fig. 1. The electromagnetic characteristics of conductive ABS: (a) permittivity and permeability; (b) absorption with different thicknesses. 2
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Fig. 2. Structure of pyramidal absorber: (a) perspective view, (b) front view; (c) absorption comparison between flat conductive ABS and conductive ABS-based pyramidal absorber.
circle. Based on the above-discussed field distributions by Eq. (3), the spatial separation between electric and magnetic fields indicates the existence of standing waves, showing a typical distribution of λ/4 resonance. The absorption mechanism at 6.1 GHz analyzed by field distribution is corresponding to the above-analysis based on the absorption comparison of flat absorbent and pyramidal absorber. Besides, the power loss is mainly focused on the top part of the pyramidal absorber, which is the location where electric field is concentrated on. Since the pyramidal absorber consists of the dielectric loss ABS, strong dielectric reactions are excited to electric field. Fig. 3(b) shows the field distributions at the second peak frequency 9.1 GHz. The electric field is confined on the right-angles of the upper three steps and the cavity between two neighbouring pyramids, while the magnetic field is focused on the central of the three electric field semi-circle. Power loss mainly occurs in the interior of right-angles. For the highest absorption peak 17.4 GHz, the electric field is mainly confined in the cavity of neighboring pyramid units as shown in Fig. 3(c), but certain electric field also takes place in the surfaces, edges and corners of the pyramid. Importantly, the relative weak spatial distribution of electric field and magnetic field can also be distinguished, and the thickness is relating to 3λ/4 approximately, indicating the λ/4 resonance. In this frequency, power loss is strengthened at the edge of bottom step. Based on the analysis of Fig. 3, λ/4 resonance takes great effects on dissipating electromagnetic wave energy of pyramidal structure. At the peak frequency 6.1 GHz and 17.4 GHz, typical characteristics of λ/4 resonance can both be found. Besides, from low frequency to high frequency, power loss moves gradually from the interior of the pyramid to its surfaces, edges and corners, because the relative wavelength gets smaller [39]. Since the applied absorbent shows certain dielectric loss, the power loss generally occurs in where electric field confined. Overall, pyramids can excite λ/4 resonance for energy dissipation over certain frequency range [31,39]. But by constructing geometrical structures, the resonance of electric field between neighboring units can also improve its absorption. So, the absorbent and its geometrical structure collaborate to promote the absorption performance.
Table 1 Performance summary with typical microwave absorption structure. Type
Bandwidth (GHz)
Thickness (mm)
Wob/t
References
Multilayer
3.7 (8.5–12.2) 2.4 (10.1–12.4)
2.0 1.7
5.4 3.2
[32] [33]
Honeycomb
13.1 (4.9–18.0) 4.0 (8.0–12.0)
8.0 7.6
5.0 1.6
[34] [35]
Pyramid
3.2 (7.9–9.8, 11.0–12.3) 6.9 (7.8–14.7) 12.7 (5.3–18.0)
5.5 5.0 6.5
1.9 3.6 6.1
[36] [37] This work
2.3. Absorption mechanism The above-mentioned λ/4 resonance indicates that the superposed reflected waves will lead to a destructive interference when the thickness of flat absorbent is about nλ/4. This resonance model can be clearly illustrated by the field distributions in flat absorbent, as the superposition of transmitted and multiple reflected waves will contribute to the formation of standing waves. For the field distributions in flat absorbent, the superposed waves show its propagation direction along with incident waves [31], while the electric and magnetic fields are supposed to be:
E1y (z , t ) = E0 cos(kz − ωt ),
B1x (z , t ) = B0 cos(kz − ωt ).
(1)
But for the superposed waves along with the anti-incident direction, their corresponding field expressions are
E2y (z , t ) = −E0 cos(kz + ωt ),
B2x (z , t ) = B0 cos(kz + ωt ).
(2)
Thus, the field of standing waves can be expressed by
Ey (z , t ) = 2E0 sin(kz ) sin(ωt ),
B y (z , t ) = 2B0 cos(kz ) cos(ωt ).
(3)
The expressions of electric and magnetic fields from Eq. (1) indicates that the traveling waves show a same filed distribution at the same position, namely the same phase condition. Known by the filed expressions from Eq. (3), the standing waves show a 90° phase difference between electric and magnetic fields, leading to the spatial separation of electric and magnetic field components. Here, the distinct fields characteristics of traveling and standing waves give great probability for the differentiation of these two waves. To understand the working mechanism of pyramidal absorber, we monitored and plotted its electric field, magnetic field and power loss at three absorption peak frequencies 6.1 GHz, 9.1 GHz and 17.4 GHz, while every distribution shows both perspective view and cross section on xoz plane, as shown in Fig. 3. As can be seen from Fig. 3(a), the electric field at 6.1 GHz is mainly concentrated on the top part of the pyramidal absorber, and a semi-circle is formed on its bottom part, while the magnetic field is mostly focused on the center of the semi-
2.4. Parameter choice Obviously, the broadband absorption is highly related to the geometry parameters. Fig. 4(a)–(c) distribute the absorption spectrum with the graded parameters p, c, and t. As discussed above, the λ/4 resonance contributes mostly to the effective absorption in the peak frequencies at 6.1 GHz and 17.4 GHz, while the λ/4 resonance is in positive correlation of the filling fraction. Here, decreased c, and increased t all increased the filling fraction of the conductive ABS, which is corresponding to the variation trade of the displayed spectrum at 6.1 GHz and 17.4 GHz. Besides, the absorption curve for the gradient parameter c in Fig. 4(b) shows a similar variation trade of the absorption spectrum 3
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Fig. 3. The distributions of electric field, magnetic field and power loss under normal incidence at (a) 6.1 GHz; (b) 9.1 GHz; (c) 17.4 GHz.
Fig. 4. Absorption spectra with gradient parameter configuration: (a) period of the unit-cell; (b) the period discrepancy of neighboring stacked plate on each side; (c) the thickness of each plate.
Fig. 5. Absorption contour with the variation of incident angles at: (a) TE polarization; (b) TM polarization.
from flat absorber to pyramidal absorber as can be seen in Fig. 1(b), which indicate the λ/4 resonance at 6.1 GHz and 17.4 GHz, as well as cavity mode at 9.1 GHz obviously. In addition, parameter p shows a little influence on the overall absorption, as the small discrepancy between the neighboring stacked plate lead to its approximately equivalent structure to the flat absorber with the thickness of 6.5 mm.
2.5. Angular tolerance As flat absorbents are usually polarization and incident angle dependent, it is worthy to learn the angular performance of the proposed pyramidal absorber. Its absorption spectrum with incident angles varies from 0° to 60° under transverse electric (TE) and transverse magnetic (TM) polarizations are displayed in Fig. 5(a) and (b). For both TE and 4
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Fig. 6. (a) Experimental setup schematic; (b) Measured absorption spectrum of the printed pyramidal absorber, with the prototype shown at the inset simultaneously.
TM polarizations, the absorption efficiency at 6.1 GHz decreased with the increasing of incident angles. It is due to that the λ/4 resonance contribute mostly to the high absorption at this frequency, and the increased incident angle is accompanied with decreased intensity of λ/4 resonance. As discussed above, the high absorption for 9.1 GHz is related to electric field related edge diffraction effects and strong magnetic confinement, so the absorption efficiency at 9.1 GHz both decreased for TE and TM polarization. Equally, the above mentioned λ/4 resonance at 17.4 GHz lead to the absorption decreasing for TE polarization but stable absorption for TM polarization as incident angle increased. Overall, the absorption bandwidth within 5.3–18 GHz is basically maintained with the incident angle less than 50° for TE polarization, and 60° for TM polarization.
polarization. Distinct from the traditional fabrication technology, the pyramidal absorber composed of conductive ABS (a kind of commercial printing filaments), can be directly fabricated by 3D printer, which greatly reduced the difficulty and cost for fabrication. Therefore, the proposed pyramidal absorber, with such an ultra-broadband and wideangle absorption, has great potential for application in radar cross section reduction and electromagnetic shielding.
2.6. Fabrication and measurement
Acknowledgments
To confirm the reliability of our simulation, the relevant experiment has been carried out. Based on the designed pyramid, the model with optimized parameter configuration was imported to the 3D printer. The detailed parameters are set as p = 37.5 mm, c = 1.8 mm and t = 1.3 mm. Finally, the conductive ABS-based model with a size of 300 × 300 mm2 (with 8 × 8 unit-cells) was directly printed with the prepared filaments. The reflection loss was measured by the vector network analyzer (AV3672B-S) with two horn antennas for transmitting and receiving electromagnetic waves, and the whole measurement was in microwave anechoic chambers, as can be seen from Fig. 6(a). Besides, the distance between pyramid and horn antennas is quite far as to ensure normal incidence. The measured curve is shown in Fig. 6(b), while the fabricated prototype is shown at its inset. The little inaccuracy of the fabricated pyramid may lead to the resonant frequency shift relating to λ/4 resonances, and the surface roughness may bring little diffuse reflection as well. Overall, the measured absorption is basically consistent with the simulated result, showing a similar absorption bandwidth within 5.3–18 GHz. Overall, the measured absorption is basically consistent with the simulated result, showing a similar absorption bandwidth within 5.3–18 GHz.
This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61378002) and the Key Research and Development Plan of Hunan Province (Grant No. 2017NK2121).
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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3. Conclusion In summary, a conductive ABS-based pyramidal absorber was demonstrated to be ultra-broadband absorption by simulation and experiment simultaneously. The broadband absorption bandwidth can be resulted from the absorbent itself and the synergistic effects of geometric structure. With the increase of frequency, power loss concentration moves gradually from the interior of pyramid to its exterior part. The simulated and measured absorption indicate that the pyramidal absorber achieved its absorption more than 90% within 5.3–18 GHz. The consistence between simulation and experiment demonstrates the reliability of the proposed absorber. Furthermore, the pyramid can basically maintain its absorption bandwidth with the incident angle less than 50° for TE polarization, and 60° for TM 5
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