Thickness optimization of a double-layered microwave absorber combining magnetic and dielectric particles

The purpose of this study is to optimize the thickness of the double-layered microwave absorber for obtaining the highest absorption. The graphenic-based carbon compounds and Fe3O4 magnetic particles were combined to fabricate the double-layered absorber. The thickness was optimized by employing a genetic algorithm (GA) to obtain high reflection loss RLmin values. These samples at a thickness of 2 mm were measured for reflection loss (RL) with a Vector Network Analyzer (VNA). Input variables, such as relatively complex permeability and relatively complex permittivity, were obtained using a conversion program that uses Nicolson-Ross-Weir (NRW) method from VNA S-parameter values (S11 and S21) data. By entering the permeability and permittivity of the complex relative to GA, the thickness can be optimized to produce high RLmin value. Optimization of the double-layer thickness of 12 absorbers produces the optimum thickness of d1 = 5.99 mm and d2 = 0.87 mm among the materials combination, which results in a high RLmin (−44.69 dB). This optimization is very important for designing double-layer radar absorbing material (RAM) which results in high RLmin values.


Introduction
In recent years, electromagnetic radiation pollution or electromagnetic interference (EMI) has become an increasingly serious, and worldwide problem because of the use of electromagnetic waves in the rapidly developing navigation, telecommunications, aviation activities, and also in the increasing use of various electronic devices [1][2][3]. The EMI not only disrupts the electronic systems but also is potentially hazardous for human health [3][4][5]. Therefore, electromagnetic wave absorbing materials are being investigated extensively to solve the EMI problem [6]. Electromagnetic wave absorber is a material that can effectively weaken the intensity of electromagnetic waves by causing magnetic loss, and dielectric loss [7]. Different types of materials have been used for microwave absorption, such as magnetic, and dielectric dampers [8]. The level of microwave absorption of these materials depends on complex permittivity, and permeability values for the particular frequency range in question [8].
The growing demand for RAM makes continuous effort to improve RAMs' microwave absorption properties necessary [8]. Microwave absorber can effectively absorb electromagnetic wave energy, and convert electromagnetic energy into heat [9][10][11][12][13][14]. Magnetite nanoparticles, such as Fe 3 O 4 , are considered as suitable microwave-absorbing material because of the magnetic loss they cause, their easy synthesis, and because they are environmentally friendly, non-toxic, and low cost [10,11,[15][16][17][18][19][20]. One effective way of improving the material's absorption of electromagnetic waves is to combine Fe 3 O 4 with dielectric materials, such as reduced graphene oxide (rGO) [10,21]. The recently tested graphene derivative (rGO) [6,15] as a new carbon material, is very Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
interesting because of its lightweight, extraordinary electrical conductivity, extraordinary chemical properties, physical properties, and mechanical properties [10,22].
Multi-layer absorber is the focus of current research [23,24]. It can give the best microwave-absorbing performance, and therefore, meet the requirements of an ideal microwave-absorbing material (RL min < −20 dB) [24]. Several studies have been conducted on design methods and techniques for RAMs, such as design optimization using the simplex method, simulated annealing method, particle swarm optimization (PSO) [24][25][26]. According to the previous study [27], heuristic methods developed to date are evolutionary computation, simulated annealing, taboo search, GA, PSO, ant colony optimization (ACO), and others. Promising heuristic methods to solve optimization problems are GA, and PSO. However, for the modeling processes, the GA approach is superior to PSO [28]. GA has several advantages. This algorithm involves very little mathematical calculations to solve a problem. The evolutionary operators used in it make this algorithm very effective in global search. It has high flexibility to hybridize with other search methods to improve their effectiveness [29].
Based on the above description, in this research absorber was designed to increase RL . min The design, among others, considers material selection (a combination of magnetic, and dielectric materials), the combinations of the arrangement of materials of the double-layer absorber, the design of the structure (multi-layer), and the selection of the thickness of each absorber to obtain a high RL min value. The purpose of this study was to optimize the thickness of the double-layer absorber with the GA method based on the transmission line model.

Sample preparation and characterization
Fe 3 O 4 powder (sample a) was obtained from the rocks of Tanah Laut (South Kalimantan, Indonesia). The rocks were ground to a coarse powder using mortar, and pestle. The coarse powder was sieved through mesh 200 to obtain fine powder consisting of uniform-sized particles that had a large surface area so that the powder is evenly distributed. The methods for the preparation of fine rGO samples (sample b) with uniform-sized particles were chemical exfoliation processes, and mechanical exfoliation processes, which have been discussed in other research [22]. In this research, the chemical exfoliation process was used. The rGO powder which had previously been heated to 400°C was mixed with 100 ml of 1 M HCl solution. The variation used in this research is the mole ratio between 1 M HCl solution, and rGO powder, which is 1: 5 (sample c), and 1:10 (sample d). Further, Fe 3 O 4, and rGO were considered, respectively, as magnetic, and dielectric particles. Then, the samples were characterized by VNA.

Design and Optimization of Double-Layer of RAM
A schematic diagram of a conductor backed double-layered absorber to form composite, consisting of combinations: magnetic-dielectric (pure), magnetic-dielectric (with treatment), and dielectric (pure)-dielectric (with treatment) materials. They have intrinsic properties μ r1 (relatively complex permeability), ε r1 (relatively complex permittivity), ), , h γ, and d 1 (thicknesses) for the layer-1 that is close to the metal plate, and μ r2 , ε r2 , , h γ, and d 2 for the layer-2 as the front-facing outward as shown in figure 1. Layer-1, and layer-2 are the absorption layers, and the matching layer, respectively [30,31]. The input impedance on the surface of the air-absorbent, and the calculation of the RL for the sample system were computed as follows [32]: The design of the optimization of RAM on the double-layer (Dallenbach layer) on GA was divided into four stages. The first stage was to determine the optimization parameters, input variables, and output variables [33]. The optimization parameters used in this study were population size (PopSize), probability of crossing over P , c ( ) and mutation probability P . ) values are obtained from VNA data, namely real S 11 (real reflection coefficient), imaginary S 11 (imaginary reflection coefficient), real S 21 (transmission coefficient real), and imaginary S 21 (imaginary transmission coefficient) are converted using the NRW conversion method in the MATLAB program. While the output variables to be sought in this study were the thickness of the material in each layer (d , 1 and d 2 ). The second stage was to determine fitness function [33]. The fitness function is defined as an individual evaluated based on a certain function as a measure of his performance [33]. Optimization using the GA method required the incorporation of a mathematical model into the fitness function. In this study, the reflection loss equation of double-layer RAM (equation (2)) was used as a mathematical model to be optimized. Because the dimension of reflection loss was predetermined limitation. A boundary mathematical model was needed to include these variables in the fitness function. This mathematical model is known as constrained optimization.
The third stage was the standard GA techniques [33] (figure 2). The sequence of steps was, first to determine the population: before determining the initial population, the first step is to determine the number of individuals in the population. For example, the number of individuals is N. After that, it will generate an initial population that has N individuals randomly [34]. The second step is to evaluate with binary encoding : an encoding where each gene can only be 0 or 1, and linear fitness ranking, namely a mechanism that aims to scale fitness values. The third step was reproduction through elitism: a process that aims to keep the individual with the highest fitness value from being lost during evolution, it is necessary to make one or more copies. Next, beyond roulette-wheel selection: this method aims to map the individuals in a circle segment sequentially so that each individual segment has the same size as its fitness size [35]. Furthermore, thru cross-over, specifically the cross-over of two chromosomes causes one chromosome to lead to a fine solution [36]. Herein after, by the way of mutation, in other words functions to replace the missing genes from the population as a result of the selection process [35]). Finally, general replacement, namely all individuals (e.g. N individuals in a population) of a generation are replaced at once by N new individuals resulting from crossovers, and mutations.
The fourth stage was the simulation, and optimization of the results [33]. Display optimization simulation of double-layered RAM showed the value of fitness during the optimization process from beginning to end as were needed to follow the course of the optimization process, and the results achieved. Meanwhile, the results achieved are the thickness of each material in the double-layered RAM. Meanwhile, the optimization results are displayed in the intermediate graph simulation (frequency of reflection loss).

Composite preparation and double-layer reflection loss characterization
The absorber materials selected in this research were sample a, sample b, sample c, and sample d. The method of preparing the samples has been discussed by another researcher [22]. For example, the two selected material combinations are sample b for layer-1 (absorption layer) and sample a for layer-2 (matching layer) (see figure 1), so the combination is called b-a (interface-a). Because the matching layer is sample a, it is called interface-a. The thickness of sample b is called d , 1 and the thickness of sample a is d .

Air-absorber interface layer
Sample combination I-II layer

Results and discussion
3.1. Reflection loss measurement of single-layer absorber Reflection loss of single-layer for all samples is shown in figure 3. Table 3 shows a relatively small RL min value, and the experimental bandwidth of all single-layer absorber samples. Thickness d ( ) of each sample is 2 mm. From figure 3, absorber layer bandwidth is defined as the frequency width f f ) where the sample RL min is more than −5 dB. The relatively small RL min indicates that with a single-layer dielectric or magnetic absorber it is difficult to achieve the impedance match and broad frequencies of wave absorption [37,38].
The design of a microwave absorber depends on the basic electromagnetic parameters such as relative complex permeability, relative complex permittivity, thickness, and frequency of microwave operation. It also depends on the material structure (multi-layer structure, core-shell structure, etc), material selection, and combination of selected materials [32,38,39]. The multi-layer structure (double-layer) can be manipulated to produce a high RL min by finding the appropriate thickness at the desired frequency with GA. Figures 4(a), and (b) show permittivity in relation with frequency. Real permittivity (e¢) is the ability to absorb microwave energy, while imaginary permittivity e) is the ability to release microwave energy [40]. The negative sign in the value of imaginary permittivity indicates that the energy was released. Figures 4(a), and (b) show that e¢ and e have two peaks in each sample. The two peaks are at∼8.   The dielectric loss tangent tan , e d (

Calculation of reflection loss from double-layer design
) and magnetic loss tangent tan m d ( )of material are quantitative loss of electrical energy, and magnetic energy due to different physical processes, such as electrical conduction, dielectric relaxation, dielectric resonance, and loss from non-linear processes [41].  that magnetic loss is a major factor in electromagnetic absorption. Figures 3(c), and (d) show that samples have a better wave absorption effect when the value of tan e d is greater than the value of e [38]. From figure 5(b) shows that sample a has a larger magnetic loss for wave absorption material. Figure 5(a) shows that the dielectric material samples b, c, and d have a tangent loss of dielectric loss values of ∼10 dB, ∼−80 dB, and ∼−30 dB respectively. The mechanical, and chemical exfoliation process by heating at 400°C of rGO (samples b, and c) can increase the value of the dielectric loss tangent. Sample c has a tangent value of dielectric loss greater than sample d because of the influence of the mole ratio between 1 M HCl solution, and the rGO powder. Figure 5(b) shows that the magnetic material sample (sample a) has a magnetic loss tangent value greater than those of the dielectric materials (samples b, c, and d). Equation The complex permeability, and permittivity of RAM (figure 4) play an important role in determining the properties of reflection. One way to reduce the reflection is by the condition of electromagnetic waves entering into the absorbent material with the greatest level (suitable characteristic impedance) [44]. According to [44], to achieve the condition of impedance matching the ratio between material, and free space should be 1. m e ¢ ¢ = / According to equation (1), if dielectric loss is present, a high value of permeability is needed so that matching impedance is reached [44]. By combining the impedance requirements that match attenuation, to reduce reflection, magnetic material should have a low e value, a high m value, and corresponding values ', e and ' m in the ratio 1 m e ¢ ¢ = / [44]. Conversely, dielectric materials should have a high value of , e low value of , m and these values ofe¢ and ' m should be in the ratio 1. m e ¢ ¢ = / Figure 6 shows the high RL min (<−20 dB) for various variations of the double-layer absorber when compared to the single-layer absorber for samples a, b, c, and d ( figure 3). From figure 5, the ideal absorber layer . This is consistent with the theory of the combination of impedance matching with attenuation to reduce reflection (in the previous paragraph).
Meanwhile, the largest bandwidth is sample 11, where the composition of the absorption layer is sample b, and the matching layer is sample d with tT 2.23 mm. Meanwhile, sample 2 (c-a) with absorption layer composition c, and the matching layer a, and total thickness (tT) 1.51 mm shows the lowest RL min (−23.89 dB) for bandwidth of ∼0.20. That is because sample 2 (dielectric-magnetic absorber) has high values of e (sample c), and m (sample a) at 10.84 GHz (figures 4(c), and (d)) so it does not fit the impedance matching combination theory with attenuation to reduce reflection (see the previous paragraph). From table 4, samples 1, and 4, samples 2, and 7, samples 3, and 10, samples 5, and 8, samples 6, and 11, and samples 9, and 12 show that the order in which materials are stacked also plays an important role in determining the final nature of RAM, by affecting the amplitude, and position of the resonant peak [46,47]. From table 3, and 4, it can be seen that the optimization of double-layer absorber thickness with GA of all samples can produce a higher RL min value (> −20 dB) from the single-layer absorber but reduces the bandwidth. From table 4, and figure 6 it can be seen that the results of the optimization of the thickness of the double-layer absorber with GA can produce RAM with the required properties, because the thickness variation, the combination of materials with different properties, and the order in which the materials are stacked can improve the RAM absorption quality.

Conclusion
The double-layer microwave absorber with a combination of samples b, and c with the thickness d 1 =5.99 mm, and d 2 =0.87 mm respectively (total thickness of 6.86 mm), at a frequency of 9.12 GHz resulted in the largest RL min (−44.69 dB) in this study. Optimization of the thickness of the double-layer microwave absorber with the GA of the twelve composite materials in this study can produce high RL min value (< −20 dB) which is much higher than a single-layer microwave absorber. Twelve composite materials used in this study are considered to be good RAM because they can absorb microwaves in X-band. It should be noted that the optimization of the thickness of the double-layer with GA is necessary to produce high RL , min and is very important step before conducting an effective and efficient experiment.

Data availability statement
The data generated and/or analyzed during the current study are not publicly available for legal/ethical reasons but are available from the corresponding author on reasonable request.