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A multi-band binary radar absorbing metamaterial based on a 3D low-permittivity all-dielectric structure
Journal of Alloys and Compounds 814 (2020) 152300
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A multi-band binary radar absorbing metamaterial based on a 3D lowpermittivity all-dielectric structure Fen Zhang a, Qiang Wang b, Tian Zhou c, Yijun Xiong d, Youquan Wen d, Chao Jiang d, *, Yan Wang d, Zuojuan Du d, **, Isaac Abrahams e, LanZhi Wang f, Xiaozhong Huang d a
School of Physics and Electronics, Central South University, Changsha, 410083, China Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, 710049, China c State Key Laboratory of Metamaterial Electromagnetic Modulation Technology, Kuang-Chi Institute of Advanced Technology, Shenzhen, 518057, China d Hunan Key Laboratory of Advanced Fibers and Composites, School of Aeronautics and Astronautics, Central South University, Changsha, 410083, China e School of Biological and Chemical Sciences, Queen Mary University of London, London, E1 4NS, UK f Beijing Institute of Aerospace Launch Technology, No.1, Nandahongmen Road, Donggaodi, Fengtai District, Beijing, 100076, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 March 2019 Received in revised form 2 September 2019 Accepted 14 September 2019 Available online 14 September 2019
A new binary-structured metamaterial absorber (MA), consisting of a 3D cross-shaped dielectric (CSD) periodic array and a metal back plane, is proposed and fabricated. This structure realized six resonant absorption peaks below 10dB in the range of 8e18 GHz. Both simulated and experimental results demonstrate the effectiveness of this design in generating multiband and low frequency absorption, which is difficult to achieve in previous 2D dielectric absorbers. The electromagnetic(EM) field and energy loss density distributions of absorption peaks were investigated as well as effects of structural parameters on the reflection loss spectra. It indicated that multimode resonance is generated by standing waves in the 3D dielectric structure. Moreover, since the structure is made of a low-permittivity dielectric resin, the fabrication is relatively easy and low-cost. The design of a three-dimensional lowpermittivity all-dielectric structure described in this work has potential applications in the EM energy capture and stealth fields. © 2019 Published by Elsevier B.V.
Keywords: Metamaterial absorber Resonance 3-D Low-permittivity all-dielectric structure Multiband
1. Introduction Metamaterial absorbers (MAs) used in electromagnetic(EM) stealth have attracted a lot of attention because of their advantages of thinness, lightness and strong absorption [1e3]. The initial MA prototype consists of a multilayer structure including a metal microstrip line pattern, a dielectric layer, and a metal backplane [4e9]. The functionality of these types of MAs mainly depends on the metal resonance surface. To meet the requirement of stealth field to multiple band or broadband MAs, the metal microstrip line patterns have to be designed complicated [10,11], which requires a complex manufacturing processes, as well as the metal patterns are easily oxidized and corroded. Thus more durable and more easily
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (C. Jiang), [email protected] (Z. Du). https://doi.org/10.1016/j.jallcom.2019.152300 0925-8388/© 2019 Published by Elsevier B.V.
manufactured devices have to be considered. In recent years, all-dielectric metamaterials have been proposed as alternatives to metal-based MAs [12e14]. Some studies indicate that the interaction between subwavelength dielectrics and EM waves leads to negative permittivity and generates multiple resonances. Holloway et al. [15] theoretically demonstrated that dielectric hosts embedded in resonant dielectric spheres has a negative effect on permittivity and permeability. Liu et al. [16] embed a dielectric cube arrays (εr ¼ 1600, tan d ¼ 0.003) in an acrylonitrile butadiene styrene polymeric (ABS) substrate (εr ¼ 2.67, tan d ¼ 0.006). It generated absorption peaks at 8.45 and 11.97 GHz by Mie resonances of the dielectric component and provided a simple way to designing metamaterial perfect absorbers. Furtherly, an all-dielectric metamaterial consisting of 2D arrays of rectangular ceramic with a high-dielectric constant (εr ¼ 115, tan d ¼ 0.0015) was designed by Li et al. [17], and the two resulting resonant peaks could be merged by adjusting the geometric parameters of the ceramic resonator. However, such metamaterials, which are made of high-permittivity ceramics, have their inherent shortcomings,
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such as high-cost, processing difficulties and brittleness of ceramic components. Comparatively speaking, low-permittivity dielectric materials show advantages in terms of thermal stability, high strength, lower processing temperatures and low cost [18,19]. Yu et al. [20] proposed a design for a low-permittivity alldielectric reflective frequency selective surface, utilizing a periodic array of holes drilled in a multilayer contiguous dielectric plate to introduce three resonances at 23.7 GHz, 24.9 GHz, and 25.8 GHz. Wang et al. [21,22] designed a series of low-permittivity alldielectric resonance surfaces to achieve absorption peaks at 14.65 GHz and 16.61 GHz with a hole array structure. These works show that two or three EM resonances in the range of 13e18 GHz can be obtained. However, the above two-dimensional structure shows difficulties to achieve multiple band absorption and low frequencies absorption below 12 GHz, which limit its application seriously. A three-dimensional (3D) metamaterial structure has been proposed and constructed by stacking up a number of identical printed circuit boards (PCBs) on a common plane [23e27]. It was found that 3D structures can provide great flexibility in designing multi-band absorption. Shen et al. [28] proposed a 3D radar absorbing structure based on the stand-up resistive film, with high absorption capacity in the broadband. The absorption mechanism can be thought as multiple standing wave modes excited by 3D structure. The idea of 3D metamaterial structure has opened up a new path to design multi-band or broadband absorbers to meet different requirements. Based on the above ideas, we present a 3D low-permittivity alldielectric radar absorbing MA. The periodic unit of this absorber is composed of a cross-shaped pure dielectric structure and a metal reflective back plane. Simulations reveal a number of absorption peaks with reflection loss below 10 dB in the range of 8e18 GHz. Dielectric resonance theory and effective medium theory under a quasi-static limit have been verified experimentally with fabrication of a test sample with multiple absorption peaks.
2. Design and simulation The basic unit of the binary absorber structure in our work is composed of a cross-shaped dielectric (CSD) and a perfect electric conductor (PEC). The dielectric component was composed of FR4 an epoxy resin with εr ¼ 4.8 and tan d ¼ 0.025. Fig. 1(a) shows the design of the absorber, where the square dimension of the base, L ¼ 30 mm, the height, H ¼ 30 mm and the thickness of the crosspieces, m ¼ 2.2 mm. Since the transmission is totally blocked by the PEC, the absorptivity, A(u), of an absorber at frequency u can be defined as:
A(u) ¼ 1 - R(u) ¼ 1 - jS211j
(1)
where R(u) is the reflectivity and S11 is the reflection coefficient. The reflection loss of absorber is determined by the following equations according to transmission line theory [29e32]:
RLðdBÞ ¼ 20lgjðZin 1Þ=ðZin þ 1Þj Zin ¼
pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi mr =εr tanh jð2pfd=cÞ mr εr
(2) (3)
where εr, mr, c, f, d and Z in correspond to the relative complex permittivity, permeability, velocity of light, microwave frequency in free space, coating thickness and input impedance of the absorber, respectively. The EM performance of the proposed all-dielectric structure was investigated by simulation using the commercial finite integration technique (FIT) based software CST Microwave Studio (CST Computer Simulation Technology GmbH). Periodic boundary conditions were applied in the basal x and y directions, with open boundaries in the z-direction. In addition, since the structure shows 4-fold rotational symmetry, the absorber can operate under dual polarization.
3. Analysis and discussion A simulated reflection loss spectrum is displayed in Fig. 1(b). A number of resonant absorption peaks are observed, six of which are below 10 dB (taken as the industry standard) at 10.004 GHz (f1), 12.192 GHz (f2), 14.304 GHz (f3), 15.456 GHz (f4), 15.76 GHz (f5) and 17.6 GHz (f6). The corresponding reflection loss are 28.58 dB, 12.8 dB, 10.21 dB, 24.64 dB, 18.6 dB, and 11.23 dB, respectively. We have presented a table showing the comparison in aspects of structure, materials, permittivity (εr) and absorption band number among the reported dielectric absorbers (Table 1). The table shows that our design achieves six absorption bands by 3D structure using epoxy resin with low permittivity and high strength as raw material. Moreover, the preparation processes are easy. It is a successful attempt to design 3D metamaterial absorbers using low permittivity dielectrics. To understand the physical mechanism of absorption, distributions of EM field were calculated for three selected peaks (f1, f3 and f6) and are shown in Fig. 2. The Figure is captured in the middle of the cross. Fig. 2(a) indicates that the electric field is enhanced in the upper and the middle parts of the dielectric structure at f1. At f3, the electric field is enhanced in three regions of the dielectric structure (Fig. 2(b)), while at f6, there are locations of enhanced electric field, from top to bottom of the dielectric structure (Fig. 2(c)). Such phenomena can be explained by standing wave theory. A standing
Fig. 1. (a) The structure of the basic absorber unit. (b) simulated reflection loss spectrum, where f1 ¼10.004 GHz, f2 ¼ 12.192 GHz, f3 ¼ 14.304 GHz, f4 ¼ 15.456 GHz, f5 ¼ 15.76 GHz and f6 ¼ 17.6 GHz.
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Table 1 Comparisons in aspects of structure, materials, permittivity (εr) and absorption band number among the reported dielectric absorbers. Ref.
Structure (thickness)
materials
εr
absorption band number
[19] [20] [33] [34] Current work
Plane (3 mm) Plane (3 mm) Plane (1 mm) Plane (1 mm) 3D structure (30 mm)
epoxy resin FR4 BST/10 wt % MgO 0.7Ba0.6Sr0.4TiO3-0.3La(Mg0.5Ti0.5)O3 FR4
4.3 4.3 272 115 4.8
2 3 1 1 6
Fig. 2. Electric field distributions in the CSD structure at (a) f1 ¼10.004 GHz, (b) f3 ¼ 14.304 GHz, and c) f6 ¼ 17.6 GHz, and (d), (e) and (f) corresponding sections of magnetic field distribution in the direction of the wave vector k. E and H denote the electric and magnetic field directions. The maximum electric intensity is 4500 V/m and the maximum magnetic intensity is 15 A/m.
wave occurs when two waves with the same amplitude traveling in the opposite direction on the same line are superimposed on each other. In practice, standing waves are more likely formed by incident and reflected waves at the interface of two media. For a dielectric resonator, standing waves are formed by reflection at the dielectric-air and the dielectric-metal interfaces when EM waves are incident on the structure, generating the resonance [35,36]. The wavelength l of the standing wave and the wavelength l of the original EM wave satisfy the following formula:
1 ln where n ¼ 1; 2; ::::::: l¼ n 2 2
(4)
When the thickness of the dielectric is an odd multiple of a quarter of the wavelength, the excitation field can form a stable standing wave in the dielectric [37,39]. Therefore, the physical mechanism to explain the reason why the dielectric structure generates resonances is called multiple standing wave modes associated with the electric field distribution. When the phase difference of two nearby reflection waves is -2p, the absorptivity reaches maximum [36]. The magnetic field distributions at frequencies f1, f3 and f6 are shown in Fig. 2(def). It can be seen that, at f1, two enhanced magnetic field rings are existed in the upper and the middle parts of the dielectric structure of the unit on the H-o-k plane, which can be equivalent to two electric dipoles on the E-o-k plane (Fig. 2(a)). The distribution in Fig. 2(e) shows three enhanced magnetic field rings in the unit on the H-o-k plane. The associated magnetic field results in three electric dipoles, which appear to be strongly coupled to the
enhanced electric field in Fig. 2(b). The magnetic field distribution at f6 in Fig. 2(f) indicates that the enhanced magnetic field are distributed near the center and the boundary of unit. It shows a strong coupling with the distribution of the enhanced electric field (Fig. 2(c)). It can be seen that associated magnetic field rings result in multiple electric dipoles distributed on the E-o-k plane. Thus the magnetic field distribution inside the CSD structure resembles that of an electric dipole. A more informative illustration of the absorption inside the CSD structure, is given by the power loss density (PLD) distributions (in Fig. 3). PLD is mainly concentrated on the upper and the middle parts of the dielectric structure at f1 (Fig. 3(a)). At f3, PLD is distributed along 3 regions of the dielectric structure (Fig. 3(b)). And there are 5 points enhanced along the dielectric structure at f6 (Fig. 3(c)). The enhanced electric field and PLD distributions confirm that the power loss is mainly caused by the electric resonance. It is difficult to introduce strong electric or magnetic resonances in the uniform low-permittivity dielectric plate. However, the design of the unit forms dielectric-air interfaces at where these resonances can occur. The cross piece design facilitates multi-band absorption. In order to study the influence of dimensional parameters on the absorption frequencies, reflection loss spectra were calculated for CSD structural models with different dimensions L, H and m. Increasing H from 28 mm to 30 mm results in a red shift for all resonant absorption peaks (Fig. 4(a)). Reflection loss of f1 resonance significantly improved from 3.72 to 28.58 as H is increased to 30 mm. Thus, increasing H allows enhancement of higher-order
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Fig. 3. PLD distributions in the CSD structure at (a) f1 ¼10.004 GHz, (b) f3 ¼ 14.304 GHz, and (c) f6 ¼ 17.6 GHz. The maximum PLD is 6 105 W/m3.
Fig. 4. Simulated reflection loss curves for the CSD structure with varying values of (a) height H, (b) cross-piece thickness m, (c) square lattice dimension L and (d) permittivity εr of the dielectric.
multipolar resonance modes. As well as, the cross-piece thickness m increasing from 1.9 mm to 2.5 mm also induces a red shift in the frequencies of the resonance peaks (Fig. 4(b)). In addition, it can be found that the position movement of the higher frequency absorption peaks are more sensitive to m and H comparing with the lower frequency absorption peaks. As Fig. 4(b) shows, the absorption frequency f1 increased from 9.82 GHz to 10.18 GHz as m decreased from 2.5 mm to 1.9 mm, while the absorption frequency f4 increased from 15.1 GHz to 15.87 GHz. Increasing L from 28 mm to 30 mm, the absorption frequency experiences a red-shift and the number of absorption peaks below 10 dB in the range of 8e18 GHz increased from three to six (Fig. 4(c)). These results indicate that resonates strongly depend on the size of structure [38,39]. Next, the effect of dielectric constant on the absorption peak are studied. As the permittivity (εr) of the dielectric FR4 is varied from 4.6 to 5, a red-shift is seen in all absorption peaks (Fig. 4(d)). And the peaks at higher frequencies (f4, f5 and f6) is more sensitive to the change of permittivity (εr), whose movements are larger than those
at lower frequencies. The effective medium theory under static limit is usually adopted to guide the design of low-permittivity dielectric metamaterials [18]. The effective permittivity is calculated using the Maxwell-Garnett formula. The relative permittivity εeff of the all-dielectric structure is given by Ref. [40]:
εeff ¼ εh
1 þ 2f au 1 f au
(5)
Where au¼(εu-εh)/(εuþ2εh) is the polarization factor, εh and εu denote the relative permittivity of the host medium and inclusions, respectively. f denotes the volume filling fraction occupied by the dielectric. According to Eq. (5), the absorption peak of the CSD structure will be modulated if εh, εu or f are changed. The observed trend suggests that the operation of the CSD structure can indeed be described by the effective medium theory. Spherical particles and other geometric shapes are known to exhibit similar properties [41e43]. Angular sensitivity of the proposed metamaterial have been shown in Fig. S1 and discussed in the supplementary material.
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Fig. 5. (a) Photograph of the fabricated CSD prototype, (b) The test of the proposed absorber in microwave anechoic chamber, (c) Measured permittivity of FR4 and (d) experimental reflection loss spectra.
Verification of simulated predictions was carried out through construction of a prototype CSD structure. The test sample consisting of 10 10 CSD units is shown in Fig. 5(a), which is fabricated by a computer numerical control (CNC) engraving machine (Guangzhou Seahawn Industrial Robotics Co., LTD.). The test of the proposed absorber in microwave anechoic chamber is shown in Fig. 5(b). Measurement was performed using NRL-arch reflectivity test system (a vector network analyzer AV3629 connects two speakers) in an EM microwave chamber. The measured and simulated reflection loss spectra in the range of 2e18 GHz was obtained and shown in Fig. 5(d), suggesting that the measured spectrum has similarities to that of simulated one. Reflection loss of resonant absorption peaks at 8.4 GHz, 9.92 GHz, 12.2 GHz, 13.56 GHz and 17.04 are 10.5 dB, 18.2 dB, 17.5 dBe15.8 dB and 7.8 dB, respectively. However, the measured reflection loss in the range of 15e16 GHz is smaller than that in the simulations. There are a number of reasons to explain the difference between experimental and simulated results. They can be summarized as follows: 1) The model used in simulation is periodically and extending infinitely in the X and Y directions, while the size of the measured sample is limited. The difference between the simulated and measured models will lead to inevitable deviation. 2) The inevitable deviation from the permittivity measurement of dielectrics. Fig. 5(c) shows that the measured value of real(εr) floats around 4.8 in the range of 2e18 GHz. 3) As seen above the reflection loss spectrum is very sensitive to the dimensional parameters of the CSD. While the machining deviations are inevitable. The precision of industrial grade CNC engraving machine is 0.1 mm. Small deviations in the engraving process could lead to such discrepancies, since they directly affect the dielectric-air interfaces, through alteration of the phase condition between the incident wave and the reflected wave in the dielectric. When the dielectric loss is very low, the change of phase difference easily affects the absorptivity [34]. According to
the previous analysis of the parameters of m and εr, the higher frequency absorption peak is more susceptible to parameter changes.
4. Conclusions In this paper, a 3D low-permittivity all-dielectric binary radar metamaterial absorber based on a CSD structure has been designed, simulated and fabricated. The structure is constructed using alldielectric material without metal resonance surface, realizing six resonant absorption peaks below 10 dB at 10.00 GHz, 12.19 GHz, 14.30 GHz, 15.46 GHz, 15.76 GHz and 17.60 GHz. It indicated that multi-band or even low-frequency absorption can be achieved by 3D low-permittivity material. The power loss is mainly caused by the electric resonances excited by multiple standing waves in the structure. The work demonstrates the effectiveness of 3D lowpermittivity all-dielectrics used as radar absorbers. The absorbers with integration of function and structure have potential applications in the EM energy capture and stealth fields.
Acknowledgements The work was supported by the Science and Technology Plan Project of Hunan Province [Grant No. 2015TP1007]; Initial Research Funding for Special Associate Professor by Central South University [Grant No. 202045002]; National Natural Science Foundation for Young Scientists of China [Grant No. 51802353]; Fundamental Research Funds for the Central Universities of Central South University [Grant No. 2018zzts330]; Opening Foundation of State Key Laboratory of Metamaterial Electromagnetic Modulation Technology [Grant No. GYL08-1443].
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
A multi-band binary radar absorbing metamaterial based on a 3D lowpermittivity all-dielectric structure Fen Zhang a, Qiang Wang b, Tian Zhou c, Yijun Xiong d, Youquan Wen d, Chao Jiang d, *, Yan Wang d, Zuojuan Du d, **, Isaac Abrahams e, LanZhi Wang f, Xiaozhong Huang d a
School of Physics and Electronics, Central South University, Changsha, 410083, China Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, 710049, China c State Key Laboratory of Metamaterial Electromagnetic Modulation Technology, Kuang-Chi Institute of Advanced Technology, Shenzhen, 518057, China d Hunan Key Laboratory of Advanced Fibers and Composites, School of Aeronautics and Astronautics, Central South University, Changsha, 410083, China e School of Biological and Chemical Sciences, Queen Mary University of London, London, E1 4NS, UK f Beijing Institute of Aerospace Launch Technology, No.1, Nandahongmen Road, Donggaodi, Fengtai District, Beijing, 100076, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 March 2019 Received in revised form 2 September 2019 Accepted 14 September 2019 Available online 14 September 2019
A new binary-structured metamaterial absorber (MA), consisting of a 3D cross-shaped dielectric (CSD) periodic array and a metal back plane, is proposed and fabricated. This structure realized six resonant absorption peaks below 10dB in the range of 8e18 GHz. Both simulated and experimental results demonstrate the effectiveness of this design in generating multiband and low frequency absorption, which is difficult to achieve in previous 2D dielectric absorbers. The electromagnetic(EM) field and energy loss density distributions of absorption peaks were investigated as well as effects of structural parameters on the reflection loss spectra. It indicated that multimode resonance is generated by standing waves in the 3D dielectric structure. Moreover, since the structure is made of a low-permittivity dielectric resin, the fabrication is relatively easy and low-cost. The design of a three-dimensional lowpermittivity all-dielectric structure described in this work has potential applications in the EM energy capture and stealth fields. © 2019 Published by Elsevier B.V.
Keywords: Metamaterial absorber Resonance 3-D Low-permittivity all-dielectric structure Multiband
1. Introduction Metamaterial absorbers (MAs) used in electromagnetic(EM) stealth have attracted a lot of attention because of their advantages of thinness, lightness and strong absorption [1e3]. The initial MA prototype consists of a multilayer structure including a metal microstrip line pattern, a dielectric layer, and a metal backplane [4e9]. The functionality of these types of MAs mainly depends on the metal resonance surface. To meet the requirement of stealth field to multiple band or broadband MAs, the metal microstrip line patterns have to be designed complicated [10,11], which requires a complex manufacturing processes, as well as the metal patterns are easily oxidized and corroded. Thus more durable and more easily
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (C. Jiang), [email protected] (Z. Du). https://doi.org/10.1016/j.jallcom.2019.152300 0925-8388/© 2019 Published by Elsevier B.V.
manufactured devices have to be considered. In recent years, all-dielectric metamaterials have been proposed as alternatives to metal-based MAs [12e14]. Some studies indicate that the interaction between subwavelength dielectrics and EM waves leads to negative permittivity and generates multiple resonances. Holloway et al. [15] theoretically demonstrated that dielectric hosts embedded in resonant dielectric spheres has a negative effect on permittivity and permeability. Liu et al. [16] embed a dielectric cube arrays (εr ¼ 1600, tan d ¼ 0.003) in an acrylonitrile butadiene styrene polymeric (ABS) substrate (εr ¼ 2.67, tan d ¼ 0.006). It generated absorption peaks at 8.45 and 11.97 GHz by Mie resonances of the dielectric component and provided a simple way to designing metamaterial perfect absorbers. Furtherly, an all-dielectric metamaterial consisting of 2D arrays of rectangular ceramic with a high-dielectric constant (εr ¼ 115, tan d ¼ 0.0015) was designed by Li et al. [17], and the two resulting resonant peaks could be merged by adjusting the geometric parameters of the ceramic resonator. However, such metamaterials, which are made of high-permittivity ceramics, have their inherent shortcomings,
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such as high-cost, processing difficulties and brittleness of ceramic components. Comparatively speaking, low-permittivity dielectric materials show advantages in terms of thermal stability, high strength, lower processing temperatures and low cost [18,19]. Yu et al. [20] proposed a design for a low-permittivity alldielectric reflective frequency selective surface, utilizing a periodic array of holes drilled in a multilayer contiguous dielectric plate to introduce three resonances at 23.7 GHz, 24.9 GHz, and 25.8 GHz. Wang et al. [21,22] designed a series of low-permittivity alldielectric resonance surfaces to achieve absorption peaks at 14.65 GHz and 16.61 GHz with a hole array structure. These works show that two or three EM resonances in the range of 13e18 GHz can be obtained. However, the above two-dimensional structure shows difficulties to achieve multiple band absorption and low frequencies absorption below 12 GHz, which limit its application seriously. A three-dimensional (3D) metamaterial structure has been proposed and constructed by stacking up a number of identical printed circuit boards (PCBs) on a common plane [23e27]. It was found that 3D structures can provide great flexibility in designing multi-band absorption. Shen et al. [28] proposed a 3D radar absorbing structure based on the stand-up resistive film, with high absorption capacity in the broadband. The absorption mechanism can be thought as multiple standing wave modes excited by 3D structure. The idea of 3D metamaterial structure has opened up a new path to design multi-band or broadband absorbers to meet different requirements. Based on the above ideas, we present a 3D low-permittivity alldielectric radar absorbing MA. The periodic unit of this absorber is composed of a cross-shaped pure dielectric structure and a metal reflective back plane. Simulations reveal a number of absorption peaks with reflection loss below 10 dB in the range of 8e18 GHz. Dielectric resonance theory and effective medium theory under a quasi-static limit have been verified experimentally with fabrication of a test sample with multiple absorption peaks.
2. Design and simulation The basic unit of the binary absorber structure in our work is composed of a cross-shaped dielectric (CSD) and a perfect electric conductor (PEC). The dielectric component was composed of FR4 an epoxy resin with εr ¼ 4.8 and tan d ¼ 0.025. Fig. 1(a) shows the design of the absorber, where the square dimension of the base, L ¼ 30 mm, the height, H ¼ 30 mm and the thickness of the crosspieces, m ¼ 2.2 mm. Since the transmission is totally blocked by the PEC, the absorptivity, A(u), of an absorber at frequency u can be defined as:
A(u) ¼ 1 - R(u) ¼ 1 - jS211j
(1)
where R(u) is the reflectivity and S11 is the reflection coefficient. The reflection loss of absorber is determined by the following equations according to transmission line theory [29e32]:
RLðdBÞ ¼ 20lgjðZin 1Þ=ðZin þ 1Þj Zin ¼
pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi mr =εr tanh jð2pfd=cÞ mr εr
(2) (3)
where εr, mr, c, f, d and Z in correspond to the relative complex permittivity, permeability, velocity of light, microwave frequency in free space, coating thickness and input impedance of the absorber, respectively. The EM performance of the proposed all-dielectric structure was investigated by simulation using the commercial finite integration technique (FIT) based software CST Microwave Studio (CST Computer Simulation Technology GmbH). Periodic boundary conditions were applied in the basal x and y directions, with open boundaries in the z-direction. In addition, since the structure shows 4-fold rotational symmetry, the absorber can operate under dual polarization.
3. Analysis and discussion A simulated reflection loss spectrum is displayed in Fig. 1(b). A number of resonant absorption peaks are observed, six of which are below 10 dB (taken as the industry standard) at 10.004 GHz (f1), 12.192 GHz (f2), 14.304 GHz (f3), 15.456 GHz (f4), 15.76 GHz (f5) and 17.6 GHz (f6). The corresponding reflection loss are 28.58 dB, 12.8 dB, 10.21 dB, 24.64 dB, 18.6 dB, and 11.23 dB, respectively. We have presented a table showing the comparison in aspects of structure, materials, permittivity (εr) and absorption band number among the reported dielectric absorbers (Table 1). The table shows that our design achieves six absorption bands by 3D structure using epoxy resin with low permittivity and high strength as raw material. Moreover, the preparation processes are easy. It is a successful attempt to design 3D metamaterial absorbers using low permittivity dielectrics. To understand the physical mechanism of absorption, distributions of EM field were calculated for three selected peaks (f1, f3 and f6) and are shown in Fig. 2. The Figure is captured in the middle of the cross. Fig. 2(a) indicates that the electric field is enhanced in the upper and the middle parts of the dielectric structure at f1. At f3, the electric field is enhanced in three regions of the dielectric structure (Fig. 2(b)), while at f6, there are locations of enhanced electric field, from top to bottom of the dielectric structure (Fig. 2(c)). Such phenomena can be explained by standing wave theory. A standing
Fig. 1. (a) The structure of the basic absorber unit. (b) simulated reflection loss spectrum, where f1 ¼10.004 GHz, f2 ¼ 12.192 GHz, f3 ¼ 14.304 GHz, f4 ¼ 15.456 GHz, f5 ¼ 15.76 GHz and f6 ¼ 17.6 GHz.
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Table 1 Comparisons in aspects of structure, materials, permittivity (εr) and absorption band number among the reported dielectric absorbers. Ref.
Structure (thickness)
materials
εr
absorption band number
[19] [20] [33] [34] Current work
Plane (3 mm) Plane (3 mm) Plane (1 mm) Plane (1 mm) 3D structure (30 mm)
epoxy resin FR4 BST/10 wt % MgO 0.7Ba0.6Sr0.4TiO3-0.3La(Mg0.5Ti0.5)O3 FR4
4.3 4.3 272 115 4.8
2 3 1 1 6
Fig. 2. Electric field distributions in the CSD structure at (a) f1 ¼10.004 GHz, (b) f3 ¼ 14.304 GHz, and c) f6 ¼ 17.6 GHz, and (d), (e) and (f) corresponding sections of magnetic field distribution in the direction of the wave vector k. E and H denote the electric and magnetic field directions. The maximum electric intensity is 4500 V/m and the maximum magnetic intensity is 15 A/m.
wave occurs when two waves with the same amplitude traveling in the opposite direction on the same line are superimposed on each other. In practice, standing waves are more likely formed by incident and reflected waves at the interface of two media. For a dielectric resonator, standing waves are formed by reflection at the dielectric-air and the dielectric-metal interfaces when EM waves are incident on the structure, generating the resonance [35,36]. The wavelength l of the standing wave and the wavelength l of the original EM wave satisfy the following formula:
1 ln where n ¼ 1; 2; ::::::: l¼ n 2 2
(4)
When the thickness of the dielectric is an odd multiple of a quarter of the wavelength, the excitation field can form a stable standing wave in the dielectric [37,39]. Therefore, the physical mechanism to explain the reason why the dielectric structure generates resonances is called multiple standing wave modes associated with the electric field distribution. When the phase difference of two nearby reflection waves is -2p, the absorptivity reaches maximum [36]. The magnetic field distributions at frequencies f1, f3 and f6 are shown in Fig. 2(def). It can be seen that, at f1, two enhanced magnetic field rings are existed in the upper and the middle parts of the dielectric structure of the unit on the H-o-k plane, which can be equivalent to two electric dipoles on the E-o-k plane (Fig. 2(a)). The distribution in Fig. 2(e) shows three enhanced magnetic field rings in the unit on the H-o-k plane. The associated magnetic field results in three electric dipoles, which appear to be strongly coupled to the
enhanced electric field in Fig. 2(b). The magnetic field distribution at f6 in Fig. 2(f) indicates that the enhanced magnetic field are distributed near the center and the boundary of unit. It shows a strong coupling with the distribution of the enhanced electric field (Fig. 2(c)). It can be seen that associated magnetic field rings result in multiple electric dipoles distributed on the E-o-k plane. Thus the magnetic field distribution inside the CSD structure resembles that of an electric dipole. A more informative illustration of the absorption inside the CSD structure, is given by the power loss density (PLD) distributions (in Fig. 3). PLD is mainly concentrated on the upper and the middle parts of the dielectric structure at f1 (Fig. 3(a)). At f3, PLD is distributed along 3 regions of the dielectric structure (Fig. 3(b)). And there are 5 points enhanced along the dielectric structure at f6 (Fig. 3(c)). The enhanced electric field and PLD distributions confirm that the power loss is mainly caused by the electric resonance. It is difficult to introduce strong electric or magnetic resonances in the uniform low-permittivity dielectric plate. However, the design of the unit forms dielectric-air interfaces at where these resonances can occur. The cross piece design facilitates multi-band absorption. In order to study the influence of dimensional parameters on the absorption frequencies, reflection loss spectra were calculated for CSD structural models with different dimensions L, H and m. Increasing H from 28 mm to 30 mm results in a red shift for all resonant absorption peaks (Fig. 4(a)). Reflection loss of f1 resonance significantly improved from 3.72 to 28.58 as H is increased to 30 mm. Thus, increasing H allows enhancement of higher-order
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Fig. 3. PLD distributions in the CSD structure at (a) f1 ¼10.004 GHz, (b) f3 ¼ 14.304 GHz, and (c) f6 ¼ 17.6 GHz. The maximum PLD is 6 105 W/m3.
Fig. 4. Simulated reflection loss curves for the CSD structure with varying values of (a) height H, (b) cross-piece thickness m, (c) square lattice dimension L and (d) permittivity εr of the dielectric.
multipolar resonance modes. As well as, the cross-piece thickness m increasing from 1.9 mm to 2.5 mm also induces a red shift in the frequencies of the resonance peaks (Fig. 4(b)). In addition, it can be found that the position movement of the higher frequency absorption peaks are more sensitive to m and H comparing with the lower frequency absorption peaks. As Fig. 4(b) shows, the absorption frequency f1 increased from 9.82 GHz to 10.18 GHz as m decreased from 2.5 mm to 1.9 mm, while the absorption frequency f4 increased from 15.1 GHz to 15.87 GHz. Increasing L from 28 mm to 30 mm, the absorption frequency experiences a red-shift and the number of absorption peaks below 10 dB in the range of 8e18 GHz increased from three to six (Fig. 4(c)). These results indicate that resonates strongly depend on the size of structure [38,39]. Next, the effect of dielectric constant on the absorption peak are studied. As the permittivity (εr) of the dielectric FR4 is varied from 4.6 to 5, a red-shift is seen in all absorption peaks (Fig. 4(d)). And the peaks at higher frequencies (f4, f5 and f6) is more sensitive to the change of permittivity (εr), whose movements are larger than those
at lower frequencies. The effective medium theory under static limit is usually adopted to guide the design of low-permittivity dielectric metamaterials [18]. The effective permittivity is calculated using the Maxwell-Garnett formula. The relative permittivity εeff of the all-dielectric structure is given by Ref. [40]:
εeff ¼ εh
1 þ 2f au 1 f au
(5)
Where au¼(εu-εh)/(εuþ2εh) is the polarization factor, εh and εu denote the relative permittivity of the host medium and inclusions, respectively. f denotes the volume filling fraction occupied by the dielectric. According to Eq. (5), the absorption peak of the CSD structure will be modulated if εh, εu or f are changed. The observed trend suggests that the operation of the CSD structure can indeed be described by the effective medium theory. Spherical particles and other geometric shapes are known to exhibit similar properties [41e43]. Angular sensitivity of the proposed metamaterial have been shown in Fig. S1 and discussed in the supplementary material.
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Fig. 5. (a) Photograph of the fabricated CSD prototype, (b) The test of the proposed absorber in microwave anechoic chamber, (c) Measured permittivity of FR4 and (d) experimental reflection loss spectra.
Verification of simulated predictions was carried out through construction of a prototype CSD structure. The test sample consisting of 10 10 CSD units is shown in Fig. 5(a), which is fabricated by a computer numerical control (CNC) engraving machine (Guangzhou Seahawn Industrial Robotics Co., LTD.). The test of the proposed absorber in microwave anechoic chamber is shown in Fig. 5(b). Measurement was performed using NRL-arch reflectivity test system (a vector network analyzer AV3629 connects two speakers) in an EM microwave chamber. The measured and simulated reflection loss spectra in the range of 2e18 GHz was obtained and shown in Fig. 5(d), suggesting that the measured spectrum has similarities to that of simulated one. Reflection loss of resonant absorption peaks at 8.4 GHz, 9.92 GHz, 12.2 GHz, 13.56 GHz and 17.04 are 10.5 dB, 18.2 dB, 17.5 dBe15.8 dB and 7.8 dB, respectively. However, the measured reflection loss in the range of 15e16 GHz is smaller than that in the simulations. There are a number of reasons to explain the difference between experimental and simulated results. They can be summarized as follows: 1) The model used in simulation is periodically and extending infinitely in the X and Y directions, while the size of the measured sample is limited. The difference between the simulated and measured models will lead to inevitable deviation. 2) The inevitable deviation from the permittivity measurement of dielectrics. Fig. 5(c) shows that the measured value of real(εr) floats around 4.8 in the range of 2e18 GHz. 3) As seen above the reflection loss spectrum is very sensitive to the dimensional parameters of the CSD. While the machining deviations are inevitable. The precision of industrial grade CNC engraving machine is 0.1 mm. Small deviations in the engraving process could lead to such discrepancies, since they directly affect the dielectric-air interfaces, through alteration of the phase condition between the incident wave and the reflected wave in the dielectric. When the dielectric loss is very low, the change of phase difference easily affects the absorptivity [34]. According to
the previous analysis of the parameters of m and εr, the higher frequency absorption peak is more susceptible to parameter changes.
4. Conclusions In this paper, a 3D low-permittivity all-dielectric binary radar metamaterial absorber based on a CSD structure has been designed, simulated and fabricated. The structure is constructed using alldielectric material without metal resonance surface, realizing six resonant absorption peaks below 10 dB at 10.00 GHz, 12.19 GHz, 14.30 GHz, 15.46 GHz, 15.76 GHz and 17.60 GHz. It indicated that multi-band or even low-frequency absorption can be achieved by 3D low-permittivity material. The power loss is mainly caused by the electric resonances excited by multiple standing waves in the structure. The work demonstrates the effectiveness of 3D lowpermittivity all-dielectrics used as radar absorbers. The absorbers with integration of function and structure have potential applications in the EM energy capture and stealth fields.
Acknowledgements The work was supported by the Science and Technology Plan Project of Hunan Province [Grant No. 2015TP1007]; Initial Research Funding for Special Associate Professor by Central South University [Grant No. 202045002]; National Natural Science Foundation for Young Scientists of China [Grant No. 51802353]; Fundamental Research Funds for the Central Universities of Central South University [Grant No. 2018zzts330]; Opening Foundation of State Key Laboratory of Metamaterial Electromagnetic Modulation Technology [Grant No. GYL08-1443].
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F. Zhang et al. / Journal of Alloys and Compounds 814 (2020) 152300
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