# Development of the Broadband Multilayer Absorption Materials with Genetic Algorithm up to 8 GHz Frequency

Authors: K. Murali Krishna; Amit Jain; Hardeep Singh Kang; Mithra Venkatesan; Anurag Shrivastava; Sitesh Kumar Singh
Journal: Security and Communication Networks
 (2022)

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## Abstract

A widely used genetic algorithm (GA) is endorsed to improve the design of a multilayer microwave radar absorbing material (MMRAM) which shows good absorption of radar waves over a broad frequency range. In this research, the authors have used genetic algorithm based on MMRAM which plays an important role in defense and civil applications. The scope of multilayer microwave radar absorbing material (MMRAM) is that it can absorb radar signals and reduce or eliminate their reflection. Its primary use is in defense and certain commercial enterprises. The multilayer RAM design demands the superiority of suitable materials to be used in different layers, a decision about multiple layers, and the optimum breadth of an individual layer. The permeability and permittivity of the materials varying with frequency in a fictitious material are used. The effect of change in thickness and the number of layers of RAM on reflectivity is studied. Since the material characteristics are frequency-dependent, different restrained conditions are used for frequency bands to identify the RAM that has good electromagnetic absorption in the frequency range of 1 to 8 GHz.


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## Body

## 1. Introduction

Multilayer microwave radar absorbers (MRAs) play a pivotal role in defense and civil applications. Although multilayer microwave radar absorbers are essential in flight traffic management, they pose a dilemma in offensive military operations because aircraft must attack and then flee without being noticed. The main intention of the design of MRA is to accomplish the minimum value of “Γ” in a specific frequency range. The absorber parameter can be varied to achieve optimum properties via an optimization technique. The performance of MRA depends on permeability, dielectric constant, frequency, angle of incidence, wave polarization [1], the thickness of layers, and the number of layers. The degree of the total reflection coefficient for the multilayer absorber is taken as a health and objective function in the MRA division. The MRA is often executed to provide a variety of high-performance designs rather than a single solution as supplied by other approaches. Chew’s recursive formula [2] is used for the evaluation of the “Γ.” This formula works for any number of layers, normal/oblique incidence, and polarizations (TE and TM). Chew’s formula is considered for normal incidence. Hence, the performance depends on a number of layers, thickness of each layer, and material [3] configuration. Genetic algorithms (GAs) are commonly used to solve a heterogeneity optimization problem in electromagnetic design. The multiobjective optimization problems with heterogeneous objectives are the ones in which the objective function components are considerably varied [4, 5].


### 1.1. Literature Survey

At the most critical radar bands of 0.2–2, 2–8, 8–12, 12–18, and 2–18 GHz, Toktas et al. [6] constructed five-layer broadband wide-incident-angle MRAMs. They used surrogate-based optimization and the Pareto front approach to build and execute the EM model optimally, considering the incident wave angle with TE and TM polarizations. Padhy et al. [7] covered in detail design and analysis of single-, two-, three-, and four-layered MRAMs. CoCr-based U-type hex ferrite MRAMs (Ba4(Co1–3xCrx)2Fe36O60) for various values of x (x = 0.05, 0.1, 0.2, and 0.25) were used as base materials. Thickness and material layers are optimized using genetic algorithm (GA). Prakash et al. [8] focused on the best multilayer absorber design using a suggested cost function that can work for both normal and oblique wave incidence up to the wide angle of incidence (0–60°) with TE and TM polarizations at the same time. This optimization approach minimizes the absorber’s maximum reflection coefficient by choosing appropriate materials from a literature library and reducing the entire thickness to the lowest attainable level. Panwar et al. [9] created ferrite-graphene (FG) composites with strong absorption and broad bandwidth, resulting in a reflection loss (RL) of −10 dB for 2 mm thickness. Ye et al. [10] converted the uniaxial perfectly matched layer into a fully passive medium and showed it experimentally on a deep subwavelength metamaterial surface. As an asymmetric single-layer perfect absorber without any impenetrable layers, Constantinos and Sergei [11] proposed a simple symmetric design of a single infinite grating of perfectly conducting rods covered by conventional dielectrics and an asymmetric single-layer perfect absorber. The performance improved even further, obtaining % absorption and arbitrary permittivity. Sudhendra and Madhu [12] suggested a unique ultrawide band dielectric radar absorber (RA) with thickness and weight restrictions. The RA panel consists of four lossy frequency selective surface (FSS) layers, each of which is made up of circular patches in a skewed grid lattice supported by RF transparent dielectric spacers and lastly backed by the shielded conducting plane. Ramya and Srinivasa [13] developed a polarization-insensitive perfect metamaterial absorber with increased bandwidth. Stealth technology employs a radar absorber panel to conceal a vehicle or building from radar detection. The absorbency of a material at a specific frequency of radar waves is determined by its composition. The outer split ring and inner asterisk-shaped resonators printed on FR4 dielectric substrate make up the suggested unit cell construction. Multilayer designs were suggested to increase absorption bandwidth. However, the structure was polarization-dependent [14]. Enhanced structures in the terahertz range bandwidth have been described in [15]. The study in [16] presented a dual-layer dual-band absorber with an increased bandwidth of 1.24 and 1.92 GHz. The single-layer arrangement achieved a bandwidth improvement of 940 MHz in [17]. Broadband absorbers were also considered in the C and Ku bands.In several papers, evolutionary techniques are used for the selection of suitable materials, to arrive at the optimum number of layers and thickness. A paper has been presented on the design of MRA using genetic algorithms (GAs) and validation using EDF [18]. The implementation of GA requires the formulation of an objective function to be minimized or maximized [19].This paper is organized as follows: problem formulation is given in Section2. Analysis of simulation results is done in Section 3. Section 4 describes validation of RAM design using Ship EDF software, and Section 5 gives conclusions.


## 1.1. Literature Survey

At the most critical radar bands of 0.2–2, 2–8, 8–12, 12–18, and 2–18 GHz, Toktas et al. [6] constructed five-layer broadband wide-incident-angle MRAMs. They used surrogate-based optimization and the Pareto front approach to build and execute the EM model optimally, considering the incident wave angle with TE and TM polarizations. Padhy et al. [7] covered in detail design and analysis of single-, two-, three-, and four-layered MRAMs. CoCr-based U-type hex ferrite MRAMs (Ba4(Co1–3xCrx)2Fe36O60) for various values of x (x = 0.05, 0.1, 0.2, and 0.25) were used as base materials. Thickness and material layers are optimized using genetic algorithm (GA). Prakash et al. [8] focused on the best multilayer absorber design using a suggested cost function that can work for both normal and oblique wave incidence up to the wide angle of incidence (0–60°) with TE and TM polarizations at the same time. This optimization approach minimizes the absorber’s maximum reflection coefficient by choosing appropriate materials from a literature library and reducing the entire thickness to the lowest attainable level. Panwar et al. [9] created ferrite-graphene (FG) composites with strong absorption and broad bandwidth, resulting in a reflection loss (RL) of −10 dB for 2 mm thickness. Ye et al. [10] converted the uniaxial perfectly matched layer into a fully passive medium and showed it experimentally on a deep subwavelength metamaterial surface. As an asymmetric single-layer perfect absorber without any impenetrable layers, Constantinos and Sergei [11] proposed a simple symmetric design of a single infinite grating of perfectly conducting rods covered by conventional dielectrics and an asymmetric single-layer perfect absorber. The performance improved even further, obtaining % absorption and arbitrary permittivity. Sudhendra and Madhu [12] suggested a unique ultrawide band dielectric radar absorber (RA) with thickness and weight restrictions. The RA panel consists of four lossy frequency selective surface (FSS) layers, each of which is made up of circular patches in a skewed grid lattice supported by RF transparent dielectric spacers and lastly backed by the shielded conducting plane. Ramya and Srinivasa [13] developed a polarization-insensitive perfect metamaterial absorber with increased bandwidth. Stealth technology employs a radar absorber panel to conceal a vehicle or building from radar detection. The absorbency of a material at a specific frequency of radar waves is determined by its composition. The outer split ring and inner asterisk-shaped resonators printed on FR4 dielectric substrate make up the suggested unit cell construction. Multilayer designs were suggested to increase absorption bandwidth. However, the structure was polarization-dependent [14]. Enhanced structures in the terahertz range bandwidth have been described in [15]. The study in [16] presented a dual-layer dual-band absorber with an increased bandwidth of 1.24 and 1.92 GHz. The single-layer arrangement achieved a bandwidth improvement of 940 MHz in [17]. Broadband absorbers were also considered in the C and Ku bands.In several papers, evolutionary techniques are used for the selection of suitable materials, to arrive at the optimum number of layers and thickness. A paper has been presented on the design of MRA using genetic algorithms (GAs) and validation using EDF [18]. The implementation of GA requires the formulation of an objective function to be minimized or maximized [19].This paper is organized as follows: problem formulation is given in Section2. Analysis of simulation results is done in Section 3. Section 4 describes validation of RAM design using Ship EDF software, and Section 5 gives conclusions.


## 2. Problem Formulation

The incident electromagnetic wave in free space makes an angleθ incident on the first interface. Depicted in Figure 1 is a structure of obliquely incident polarized wave multilayer microwave absorbers (MMAs). The multilayer radar absorber under design has N layers of different materials with changing permeability and permittivity values. Reversed PEC is a perfect electric conductor that is the final layer N + 1 as depicted in Figure 2. Because of physical realisation, the thickness range of a given layer has been fixed from 0.1 cm to 2 mm for layer optimization. Coating thicknesses of less than 0.01 cm are challenging to achieve. The aim is to design multilayer radar absorber materials chosen from a predefined database [3] with the minimum reflection coefficient Γmin in the frequency response range of 1 GHz to 8 GHz. The following expressions are recursive; i.e., Ri,i+1 is in the form of Ri+1,i+2:(1)Ri,i+1TE/TM=ri,i+1TE/TM+Ri+1,i+2TE/TMe−j2ki+1,zti+11+ri,i+1TE/TMRi+1,i+2TE/TMe−j2ki+1,zti+1.Figure 1
Obliquely incident polarized wave MMA structure.Figure 2
Multilayered RAM coating structure.For TE polarization,(2)ri,i+1TE=μi+1ki,z−μiki+1,zμi+1ki,z+μiki+1,z.For TM polarization,(3)ri,i+1TM=εi+1ki,z−εiki+1,zεi+1ki,z+εiki+1,z.εi is the complex permittivity, μi is the permeability, and ki,z is the wave number ki,zat ith layer. Z indicates the direction of EM wave propagation. ki,z=kicosθi, where the transmission angle θi is in the ith layer. Based on Snell’s law, ki,z for the oblique incidence and normal incidence θ=0 can be given by the following equations respectively:(4)ki,z=2∗π∗f∗μiεi−μ0ε0sin2θ,(5)ki,z=2∗π∗f∗μiεi.The total Γ of the MMA can be attained by evaluating recursively fromRN−1,N to R0,1. The fitness function is designed [20] for the perfect conductor (PEC) which shows infinite electrical conductivity at the N + 1th layer, and RN,N+1=−1 for TE and TM polarizations [21–23] to obtain the absorption in 1 GHz to 8 GHz wideband frequency response as selected from Figure 2,(6)F1=0,R0,1>R1,1,R0,1≤R1,1≤f≤2GHz,F2=0,R0,1>R2,1,R0,1≤R2,2<f≤4GHz,F3=0,R0,1>R3,1,R0,1≤R3,4<f≤8GHz.Restrained conditions are demoted asR1, R2, and R3, respectively. However, for FStep=0.3GHz, the points are N1,N2,andN3.(7)N1=4−2FStep+1=2FStep+1,N2=8−4FStep=4FStep,N3=12−8FStep=4FStep.Hence, the fitness function to genetic algorithm is(8)F=max∑i=1N1F1i+∑i=1N2F2i+∑i=1N3F3iNf.The lossy dielectric material is one in which the electrical resistance is not equivalent to 0 but the conductivity is poor. However, the lossy magnet material is a substance that dissipates energy from passing magnetic or auditory radiation.The database [21] is briefly summarized in Table 1. A fitness function and a material database are essential inputs to the GA tool. They are routinely used to find optimal or near-optimal solutions to tough problems that would take an eternity to solve otherwise. A fictitious database of materials whose dielectric and magnetic properties vary with frequency is taken from [3] and is given in Table 1.Table 1
Database of the predefined materials [7].
μr=1+j0 (LDM)εr=15+j0LMMεrμr1GHzμi1GHz10 +j051050 +j0315712εr=15+j0LRTMMμr=1+j0LDMμr1GHz×1E7μi1GHz×1E7εr1GHzεi1GHz0.02240.2800580.00870.17508100.03000.30001060.00450.0900Lossy relaxation−type magnetic materialsLRTMMsMaterialsLRTMM, Lossy dielectric materials (LDMs)Lossy magnetic materials (LMMs)Lossless dielectric materials (LLDMs)0.04500.30000.18750.75000.12000.60000.30620.8750


## 3. Analyses of Simulation Results

The optimization method (GA) is an iterative that starts at random selection population of possible solutions and gradually develops superior result through the genetic operators [24]. Selection, crossover, and mutation operators are often referred to as the three operators for iterative search. The probabilistic nature of all operators significantly increases the algorithm’s ability to seek maximum global fitness rather than local fitness functions.The population size, generations, and crossover are 100, 100, and 0.8, respectively. The optimization technique [25, 26] is shown in Figure 3. The minimum and maximum thicknesses for each layer are 0.01 mm and 2 mm, respectively. The MMRAM materials are selected from 16 different kinds of materials. Demonstration of frequency GHz versus reflection coefficient dB from Figures 4–7 is a worthwhile observation [27]. Hence, RAM performance improved with a frequency of 1 GHz to 8 GHz with an increase in thickness from 2 mm to 5 mm; particularly, RAM performance is improved in the low-frequency range through thickness increase of RAM [28]. The design of coatings is measured in (1 to 8)-GHz frequency band. When the thickness is 5 mm, the Γ completely meets the required conditions and approach −17 dB in the frequency range. Consequently, for thickness value, more than five layer RAM, it does not perform extremely well in the above frequency range [29]. The best possible results for RAM with respect to the total density of various thicknesses are displayed in Tables 2–5. The most favorable outcome of five-layer RAM for material sequence and complete thickness varied with respect to Tables 6 and 7 and is shown in Figures 8 and 9.Figure 3
Flowchart of the basic genetic algorithm optimiser.Figure 4
Results of RAMw.r.tw.r.t. total thickness ≤ 2 mm.Figure 5
Results of RAM w.r.t.w.r.t total thickness ≤ 3 mm.Figure 6
Optimal results of RAM with respect to total thickness ≤ 4 mm.Figure 7
Results of RAM with respect to total thickness ≤ 5 mm.Table 2
Best possible results of RAMwwith respect to the total density less than or equal to 2 mm.
Layer numberSubstance number/depth or thickness (mm)Fitness19/1.70830.3239/1.0846 + 5/0.2179 + 3/0.60820.40514/0.1151 + 9/0.8634 + 9/0.5014 + 4/0.1907 + 9/0.05510.40714/0.2860 + 14/0.0759 + 9/0.1283 + 9/0.1211 + 4/0.4077 + 3/0.2037 + 9/0.66680.441014/0.2215 + 5/0.3747 + 14/0.0609 + 4/0.7978 + 14/0.0705 + 13/0.0788 + 14/0.0290 + 13/0.0594 + 9/0.2722 + 5/0.02610.44Table 3
Best possible results of RAM with total thickness ≤ 4 mm.
Layer numberSubstance number/depth or thickness (mm)Fitness19/1.64520.32316/0.4726 + 3/1.0497 + 10/1.11540.64516/0.7104 + 2/0.3398 + 5/1.4958 + 9/0.6192 + 14/0.08720.76716/0.4534 + 6/0.6160 + 12/0.3243 + 7/0.5981 + 12/0.05675/0.6335 + 11/0.98910.841016/0.5091 + 7/0.6357 + 4/0.5688 + 6/0.0648 + 2/0.1349 + 5/0.2291 + 5/0.4521 + 9/0.1600 + 3/0.2788 + 11/0.64800.88Table 4
Best possible results of RAM with respect to total density less than or equal to 3 mm.
Layer numberSubstance number/depth or thickness (mm)Fitness19/1.61560.32316/0.4947 + 10/1.6182 + 12/0.62570.52516/0.6287 + 12/0.3816 + 2/0.1801 + 10/1.5089 + 8/0.12980.68716/0.4830 + 5/0.8640 + 2/0.2058 + 11/0.2274 + 9/0.2497 + 12/0.1194 + 10/0.70090.721016/0.4482 + 14/0.1467 + 5/0.0801 + 4/0.1345 + 8/0.0646 + 2/0.4171 + 6/0.0895 + 7/0.2251 + 4/0.0886 + 9/0.93070.84Table 5
Best possible results of RAM with total density less than or equal to 5 mm.
Layer numberSubstance number/depth or thickness (mm)Fitness19/1.69600.32316/0.5164 + 7/1.5099 + 11/1.72480.72516/0.4968 + 7/1.5463 + 5/0.7403 + 13/1.6671 + 10/0.32221.00716/0.5181 + 1/0.5493 + 6/1.3662 + 12/0.8952 + 9/0.4493 + 15/0.1159 + 10/0.86901.001016/0.4525 + 7/0.2834 + 6/0.6147 + 10/0.3016 + 7/0.6677 + 3/0.8684 + 9/0.6222 + 6/0.1284 + 5/0.5792 + 4/0.28371.00Table 6
The best possible results of 5-layer RAM withd1 + d2 + d3 + d4 + d5 ≤ thickness.
LayersSubstance number/depth or thickness (mm)Fitness214/0.1151 + 9/0.8634 + 9/0.5014 + 4/0.1907 + 9/0.05510.40316/0.6287 + 12/0.3816 + 2/0.1801 + 10/1.5089 + 8/0.12980.68416/0.7104 + 2/0.3398 + 5/1.4958 + 9/0.6192 + 14/0.08720.76516/0.4968 + 7/1.5463 + 5/0.7403 + 13/1.6671 + 10/0.32221.00Table 7
The best possible results of 5-layer RAM withd1 + d2 + d3 + d4 + d5 ≤ thickness.
LayersSubstance number/depth or thickness (mm)Fitness216/0.6860 + 7/0.01 + 5/0.01 + 13/0.0510 + 10/0.97510.06316/0.5100 + 7/0.3801 + 5/0.5100 + 13/0.010 + 10/1.51000.72416/0.4713 + 7/0.9042 + 5/1.1499 + 13/0.9628 + 10/0.50171.00516/0.5021 + 7/1.6188 + 5/1.2222 + 13/0.7845 + 10/0.76821.00Figure 8
The most favorable outcome of five-layer RAM with material sequence and complete thickness varied with respect to Table6.Figure 9
The most favorable outcome of five-layer RAM when material sequence is constant but whole thickness changesw.r.w.r.t. Table 7.The differentiation of both outcomes shows that the changing constraints in the maximum frequency band of 1–8 GHz are as presented in Figure10 and Table 8 shows the respective constituencies [30]. Within the frequency response of (1–2, 2–4, 4–8) GHz, the restricted conditions shall then be chosen as −12 dB, −18 dB, and −22 dB. The reflections are lower than −20 dB in the 1.4 GHz–8 GHz frequency range, in particular −24 dB in the 1.7–7 GHz frequency range. The comparison of the two results shows that the improved circumstances in the material series are considerably superior and the overall thickness of the layers is nearly equal.Table 8
Best possible outcome of two conditions with complete thickness ≤ 5 mm for five-layer RAM.
StateSubstance/depth or thickness (mm)FitnessR1 = −10 dBR2 = −18 dBR3 = −20 dB14/0.4587 + 6/0.4523 + 6/1.2608 + 3/0.9251 + 4/1.60471.00R1 = −12 dBR2 = −18 dBR3 = −22 dB16/0.4362 + 6/0.8501 + 6/1.2739 + 11/0.2290 + 11/1.74950.96Figure 10
The best possible outcome of both the conditions (5 mm) of Table8.


## 4. Ship Electromagnetic Design Framework (EDF) Software for Validation of Radar Absorbing Material Design

Ship EDF is a software framework designed for marine vessel electromagnetic (EM) design. It is a complete system that provides concurrent EM modelling and simulation, aiding in the optimization of the electromagnetic environment issues of a naval platform (E3).A three-layer structure with a conductive sheet backrest has been established for the radar absorbing material. A better result has been reached in a certain frequency band by gently modifying or moving the RC optimization to achieve the desirable fit. The GA yielded the best possible results of three-layer RAM. The maximum total thickness is 5 mm, the maximum thickness of each layer is 2 mm, and the designed frequency band is 0.85 GHz to 5.4 GHz depicted in Table9. Here, the restrained condition is R = −20 dB. For the optimum three-layer RAM obtained using GA, the reflectivity is computed over the frequency range of 0.85–5.4 GHz at a step of 0.3 GHz and the computed reflectivity values are validated with material editor Ship EDF software (first design) [31]. The comparison of the two findings indicates that the modified conditions in the material series are much better as well as the total thickness of the layers is found to be almost equal for a full frequency range of 1 to 8 GHz, as obtained from Figure 11 and Tables 9 and 10. Within the range of 2.5–8 GHz, “Γ” is lower than −20 dB. Particularly, the restricted conditions shall be then chosen as −14 dB within the 2–4 GHz frequency range and −20 dB within the 4–8 GHz frequency range.Table 9
The possible designs of three-layer RAM with total thickness ≤ 5 mm, (0.85–5.4) GHz, andR = −20 dB.
Layer no.1st design2nd design3rd designMaterial orderDepth (mm) (thickness)Material orderDepth (mm) (thickness)Material orderDepth (mm) (thickness)Layer1160.6364160.6385160.6962Layer231.814651.9101121.4943Layer341.807641.648841.8689Figure 11
The best results of 3-layer RAM with a total thickness ≤ 5 mm conformed by Table10 using Ship Electromagnetic Design Framework software.Table 10
Validation results of Ship EDF software (first design).
Frequency (GHz)R (dB) by GAR (dB) by Ship EDFFrequency (GHz)R (dB) by GAR (dB) by Ship EDF0.85−30.7773−30.7693.25−24.553−24.5691.15−36.1377−35.5533.55−25.828−25.8901.45−27.1259−26.8673.85−26.752−26.8551.75−23.8674−23.6964.15−26.749−26.8472.05−22.5257−22.4404.45−25.742−26.1322.35−22.2039−22.3534.75−24.233−24.2162.65−22.5514−22.5765.05−22.662−22.7402.95−23.3840−22.6665.35−21.212−21.250


## 5. Conclusion

The optimization technique (GA) is used for the design of multilayered radar absorbing materials in the frequency range of 1–8 GHz. As the maximum total density (thickness) of 5 mm is kept constant for varying number of layers such as 3 and 4, reflection of RAM coefficients are cannot fulfil the necessary conditions of restriction (RC). The radar absorbing material improved in a low-frequency band with an increased total density (thickness), and the Γ of the coatings is lower than −17 dB in the band of 1–8 GHz, since the overall depth (thickness) is 5 mm [32]. A better result is obtained in a certain frequency range by altering or moving slightly to achieve the desired fit on the RC optimization. For the optimum three-layer RAM obtained using the GA, the reflectivity is computed over the bandwidth of 0.85–5.4 GHz. The RAM performance is better under restrained conditions of –10 dB, –18 dB, and –20 dB with reflection coefficients in operating frequency L, S, and C bands, respectively. Some obstacles are found in the process of genetic algorithm. For example, defining a representation for the problem is perhaps the most critical step in developing a genetic algorithm. The language used to describe possible solutions must be resilient; that is, it must be able to endure random modifications without resulting in fatal errors.The material sequence and the total thickness of the layers are compared and found to be nearly equal. For the optimum three-layer RAM obtained using the GA, the reflectivity is computed over the frequency response of 0.85–5.4 GHz. These layers are compared with each other on the basis of thickness and different frequency bands. The RAM performance is better under restrained conditions of –10 dB, –18 dB, and –20 dB with reflection coefficients in the frequency response bands of L, S, and C.



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