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Design and preparation of an ultrathin broadband metamaterial absorber with a magnetic substrate based on genetic algorithm
Journal Pre-proofs Design and preparation of an ultrathin broadband metamaterial absorber with a magnetic substrate based on genetic algorithm Benfang Duan, Junming Zhang, Peng Wang, Guowu Wang, Donglin He, Liang Qiao, Tao Wang PII: DOI: Reference:
S0304-8853(19)34084-3 https://doi.org/10.1016/j.jmmm.2020.166439 MAGMA 166439
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
2 December 2019 9 January 2020 10 January 2020
Please cite this article as: B. Duan, J. Zhang, P. Wang, G. Wang, D. He, L. Qiao, T. Wang, Design and preparation of an ultrathin broadband metamaterial absorber with a magnetic substrate based on genetic algorithm, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166439
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier B.V.
Design and preparation of an ultrathin broadband metamaterial absorber with a magnetic substrate based on genetic algorithm Benfang Duan, Junming Zhang, Peng Wang, Guowu Wang, Donglin He, Liang Qiao, Tao Wang*. Institute of Applied Magnetics, Key Laboratory of Magnetism and Magnetic Materials of the Ministry of Education, Key Laboratory of Special Function Materials and Structure Design, Lanzhou University, Lanzhou 730000, People’s Republic of China
Abstract High-efficiency microwave absorption materials are widely used in electronic equipment and communication facilities. This study aims to develop a broad-bandwidth metamaterial absorber based on the magnetic substrate with a central frequency selective surface (FSS). It is however, different from the strategy of expanding the bandwidth for metamaterial absorbers reported in other literatures, in this study, a unique development strategy that involves selecting the most suitable magnetic substrate from a database using genetic algorithm is adopted. By adding an optimized FSS layer to the magnetic substrate, its loss performance and impedance matching performance are considerably improved, and the resulting metamaterial absorber exhibits excellent absorption properties. At a thickness of 3.1 mm, the reflection loss in the range from 2.5 to 17.2 GHz is below –10 dB, which is significantly better than the values reported in previous studies. In addition, the prepared metamaterial absorber possesses excellent absorption characteristics under oblique incidence conditions. The strategy proposed in this study leads to the successful development of a high-efficiency metamaterial absorber and represents a more effective approach than those previously used in the field. Keywords: Magnetic substrate, genetic algorithm, frequency selective surface, microwave absorption
1. Introduction The advent of 5G technology has increased the demand for microwave absorbing materials (MAMs), which play a vital role in electronic equipment and communication facilities [1]. Traditional MAMs include silicon carbide, ferrite, graphite, and magnetic metal powders that possess excellent microwave absorption properties in a narrow frequency range. Previous studies [2-4] have demonstrated that structural absorbers can offer broader absorption bandwidths. Chen et al. prepared an absorber from carbon nanotubes/graphene and foam plastics with a thickness of 10 mm that exhibited reflection losses (RLs) below – 10 dB in the range from 2 to 18 GHz. Hou et al. reported an absorber with a thickness of 15 mm and RL values below –10 dB in the same frequency range fabricated from graphene oxide and polypropylene fabric. Thus, broader bandwidths were achieved using thicker structural absorbers, which considerably limited their applications. Magnetic materials have large refractive indices and possess the ability to compress incident electromagnetic waves, both magnetic and dielectric losses [5-8]. Hence, it is preferable for them to have a broad bandwidth and relatively small thickness. Rozanov [9] studied the relationship between the operational bandwidth and absorber thickness; as a result, an RL below –10 dB was achieved at a thickness less than 1/17.2 of the maximum operational wavelength. As commonly used filter in microwave and optics, frequency selective surface (FSS) has easy-to-adjust electromagnetic characteristics, and its size can be controlled by adjusting the periodic structure, geometry, and size of the FSS. It also has the characteristics of thin thickness, strong absorption intensity, wide incident angle, and no surface loss layer [10-12]. In addition, it has been recently reported that the microwave absorption properties of a magnetic substrate may be improved through the addition of an FSS [13-16]. Yang et al. prepared a metamaterial absorber composed of ferrite and FSS with a thickness of 4.13 mm and RL below –10 dB in the range from 4 to 10 GHz, while Li et al. used Fe-Co and FSS to fabricate an absorber with a thickness of 3 mm and RL below –10 dB in the range from 2 to 4.4 GHz. Although the absorption performances of these absorbers were considerably improved, increasing the bandwidth and achieving good low-frequency absorption properties at smaller thicknesses remains a difficult task. A magnetic substrate with excellent absorption characteristics can be further improved through the addition of an FSS layer, which represents the most viable route for developing a high-efficiency metamaterial absorber. Genetic algorithm is a random search technique that is commonly used to identify the global maximum of a multidimensional objective function in defined parameter space and produce an optimal result for a given set of design variables [17]. Numerous studies utilized genetic algorithms to optimize the electromagnetic properties of materials [18-20]. However, in a very few of them, genetic algorithms were used to select a magnetic substrate for a high-efficiency metamaterial absorber. Our laboratory has been developing soft magnetic materials for decades, whose parameters are inputted into a large database [21-25]. In this study, we use a genetic algorithm to select a suitable magnetic substrate from this database and then apply an FSS layer to its center. The periodic structure and geometric parameters of the FSS layer are optimized to obtain a metamaterial
absorber with superior microwave absorption properties.
2. Materials and methods 2.1 Fabrication of the metamaterial absorber 128 composite samples with different volume fractions of Fe-Ni, Fe-Si, Fe-Si-Al, Fe-Co, ferrite, and carbonyl iron powders are produced by mixing them with polyurethane. The powders are dispersed uniformly by ultrasonic stirring, and the resulting suspensions are coated smoothly onto substrate surfaces and dried. The obtained samples are pressed into toroidshaped specimens with an outer diameter of 7.00 mm, an inner diameter of 3.04 mm, and a thickness of 0.8–1.0 mm. The electromagnetic properties of these specimens and RLs of the metamaterial absorbers are measured by a vector network analyzer and an arch method, respectively. The detailed preparation diagram of the metamaterial absorber and the digital photographs of the fabricated metamaterial absorber are shown in Fig. 1(a) and (b).
Fig. 1 (a) The detailed preparation diagram of the metamaterial absorber, (b) the digital photographs of the fabricated metamaterial absorber.
2.2 Structural design and simulation Genetic algorithm is generally used to find the global maximum of a multi-dimensional objective function in defined parameter space. This non-linear optimization method has been widely applied to optimize the electromagnetic properties of optic materials, especially the multilayer magnetic ones. It produces a combination of various design parameters that correspond to the optimal absorption properties in a specific frequency range. The variable parameters in this study included the type and thickness of the material, while the bandwidths and RLs of
the MAMs are the objective functions. To apply a genetic algorithm, all parameters are encoded and concatenated to form a binary string of chromosomes, which represented the actual parameter values. A population of chromosomes is randomly created, and the corresponding fitness functions are determined. These functions select individual chromosomes to reproduce and form a new generation. Genetic operators, such as crossover and mutation, play an important role in ensuring the diversity of the population. The described evolution process continued over a few iterations to produce an optimal solution. The structural diagram and coding scheme of the magnetic substrate designed by the genetic algorithm are shown in Fig. 2. Here, the 128 samples are represented by 7 bits, and the total thickness of the magnetic substrate is limited to 3 mm and coded by 4 bits. The actual thickness of each layer is defined by the proportion represented by the different layers of code. Consequently, each layer is represented by a binary string of 11 bits (Fig. 2(b)), which is evolved to generate the optimal solution. The magnetic substrate consists of two different materials (Fig. 2(a)), and their electromagnetic parameters are shown in Fig. 3. The bottom and top layers in this figure are denoted S1 and S2, respectively.
Fig. 2. (a) A structural diagram and (b) a coding scheme of the magnetic substrate.
To further improve the microwave absorption properties of the magnetic substrate, an FSS layer is applied to its center to form a metamaterial absorber (see Figs. 3(a) and (b)). The magnetic substrate included a 1.3 mm thick S2 layer and a 1.7 mm thick S1 layer. The intermediate FSS layer (300 mm × 300 mm) prepared by an etching process is composed of an FR4 layer with a thickness of 0.08 mm, the dielectric constant of 4.4, and tangent of loss angle equal to 0.02 and a copper superficial layer with a thickness of 0.02 mm. The unit structure of the FSS layer include four circles with different radii (r1 = ab/2, r2 = abc/2, r3 = abcd/2, and r4 = abcde/2), as shown in Fig. 3(c). A finite element method is applied to simulate the design metamaterial absorber using the HFSS 13.0 electromagnetic simulation software package. The structural diagram of the metamaterial absorber in the simulation environment depicts in Fig. 3(d) indicates that the direction of electric field E matches the +X direction, the direction of magnetic field H matches the +Y direction, and the electromagnetic wave is oriented normally towards the metamaterial absorber along the –Z direction. The electromagnetic simulation is conducted under master-
slave boundary conditions for the unit elements oriented in the X and Y directions.
Fig. 3. (a) and (b) Structural diagrams of the metamaterial absorber. (c) A unit structure of the FSS layer. (d) A structural diagram of the metamaterial absorber constructed using the HFSS software.
3. Results and discussion The electromagnetic parameters of the two magnetic materials selected by the genetic algorithm are described in Fig. 4. It is obvious that the permittivity and permeability of S1 and S2 are quite different. This means that the impedance matching performance of the two materials is different. The magnetic substrate designed by a genetic algorithm, with S1 as the bottom layer and S2 as the top layer, has been reported by many people and proved to be effective in expanding bandwidth. With respect to S1, S2 has a dielectric constant that matches the permeability, which means that the impedance matching performance is better, which makes it easier for electromagnetic waves to enter the absorber [26-28]. The top layer (S2) also plays an important role in the attenuation of the electromagnetic wave energy. The bottom layer (S1) has high permeability and dielectric constant, which allow effective absorption and attenuation of electromagnetic waves. The high electromagnetic parameters of S1 are beneficial for thin absorbers.
Fig. 4. Permeability and permittivity values of the bottom (S1) and top (S2) layers.
The microwave absorbing performance of MAMs is generally evaluated by RL. According to the transmission line theory, when the electromagnetic wave is normally incident into the absorber backed by the metal plate, its RL can be calculated by the following equation:
|
𝑅𝐿 = 20𝑙𝑜𝑔
𝑍𝑖𝑛 + 𝑍0
(1)
(( ) ) (( ) )
𝑍2(𝑍1 + 𝑍2𝑡𝑎𝑛ℎ 𝑗 𝑍𝑖𝑛 =
|,
𝑍𝑖𝑛 ― 𝑍0
𝑍2 + 𝑍1𝑡𝑎𝑛ℎ 𝑗
2𝜋𝑓𝑑2 𝑐
2𝜋𝑓𝑑2 𝑐
𝜇2𝜀2)
,
(2)
𝜇2𝜀2)
where Z0 is the free space impedance, and Z1 and Z2 are the characteristic impedances of S1 and S2, respectively.
The absorption properties of the magnetic substrate designed by the genetic algorithm are shown in Fig. 5. RL values
below –10 dB were achieved in the ranges of 3.15–6.15 and 14–17.6 GHz with a minimum of –32 dB centered at 4.35 GHz (99.9% absorption). The magnetic substrate designed by the genetic algorithm exhibited excellent absorption characteristics at low frequencies, and the operating bandwidth reached a magnitude of 6.6 GHz, which was significantly larger than the values obtained in previous studies. The absorption performance of the substrate was expected to be improved with the addition of an FSS layer to its center, which would assist in the development of a high-efficiency metamaterial absorber with a broad bandwidth, low thickness, and excellent absorption performance at low frequencies. Fig. 5. RL values of the magnetic substrate designed by the genetic algorithm.
The electromagnetic characteristics of FSS (including its adsorption properties) are easy to adjust by changing the material’s size, periodic structure, and pattern. The periodic structure and unit size of the FSS layer in this work were varied by changing the geometric parameters a, b, c, d, and e. According to Fig. 6, the metamaterial absorber exhibits the best microwave absorption performance at a = 15, b = 0.5, c = 0.5, d = 0.9, and e = 0.9. Its RL was less than –10 dB in the frequency range of 2.5–17.2 GHz corresponding to an effective operating bandwidth of 14.7 GHz.
Fig. 6. Absorption properties of the metamaterial absorbers with different periodic structures and FSS unit sizes.
The microwave absorption properties of the metamaterial absorbers reveal that the addition of an optimized FSS layer to the middle of the magnetic substrate decreased its RL below –10 dB in the range from 2.5 to 17.2 GHz (Fig. 7). The effective operating bandwidth is more than doubled after this addition from 6.6 to 14.8 GHz, and the effective operational frequency is lowered from 3.15 to 2.5 GHz. These results indicate that the addition of the FSS layer can improve the absorption performance of a magnetic substrate. The parameters of various metamaterial absorbers consisting of magnetic substrates and FSS layers fabricated in previous studies are listed in Table 1. The metamaterial absorber developed in this work via genetic algorithm
optimization is thinner than those reported previously, possesses a larger operational bandwidth and exhibits excellent lowfrequency absorption properties. Fig. 7. Absorption properties of the magnetic substrate (blue) and metamaterial absorber (red).
Table 1. Experimental properties of various metamaterial absorbers determined at RL < –10 dB. Absorber
Fmin (GHz)
Fbandwidth (GHz)
Thickness (mm)
Reference
Carbon nanotube with FSS
4.0
4–10; 14.5–18
4.13
[29]
Magnetic substrate with FSS
2.55
2.55–5.68
2.20
[30]
Carbonyl iron with FSS
2.5
2.50–5.0
2.00
[31]
Glass fiber with FSS
8.0
8–18
3.50
[32]
Magnetic substrate with FSS
2.5
2.5–17.2
3.10
Current paper
The role of FSS was highlighted by comparing the magnetic substrate (without FSS) and metamaterial absorber (with FSS). The absorption performance of an absorber is generally evaluated by studying its loss performance and impedance matching performance. Figs. 8(a), (b) and (c) depict interference losses, intrinsic losses and total losses of metamaterial absorber and magnetic substrate calculated based on the symmetry model, respectively [33]. All these parameters obtained for the metamaterial absorber are systematically higher than the values measured for the magnetic substrate in most frequency bands for the following reason. When an electromagnetic wave enters the metamaterial absorber, it is first attenuated by the
top layer and then enter on the FSS layer. Because the latter represents a periodic structure composed of the FR4 substrate and copper, it acts as an additional interfacial layer that promotes multiple internal reflections, scattering, and ohmic losses of the electromagnetic wave. In addition, FSS has good filtering characteristics due to its planar periodic structure and reflects incident waves in a specific frequency range depending on its shape, unit size, and substrate properties. In this work, the electromagnetic wave filtered by FSS is converted to numerous discrete periodic non-uniform plane waves, which enters the bottom layer of the magnetic substrate and underwent further attenuation. These phenomena result in higher losses of the metamaterial absorber as compared with those of the magnetic substrate alone. Besides, the interference losses and intrinsic losses of the metamaterial absorber are reduced in the range from 3.3 to 5.8 GHz, but the total loss reaches a 90% absorption. Fig. 8. (a) Interference losses, (b) intrinsic losses, (c) total losses and (d) effective impedances of the metamaterial absorber and magnetic substrate.
An improvement of the absorber impedance matching performance can enhance its absorption performance with the best possible effective impedance value equal to 1. Therefore, the effect of FSS addition on the impedance matching performance of the absorber was studied by calculating its effective impedance via the following formula [34-35]:
𝑍𝑒𝑓𝑓 =
(1 + 𝑆11)2 ― 𝑆212 (1 ― 𝑆11)2 ― 𝑆212
(3)
Because a metal backing plate was used for calculating the RL, formula (3) was simplified as follows: 𝑍𝑒𝑓𝑓 =
(1 + 𝑆11)2 (1 ― 𝑆11)2
(4)
The effective impedance was closest to 1 in the range from 2.5 to 17.2 GHz, where the impedance matching performance of the metamaterial absorber was superior to that of the magnetic substrate (Fig. 8(c)). The addition of an FSS layer to the magnetic substrate resulted in a loss of performance and improved the impedance matching performance indicating that it was possible to design metamaterial absorbers with low thicknesses, broad bandwidths, and excellent low-frequency absorption performance by the proposed method. The use of the genetic algorithm for selecting a suitable magnetic substrate with good absorption properties from a database represented a critical step in developing a high-efficiency metamaterial absorber. The microwave absorption characteristics of the metamaterial absorber under the normal incidence conditions are excellent. However, there is an increasing demand for the absorption of electromagnetic waves in the near field, which makes the material absorption properties under oblique incidence conditions equally important. We further studied the absorbing properties of metamaterial absorber in transverse electric (TE) and transverse magnetic (TM) polarizations. The simulated reflectivity of oblique incidence in TM and TE modes is shown in Fig. 9. It can be seen that the microwave absorption performance of the metamaterial absorber studied at different incident angles reveals that TE mode decreases the absorption intensity with an increase in the incident angle. At an incident angle of 60°, the RL is below −5 dB in the range from 2.5 to 18 GHz. In contrast, TM mode initially increases the absorption intensity and then decreases it with increasing incident angle. The metamaterial absorber has excellent absorption properties in the range from 0° to 60°, and the RL reaches –10 dB between 2.5 and 18 GHz at an incident angle of 60°. The RL is as low as –30 dB in the range from 6.5 to 13 GHz, where 99.9% of the incident electromagnetic wave is absorbed, and the effective bandwidth is 6.5 GHz. At an incident angle of 80°, the absorption intensity decreases sharply because the propagation distance of the incident wave in the metamaterial absorber is much greater than 1/4 of the wavelength, which negatively affects its impedance matching and microwave absorption characteristics [36]. Overall, the metamaterial absorber exhibits excellent absorption properties under the normal incidence and oblique incidence conditions and meets the application requirements for a high-efficiency absorber.
Fig. 9. Absorption properties of the metamaterial absorber determined at different incident angles.
The comparison of the simulation and experimental data obtained for the magnetic substrate and metamaterial absorber reveals that these two data sets are in good agreement with each other and that their absorption intensities differ only slightly (Fig. 10 (a) and (b)). Hence, the simulation model designed by HFSS is reliable, and electromagnetic simulations can be used to predict the absorber performance and improve research efficiency.
Fig. 10. (a) and (b) Simulated and experimental RL values of the magnetic substrate and metamaterial absorber, respectively.
4. Conclusion A novel strategy involving the genetic algorithm is adopted to design a metamaterial absorber consisting of an FSS and a magnetic substrate. The magnetic substrate with excellent absorption characteristics is selected from a database using the genetic algorithm, and an optimized FSS is added to its center. The absorption performance of the resulting material is tested both theoretically and experimentally, and the obtained data sets are in good agreement with each other. The RL of the metamaterial absorber is below –10 dB in the range from 2.5 to 17.2 GHz under the normal incidence conditions and reaches a minimum value of –30 dB in the range from 6.5 to 13 GHz at an incident angle of 60°. In our design, the design of the frequency selective surface pattern does not rely on the genetic algorithm, and the complete metamaterial absorber is not designed automatically. Therefore, it is possible that our current results are not the global optimal solution. If the magnetic substrate can be selected by a genetic algorithm, and the geometric parameters of the frequency selective surface can be designed and optimized automatically, a better solution may be obtained. Overall, the use of the genetic algorithm proves to be an effective approach for selecting a magnetic substrate with good absorption properties, which is a critical step in developing a high-efficiency metamaterial absorber.
Acknowledgment This work was supported by the National Natural Science Foundation of China (No.11574122) and Joint Fund of Equipment Pre-Research and Ministry of Education (No.6141A02033242).
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Benfang Duan ： Data curation, Writing- Original draft preparation. Conceptualization, Methodology, Software ， Writing- Reviewing and Editing
Junming Zhang：Conceptualization, Methodology，Software Peng Wang；Guowu Wang；Donglin He；Liang Qiao：Validation，Formal analysis
The authors declared that they have no conflicts of interest to this work.
Highlights 1. A unique development strategy was adopted to design an ultrathin broadband metamaterial absorber. 2. The magnetic substrate selected from a database by genetic algorithm and then applied an optimized FSS layer to its center. 3. The loss performance and impedance matching performance were considerably improved. 4. At a thickness of 3.1 mm, the reflection loss is below −10 dB in the frequency range from 2.5 to 17.2 GHz.
S0304-8853(19)34084-3 https://doi.org/10.1016/j.jmmm.2020.166439 MAGMA 166439
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Revised Date: Accepted Date:
2 December 2019 9 January 2020 10 January 2020
Please cite this article as: B. Duan, J. Zhang, P. Wang, G. Wang, D. He, L. Qiao, T. Wang, Design and preparation of an ultrathin broadband metamaterial absorber with a magnetic substrate based on genetic algorithm, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166439
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier B.V.
Design and preparation of an ultrathin broadband metamaterial absorber with a magnetic substrate based on genetic algorithm Benfang Duan, Junming Zhang, Peng Wang, Guowu Wang, Donglin He, Liang Qiao, Tao Wang*. Institute of Applied Magnetics, Key Laboratory of Magnetism and Magnetic Materials of the Ministry of Education, Key Laboratory of Special Function Materials and Structure Design, Lanzhou University, Lanzhou 730000, People’s Republic of China
Abstract High-efficiency microwave absorption materials are widely used in electronic equipment and communication facilities. This study aims to develop a broad-bandwidth metamaterial absorber based on the magnetic substrate with a central frequency selective surface (FSS). It is however, different from the strategy of expanding the bandwidth for metamaterial absorbers reported in other literatures, in this study, a unique development strategy that involves selecting the most suitable magnetic substrate from a database using genetic algorithm is adopted. By adding an optimized FSS layer to the magnetic substrate, its loss performance and impedance matching performance are considerably improved, and the resulting metamaterial absorber exhibits excellent absorption properties. At a thickness of 3.1 mm, the reflection loss in the range from 2.5 to 17.2 GHz is below –10 dB, which is significantly better than the values reported in previous studies. In addition, the prepared metamaterial absorber possesses excellent absorption characteristics under oblique incidence conditions. The strategy proposed in this study leads to the successful development of a high-efficiency metamaterial absorber and represents a more effective approach than those previously used in the field. Keywords: Magnetic substrate, genetic algorithm, frequency selective surface, microwave absorption
1. Introduction The advent of 5G technology has increased the demand for microwave absorbing materials (MAMs), which play a vital role in electronic equipment and communication facilities [1]. Traditional MAMs include silicon carbide, ferrite, graphite, and magnetic metal powders that possess excellent microwave absorption properties in a narrow frequency range. Previous studies [2-4] have demonstrated that structural absorbers can offer broader absorption bandwidths. Chen et al. prepared an absorber from carbon nanotubes/graphene and foam plastics with a thickness of 10 mm that exhibited reflection losses (RLs) below – 10 dB in the range from 2 to 18 GHz. Hou et al. reported an absorber with a thickness of 15 mm and RL values below –10 dB in the same frequency range fabricated from graphene oxide and polypropylene fabric. Thus, broader bandwidths were achieved using thicker structural absorbers, which considerably limited their applications. Magnetic materials have large refractive indices and possess the ability to compress incident electromagnetic waves, both magnetic and dielectric losses [5-8]. Hence, it is preferable for them to have a broad bandwidth and relatively small thickness. Rozanov [9] studied the relationship between the operational bandwidth and absorber thickness; as a result, an RL below –10 dB was achieved at a thickness less than 1/17.2 of the maximum operational wavelength. As commonly used filter in microwave and optics, frequency selective surface (FSS) has easy-to-adjust electromagnetic characteristics, and its size can be controlled by adjusting the periodic structure, geometry, and size of the FSS. It also has the characteristics of thin thickness, strong absorption intensity, wide incident angle, and no surface loss layer [10-12]. In addition, it has been recently reported that the microwave absorption properties of a magnetic substrate may be improved through the addition of an FSS [13-16]. Yang et al. prepared a metamaterial absorber composed of ferrite and FSS with a thickness of 4.13 mm and RL below –10 dB in the range from 4 to 10 GHz, while Li et al. used Fe-Co and FSS to fabricate an absorber with a thickness of 3 mm and RL below –10 dB in the range from 2 to 4.4 GHz. Although the absorption performances of these absorbers were considerably improved, increasing the bandwidth and achieving good low-frequency absorption properties at smaller thicknesses remains a difficult task. A magnetic substrate with excellent absorption characteristics can be further improved through the addition of an FSS layer, which represents the most viable route for developing a high-efficiency metamaterial absorber. Genetic algorithm is a random search technique that is commonly used to identify the global maximum of a multidimensional objective function in defined parameter space and produce an optimal result for a given set of design variables [17]. Numerous studies utilized genetic algorithms to optimize the electromagnetic properties of materials [18-20]. However, in a very few of them, genetic algorithms were used to select a magnetic substrate for a high-efficiency metamaterial absorber. Our laboratory has been developing soft magnetic materials for decades, whose parameters are inputted into a large database [21-25]. In this study, we use a genetic algorithm to select a suitable magnetic substrate from this database and then apply an FSS layer to its center. The periodic structure and geometric parameters of the FSS layer are optimized to obtain a metamaterial
absorber with superior microwave absorption properties.
2. Materials and methods 2.1 Fabrication of the metamaterial absorber 128 composite samples with different volume fractions of Fe-Ni, Fe-Si, Fe-Si-Al, Fe-Co, ferrite, and carbonyl iron powders are produced by mixing them with polyurethane. The powders are dispersed uniformly by ultrasonic stirring, and the resulting suspensions are coated smoothly onto substrate surfaces and dried. The obtained samples are pressed into toroidshaped specimens with an outer diameter of 7.00 mm, an inner diameter of 3.04 mm, and a thickness of 0.8–1.0 mm. The electromagnetic properties of these specimens and RLs of the metamaterial absorbers are measured by a vector network analyzer and an arch method, respectively. The detailed preparation diagram of the metamaterial absorber and the digital photographs of the fabricated metamaterial absorber are shown in Fig. 1(a) and (b).
Fig. 1 (a) The detailed preparation diagram of the metamaterial absorber, (b) the digital photographs of the fabricated metamaterial absorber.
2.2 Structural design and simulation Genetic algorithm is generally used to find the global maximum of a multi-dimensional objective function in defined parameter space. This non-linear optimization method has been widely applied to optimize the electromagnetic properties of optic materials, especially the multilayer magnetic ones. It produces a combination of various design parameters that correspond to the optimal absorption properties in a specific frequency range. The variable parameters in this study included the type and thickness of the material, while the bandwidths and RLs of
the MAMs are the objective functions. To apply a genetic algorithm, all parameters are encoded and concatenated to form a binary string of chromosomes, which represented the actual parameter values. A population of chromosomes is randomly created, and the corresponding fitness functions are determined. These functions select individual chromosomes to reproduce and form a new generation. Genetic operators, such as crossover and mutation, play an important role in ensuring the diversity of the population. The described evolution process continued over a few iterations to produce an optimal solution. The structural diagram and coding scheme of the magnetic substrate designed by the genetic algorithm are shown in Fig. 2. Here, the 128 samples are represented by 7 bits, and the total thickness of the magnetic substrate is limited to 3 mm and coded by 4 bits. The actual thickness of each layer is defined by the proportion represented by the different layers of code. Consequently, each layer is represented by a binary string of 11 bits (Fig. 2(b)), which is evolved to generate the optimal solution. The magnetic substrate consists of two different materials (Fig. 2(a)), and their electromagnetic parameters are shown in Fig. 3. The bottom and top layers in this figure are denoted S1 and S2, respectively.
Fig. 2. (a) A structural diagram and (b) a coding scheme of the magnetic substrate.
To further improve the microwave absorption properties of the magnetic substrate, an FSS layer is applied to its center to form a metamaterial absorber (see Figs. 3(a) and (b)). The magnetic substrate included a 1.3 mm thick S2 layer and a 1.7 mm thick S1 layer. The intermediate FSS layer (300 mm × 300 mm) prepared by an etching process is composed of an FR4 layer with a thickness of 0.08 mm, the dielectric constant of 4.4, and tangent of loss angle equal to 0.02 and a copper superficial layer with a thickness of 0.02 mm. The unit structure of the FSS layer include four circles with different radii (r1 = ab/2, r2 = abc/2, r3 = abcd/2, and r4 = abcde/2), as shown in Fig. 3(c). A finite element method is applied to simulate the design metamaterial absorber using the HFSS 13.0 electromagnetic simulation software package. The structural diagram of the metamaterial absorber in the simulation environment depicts in Fig. 3(d) indicates that the direction of electric field E matches the +X direction, the direction of magnetic field H matches the +Y direction, and the electromagnetic wave is oriented normally towards the metamaterial absorber along the –Z direction. The electromagnetic simulation is conducted under master-
slave boundary conditions for the unit elements oriented in the X and Y directions.
Fig. 3. (a) and (b) Structural diagrams of the metamaterial absorber. (c) A unit structure of the FSS layer. (d) A structural diagram of the metamaterial absorber constructed using the HFSS software.
3. Results and discussion The electromagnetic parameters of the two magnetic materials selected by the genetic algorithm are described in Fig. 4. It is obvious that the permittivity and permeability of S1 and S2 are quite different. This means that the impedance matching performance of the two materials is different. The magnetic substrate designed by a genetic algorithm, with S1 as the bottom layer and S2 as the top layer, has been reported by many people and proved to be effective in expanding bandwidth. With respect to S1, S2 has a dielectric constant that matches the permeability, which means that the impedance matching performance is better, which makes it easier for electromagnetic waves to enter the absorber [26-28]. The top layer (S2) also plays an important role in the attenuation of the electromagnetic wave energy. The bottom layer (S1) has high permeability and dielectric constant, which allow effective absorption and attenuation of electromagnetic waves. The high electromagnetic parameters of S1 are beneficial for thin absorbers.
Fig. 4. Permeability and permittivity values of the bottom (S1) and top (S2) layers.
The microwave absorbing performance of MAMs is generally evaluated by RL. According to the transmission line theory, when the electromagnetic wave is normally incident into the absorber backed by the metal plate, its RL can be calculated by the following equation:
|
𝑅𝐿 = 20𝑙𝑜𝑔
𝑍𝑖𝑛 + 𝑍0
(1)
(( ) ) (( ) )
𝑍2(𝑍1 + 𝑍2𝑡𝑎𝑛ℎ 𝑗 𝑍𝑖𝑛 =
|,
𝑍𝑖𝑛 ― 𝑍0
𝑍2 + 𝑍1𝑡𝑎𝑛ℎ 𝑗
2𝜋𝑓𝑑2 𝑐
2𝜋𝑓𝑑2 𝑐
𝜇2𝜀2)
,
(2)
𝜇2𝜀2)
where Z0 is the free space impedance, and Z1 and Z2 are the characteristic impedances of S1 and S2, respectively.
The absorption properties of the magnetic substrate designed by the genetic algorithm are shown in Fig. 5. RL values
below –10 dB were achieved in the ranges of 3.15–6.15 and 14–17.6 GHz with a minimum of –32 dB centered at 4.35 GHz (99.9% absorption). The magnetic substrate designed by the genetic algorithm exhibited excellent absorption characteristics at low frequencies, and the operating bandwidth reached a magnitude of 6.6 GHz, which was significantly larger than the values obtained in previous studies. The absorption performance of the substrate was expected to be improved with the addition of an FSS layer to its center, which would assist in the development of a high-efficiency metamaterial absorber with a broad bandwidth, low thickness, and excellent absorption performance at low frequencies. Fig. 5. RL values of the magnetic substrate designed by the genetic algorithm.
The electromagnetic characteristics of FSS (including its adsorption properties) are easy to adjust by changing the material’s size, periodic structure, and pattern. The periodic structure and unit size of the FSS layer in this work were varied by changing the geometric parameters a, b, c, d, and e. According to Fig. 6, the metamaterial absorber exhibits the best microwave absorption performance at a = 15, b = 0.5, c = 0.5, d = 0.9, and e = 0.9. Its RL was less than –10 dB in the frequency range of 2.5–17.2 GHz corresponding to an effective operating bandwidth of 14.7 GHz.
Fig. 6. Absorption properties of the metamaterial absorbers with different periodic structures and FSS unit sizes.
The microwave absorption properties of the metamaterial absorbers reveal that the addition of an optimized FSS layer to the middle of the magnetic substrate decreased its RL below –10 dB in the range from 2.5 to 17.2 GHz (Fig. 7). The effective operating bandwidth is more than doubled after this addition from 6.6 to 14.8 GHz, and the effective operational frequency is lowered from 3.15 to 2.5 GHz. These results indicate that the addition of the FSS layer can improve the absorption performance of a magnetic substrate. The parameters of various metamaterial absorbers consisting of magnetic substrates and FSS layers fabricated in previous studies are listed in Table 1. The metamaterial absorber developed in this work via genetic algorithm
optimization is thinner than those reported previously, possesses a larger operational bandwidth and exhibits excellent lowfrequency absorption properties. Fig. 7. Absorption properties of the magnetic substrate (blue) and metamaterial absorber (red).
Table 1. Experimental properties of various metamaterial absorbers determined at RL < –10 dB. Absorber
Fmin (GHz)
Fbandwidth (GHz)
Thickness (mm)
Reference
Carbon nanotube with FSS
4.0
4–10; 14.5–18
4.13
[29]
Magnetic substrate with FSS
2.55
2.55–5.68
2.20
[30]
Carbonyl iron with FSS
2.5
2.50–5.0
2.00
[31]
Glass fiber with FSS
8.0
8–18
3.50
[32]
Magnetic substrate with FSS
2.5
2.5–17.2
3.10
Current paper
The role of FSS was highlighted by comparing the magnetic substrate (without FSS) and metamaterial absorber (with FSS). The absorption performance of an absorber is generally evaluated by studying its loss performance and impedance matching performance. Figs. 8(a), (b) and (c) depict interference losses, intrinsic losses and total losses of metamaterial absorber and magnetic substrate calculated based on the symmetry model, respectively [33]. All these parameters obtained for the metamaterial absorber are systematically higher than the values measured for the magnetic substrate in most frequency bands for the following reason. When an electromagnetic wave enters the metamaterial absorber, it is first attenuated by the
top layer and then enter on the FSS layer. Because the latter represents a periodic structure composed of the FR4 substrate and copper, it acts as an additional interfacial layer that promotes multiple internal reflections, scattering, and ohmic losses of the electromagnetic wave. In addition, FSS has good filtering characteristics due to its planar periodic structure and reflects incident waves in a specific frequency range depending on its shape, unit size, and substrate properties. In this work, the electromagnetic wave filtered by FSS is converted to numerous discrete periodic non-uniform plane waves, which enters the bottom layer of the magnetic substrate and underwent further attenuation. These phenomena result in higher losses of the metamaterial absorber as compared with those of the magnetic substrate alone. Besides, the interference losses and intrinsic losses of the metamaterial absorber are reduced in the range from 3.3 to 5.8 GHz, but the total loss reaches a 90% absorption. Fig. 8. (a) Interference losses, (b) intrinsic losses, (c) total losses and (d) effective impedances of the metamaterial absorber and magnetic substrate.
An improvement of the absorber impedance matching performance can enhance its absorption performance with the best possible effective impedance value equal to 1. Therefore, the effect of FSS addition on the impedance matching performance of the absorber was studied by calculating its effective impedance via the following formula [34-35]:
𝑍𝑒𝑓𝑓 =
(1 + 𝑆11)2 ― 𝑆212 (1 ― 𝑆11)2 ― 𝑆212
(3)
Because a metal backing plate was used for calculating the RL, formula (3) was simplified as follows: 𝑍𝑒𝑓𝑓 =
(1 + 𝑆11)2 (1 ― 𝑆11)2
(4)
The effective impedance was closest to 1 in the range from 2.5 to 17.2 GHz, where the impedance matching performance of the metamaterial absorber was superior to that of the magnetic substrate (Fig. 8(c)). The addition of an FSS layer to the magnetic substrate resulted in a loss of performance and improved the impedance matching performance indicating that it was possible to design metamaterial absorbers with low thicknesses, broad bandwidths, and excellent low-frequency absorption performance by the proposed method. The use of the genetic algorithm for selecting a suitable magnetic substrate with good absorption properties from a database represented a critical step in developing a high-efficiency metamaterial absorber. The microwave absorption characteristics of the metamaterial absorber under the normal incidence conditions are excellent. However, there is an increasing demand for the absorption of electromagnetic waves in the near field, which makes the material absorption properties under oblique incidence conditions equally important. We further studied the absorbing properties of metamaterial absorber in transverse electric (TE) and transverse magnetic (TM) polarizations. The simulated reflectivity of oblique incidence in TM and TE modes is shown in Fig. 9. It can be seen that the microwave absorption performance of the metamaterial absorber studied at different incident angles reveals that TE mode decreases the absorption intensity with an increase in the incident angle. At an incident angle of 60°, the RL is below −5 dB in the range from 2.5 to 18 GHz. In contrast, TM mode initially increases the absorption intensity and then decreases it with increasing incident angle. The metamaterial absorber has excellent absorption properties in the range from 0° to 60°, and the RL reaches –10 dB between 2.5 and 18 GHz at an incident angle of 60°. The RL is as low as –30 dB in the range from 6.5 to 13 GHz, where 99.9% of the incident electromagnetic wave is absorbed, and the effective bandwidth is 6.5 GHz. At an incident angle of 80°, the absorption intensity decreases sharply because the propagation distance of the incident wave in the metamaterial absorber is much greater than 1/4 of the wavelength, which negatively affects its impedance matching and microwave absorption characteristics [36]. Overall, the metamaterial absorber exhibits excellent absorption properties under the normal incidence and oblique incidence conditions and meets the application requirements for a high-efficiency absorber.
Fig. 9. Absorption properties of the metamaterial absorber determined at different incident angles.
The comparison of the simulation and experimental data obtained for the magnetic substrate and metamaterial absorber reveals that these two data sets are in good agreement with each other and that their absorption intensities differ only slightly (Fig. 10 (a) and (b)). Hence, the simulation model designed by HFSS is reliable, and electromagnetic simulations can be used to predict the absorber performance and improve research efficiency.
Fig. 10. (a) and (b) Simulated and experimental RL values of the magnetic substrate and metamaterial absorber, respectively.
4. Conclusion A novel strategy involving the genetic algorithm is adopted to design a metamaterial absorber consisting of an FSS and a magnetic substrate. The magnetic substrate with excellent absorption characteristics is selected from a database using the genetic algorithm, and an optimized FSS is added to its center. The absorption performance of the resulting material is tested both theoretically and experimentally, and the obtained data sets are in good agreement with each other. The RL of the metamaterial absorber is below –10 dB in the range from 2.5 to 17.2 GHz under the normal incidence conditions and reaches a minimum value of –30 dB in the range from 6.5 to 13 GHz at an incident angle of 60°. In our design, the design of the frequency selective surface pattern does not rely on the genetic algorithm, and the complete metamaterial absorber is not designed automatically. Therefore, it is possible that our current results are not the global optimal solution. If the magnetic substrate can be selected by a genetic algorithm, and the geometric parameters of the frequency selective surface can be designed and optimized automatically, a better solution may be obtained. Overall, the use of the genetic algorithm proves to be an effective approach for selecting a magnetic substrate with good absorption properties, which is a critical step in developing a high-efficiency metamaterial absorber.
Acknowledgment This work was supported by the National Natural Science Foundation of China (No.11574122) and Joint Fund of Equipment Pre-Research and Ministry of Education (No.6141A02033242).
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Benfang Duan ： Data curation, Writing- Original draft preparation. Conceptualization, Methodology, Software ， Writing- Reviewing and Editing
Junming Zhang：Conceptualization, Methodology，Software Peng Wang；Guowu Wang；Donglin He；Liang Qiao：Validation，Formal analysis
The authors declared that they have no conflicts of interest to this work.
Highlights 1. A unique development strategy was adopted to design an ultrathin broadband metamaterial absorber. 2. The magnetic substrate selected from a database by genetic algorithm and then applied an optimized FSS layer to its center. 3. The loss performance and impedance matching performance were considerably improved. 4. At a thickness of 3.1 mm, the reflection loss is below −10 dB in the frequency range from 2.5 to 17.2 GHz.