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3D Electromagnetic Analysis and Optimization of Metamaterial Constructed by SRR Using the MOGA Algorithm for Performance Improvement

The study presents 3D electromagnetic analysis and optimization of metamaterial constructed split ring resonator. The analysis was carried out under electromagnetic analysis conditions by using electromagnetic boundary conditions master and slave. The operating frequency range, in other words the performance characteristic, has been analysed from 1 GHz to 20 GHz. The split-ring resonator design has been analysed on triple co-axes in accordance with its actual use. Surface current density, electric field strength and magnetic field strength values were examined in the analysis. Metamaterial based split-ring resonators are used in many fields. Today, it has many applications as measurement and sensor or as antenna in 5G applications. In order to obtain a suitable design at high frequencies, micron-level designs are required. Newly developed objective functions are presented in the study. In this study, good results were obtained with an optimized SRR design by using multi-objective genetic algorithm in the range up to 20 GHz that can achieve negative refractive index capacity. These results are presented in the study with the relationship between permittivity and permeability. Furthermore, when the results obtained from the design are examined, it is seen that it is suitable for wireless applications. Performance improvement have been carried out SRR negative refractive index capacity which before has 11 GHz was increased to 15.5 GHz.


I. INTRODUCTION
Recently, split-ring resonators have been used in many fields from healthcare to materials science, from antenna to sensor [1]. Its wide use has increased the interest in split-ring resonators. The fact that its geometric shapes can be changed which is one of its biggest advantages [2][3]. Metamaterial, an artificially structured substance with exceptional electromagnetic characteristics that are not, or are not readily, accessible in nature [4]. Since the early 2000s, metamaterials in physics, electrical engineering, materials research, optics and nanoscience have grown into a fast-growing interdisciplinary field [5]. The properties of metamaterials are suited to their internal physical configuration by controlling them. This varies strikingly from natural materials, whose properties are determined primarily by their chemical elements and their interactions [6][7]. Metamaterial consists of artificial objects that are regularly or randomly spaced out that are much smaller in scale and spacing than the wavelengths of electromagnetic input [8]. As a consequence, the wave cannot overcome the microscopic information of these internal structures. For instance, it is hard to see the features of metamaterials which work with visible light at optical wavelengths and electromagnetic radiation of a shorter wavelength, such as an Xray, for image and scan. Researcher can estimate the assembly and description of their efficient material properties on a macroscopically basis of inhomogeneous individual structures as a continuous product [9][10][11]. The two main parameters which qualify the electromagnetic characteristics environment are electrical permittivity () and magnetic permeability (μ) [12]. Both parameters can be changed and now commonly used structures such as metallic wire arrays and Split-Ring Resounds (SRRs) [13]. The electric permittivity (measurement of the tendency of the electric charge within the material to decrease in electric field) can be "adjusted" to the desired value by changing the width and size of elements within metal wire arrays [14]. SRRs consist of one or two rings or squares which have a gap through which the magnetic permeability of a material can be created [15]. If an SSR is put in an external magnetic field which oscillates in the resonance frequency of the SSR, electrical current flows around the coil, which causes a small magnetic effect called a dipole magnetic moment [16][17][18][19]. With the outward oscillating field the induced dipole moment in the satellite radiography may be calibrated for a positive or negative magnetic permeability either in or out step. Thus, even though the metal used to create the SRR is non magnet, an artificial magnetism can be obtained [20][21][22]. Analysing such small size electromagnetic devices and sensors in two dimensions is not preferred. Very small electric field generation or surface current density on small surfaces can cause undesirable phenomena in high frequency applications. For this, making a real three-dimensional design that includes all small surfaces in the calculation will provide realistic results in the analysis. It is expected that the dimensions of the electromagnetic device pre-designed for this analysis will be simulated in all details in the analysis model. In this way, it will be possible to obtain more precise results by establishing a detailed mesh for the regions to be analysed. The SRR model used in this study is in micron dimensions.
In response to an electromagnetic oscillating field, SRR could create an effect of being electrically smaller. The synthesis of the left hand and negative index media are used when the importance of the negative productive permeability due to the existence of the SRRs is required. When an assortment of electro-small SRRs is excited through a changing duration of magnetic field, the arrangement serves as an effective medium in a narrow band over SRR resonance [23]. The first proof of a negative refraction index was regularly assigned to the collection of SRR [24]. This proof was based on square shaped Split ring resonators in the form of a periodical, mounted cell arrangement with lined wire configuration [25]. There are various types of split-ring resonators, especially the negative refractive index. On other hand, most of the SRRs have a gap [26][27]. That is to say, each ring has a gap in its dual-ring configuration [28]. The 1-D Split Ring Structure has two square triangles, one inside [29]. The arrangement of the symmetrical ring is distinct. The structure of the Omega has a ring-structure, as the nomenclature explains [30]. The pairing form "S" was another modern metamaterial [31][32][33][34][35]. In this study, three-dimensional model of SRR, which was pre-designed by numerical calculation, was created with Ansoft HFSS program and boundary conditions were determined under electrostatic analysis conditions. The model created to be close to its real application that is not from a single SRR, but with triple placement and back conductor similar to the real life application and simulated for analysis. Objective functions were developed by using analysed parameters and SRR geometric dimension parameters to improve the performance of the analysed model. Performance improvement has been achieved with the multi-objective genetic algorithm (MOGA). Results from FEA, optimization results and other detailed evaluations are discussed in detail in the results section. The algorithm used for optimization includes a genetic evolutionary calculation method. Optimization of such a detailed and three-dimensional model with many parameters; it only takes weeks to prepare the simulation model. The solution to the problem takes months. Although the information processing speed of computers increases, the data and dimensions of the models simulated and analysed are also increasing at the same rate. The design values, boundary conditions, excitation areas and other details of the analysis were explained in detail in the study. It can be seen in Figure 1 designed SRR model.

II. THREE DIMENSIONAL ANALYSIS OF SPLIT-RING RESONATOR A. DESIGN OF SPLIT-RING RESONATOR
It is necessary to create a model that includes all the details of the model to be electromagnetic analysis. Material selection should be made for the design whose model is created. It is necessary to know all the electrical and electromagnetic values of the selected material in terms of compliance with the real model. The design information of designed SRR in this study is presented in the study. Figure 2 shows the SRR geometric parameters of the designed model.
The split-ring resonator design varies according to the area where it will be used, health, antenna, and sensor as well as measuring and emitting. But basically they are designed on the basis of this situation as they operate at the point where the resonance frequency is captured. The model of SRR designed in this study is shown in Figure 2. In Figure 2, h is height of substrate, g is gap between rings, Lw is substrate width, wi is width of inner ring, wo is width of outer ring, d is width of slit in ring, s is permittivity of substrate material and c is permittivity of ring material respectively. Table 1 presents initial design parameters of designed SRR.
Eq.1, Eq.2 and Eq.3 presents sizing equations of SRR. L1 and L2 are inductances of outer and inner split ring resonator, respectively. C is capacitance of SRR. f1 and f2 are resonant frequency of SRR. Copper conductivity value is 5.96×10 7 S/m at 20 C o . The loss tangent value ranged from 0.01 to 0.035 in the 5 GHz to 20 GHz frequency band.

B. BOUNDARY CONDITIONS FOR DESIGN
The correct determination of the boundary conditions is vital for the correct analysis of the three dimensional simulation model. It can be seen in Figure 3 master and slave boundary conditions of designed SRR which are y-z master-slave boundary and x-z master-slave boundary respectively. Master and slave boundary empower to demonstrate planes of periodicity where the E-field at each point on the slave boundary surface is compelled to coordinate the E-field of each relating point on the master limit surface. The change used to plan the E-field from the expert to the slave is controlled by determining an arrange framework on both the expert and slave limits. Both master and slave boundary consist of two main vectors U and V. In this study there are two master and two slave boundaries in the purposed model. Analysis of SRR model excitation system consist of two symmetrical direction port. These ports allow the SRR designed in the analysis to be analysed accurately under the applied magnetic field. It can be seen in Figure 4 excitation ports of designed SRR which are x-y-(z+) direction excitation port-1, and xy-(z-) direction excitation port-2. The simulation model analysis for FEA is completed after when defined in the excitation system within the defined boundary conditions. Also on either side of a border are normally electrostatic fields of varying amplitudes and directions. Some limits have a surface charge, as well as surface currents which affect adjacent fields in both dynamic and static situations. The vector field flow from master to slave is always perpendicular to the surface for this boundary condition.  -1, b) x-y-(z-) direction excitation port-2.

III. ELECTROMAGNETIC ANALYSIS RESULTS
The results interpreted by the designers by adding their own experiences are important for the electromagnetic device being analysed. Three main electromagnetic parameters have been analysed which are electrical field (V/m), magnetic field intensity (A/m) and surface current density (A/m). In order to obtain FEA results, the mesh in the solution range is increased with 0.001 precision in each iteration of 15 iterations. 98765435 elements were used in total iterations. Resolution is 0.001 for this analysis and analysis takes 22 hours with 10 th generation i5 processor with 6 core and 8 Gb RAM.

Figure 5. Electric field distribution of designed SRR a) E-general distribution, b) E-vector distribution.
When the three dimensional electrostatic analysis is made with a detailed simulation with real geometric dimension values, the results are remarkable. When the simulation results of this study are examined, it can be clearly seen in Figure 5, within the boundary conditions, the electric field is concentrated on the rings, while decreases in the dielectric substrate. Electric field vector distribution in SRR model is smooth and perpendicular the rings. It can be seen in Figure 6, within the boundary conditions, the magnetic field intensity is concentrated on the rings, while decreases in the dielectric substrate. Magnetic field intensity vector distribution in SRR model is smooth and parallel the rings. While the electric field value in the copper ring area with a large surface area is 9842 V/m, it decreases to 4921 V/m in the area where the surface area is small. It should be well understood that the amount of current passing through a cross section of the SRR is the magnetic field intensity but does not mean surface current density. The two should not be confused with each other. While the magnetic field strength acts as a vector magnitude and at the same time as a vector field, the surface current density expresses the amount of current passing through the relevant surface instantaneously. While the magnetic field intensity value is 15.91 A / m in the copper ring where the surface area is large, it decreases to 10.21 A / m in the area where the surface area is small.

Figure 6. Magnetic field intensity distribution of designed SRR a) H-general distribution, b) H-vector distribution.
When the surface current density in Figure 7 is examined in SRR rings, it is seen that there is a distribution between 13.6 and 9.63 A/m. It can be seen that the surface current density is smooth enough to form positive and negative poles and its distribution is such that it does not disrupt the operation of the SRR. If the surface current density had an uneven distribution between the SRR rings, the ring capacitance and inductance values would change and the resonance frequency would change accordingly.

IV. OPTIMIZATION OF SPLIT-RING RESONATOR
Optimisation is called technology/methods used to build or adjust some device/tool for the best/optimal use. The goal or purpose of optimization is to achieve a solution for a problem that is perfect, most beneficial or efficient [36][37][38]. This is true when dependency and limitation of the objective function (parameter to be optimized) are known to other parameters. The detection of similar parameters is therefore primarily important. Effects for objective function of these parameters are analysed, forming the basis for algorithm creation [39][40][41][42]. Under such conditions or constraints algorithms are programmed to improve (max or minimize) the objective function. In any area that needs successful solutions, optimization can be used [43][44].
Developed objective functions for SRR are shown in Eq. 4 and Eq. 5. Here, E: electric field, H: magnetic field strength, j: surface current density and f: frequency respectively. X1, X2 and X3 are status values of objective functions. Status values can be 1 or 0 depending on the type of improvement targeted. When the status values are X1=1, X2=1 and X3=1, this means performance improvement. Objective functions take the results with results varying between 0 and 1. Results between 0 and 0.3 were defined as low correlation, between 0.3 and 0.6 as medium correlation, and between 0.6 and 1.0 as good correlation. Objective functions are used when the X parameters yielded results in a good correlation range according to their condition.
Multi-objective genetic algorithm scheme can be seen in Figure 8. Initially SRR selected optimization parameters population updated by genetic algorithm. Then MOGA generates new population for the optimization problem in solving area. Firstly parents used for next generation children. If the objective function constraint conditions are not met, then both the old parents and the new parents from the new population are randomly selected to generate the new generation for the new generation. If this mutation meets the desired values, a new population is no longer produced. The values of the design parameters for optimum values are then updated according to these ideal results. Finally, the integrity of the optimum values obtained in the algorithm is checked, and if appropriate, the solution is completed, if not, the same cycle continues until the solution is found. The electromagnetic parameters selected for the objective functions developed in this study vary depending on the geometric dimension values and the frequency at the same time. Although this makes the problem much more difficult, it is the closest to a real-world simulation. In MOGA, more than one objective function can be defined independently or interdependently. This is the difference from other optimization methods. The solution is found by a genetic algorithm-based search, but multiple objective functions are used instead of a single objective function. This algorithm allows the above described to be done. That's why it was chosen.   Table 2. f Frequency, Lw substrate width, wi width of inner ring and wo width of outer ring are selected for the optimization variable. Because these selected parameters directly affect SRR performance. The initial values and solution ranges are shown in Table 2. S11 and S21 are S-parameters of designed SRR which are analysed in the study. It can be seen in Figure  9 SRR S-parameters. In Figure 9 a, magnitude of S11 and S21 with varying frequency from 1 GHz to 20 GHz. S11 and S21 parameter values intersect in the range between 11.5 GHz and 12 GHz. Phase of S11 and S21 can be seen in Figure 9 b. It can be seen in Figure 10 a, refractive index of designed SRR. This figure clearly showed that designed SRR normally produce negative refractive index characteristic to 15.5 GHz. The same situation can be seen in the other Figure 10 b, the effective permittivity value produces negative refractive index characteristic to 15.5 GHz. This is also an indication that this design, which can normally run up to 11 GHz, has been optimized to increase the operating range to 15.5 GHz. The metamaterial designed SRR analysed in this way has produced values suitable for design and optimization purposes.
Designed SRR sphere phase degrees shown in Figure 11. S11 sphere phase degree in figure "a" and "b" for S21 sphere phase degree. The limits of the spherical phase degrees for each S-parameter are clearly visible. The optimization problem defined in Table 2 and the solution of the optimization problem for the solution intervals are presented in Table 3. In the optimization problem, in this study, the aim of optimization is to improve the objective functions.  Table 3. In reality the optimum points include not only a numerical value but a solution set. The simulations made showed that the SRR design subject to the study can be used in a wide range of applications from wireless applications to antenna applications, from health applications to advanced measurement applications. SRR negative refractive index capacity was increased by approximately 4.5 GHz with the optimization work. This value corresponds to an increase of % 41. Reflection coefficients consists of S parameters and S11&S21 in dB 11 = 20 10 | ⁄ | = 10 10 | ⁄ | 2 , where Er and Ei are the reflected and incident electric fields, respectively. In general, S11 and S21 are complex quantities. However, the question asked about S11&S21 in dB, thus, from the above analysis, negative return loss provide positive S parameters.

V. CONCLUSION
In the study, three dimensional electromagnetic analysis of SRR and optimization presented. Newly developed objective functions and their status values discussed in advanced and presented in the study. Ansoft HFSS which is commercial design and analyse software used for the analysing the purposed system. Multi-objective genetic algorithm used for the solving the optimization problem. Effective parameters of designed SRR are investigated such as S11 and S21. Negative refractive index capacity increased almost 4.5 GHz. Finite element analysis results presented in the study such as electric field, magnetic field intensity and surface current density which are very important for the SRRs. The simulations made showed that the SRR design subject to the study can be used in a wide range of applications from wireless applications to antenna applications, from health applications to advanced measurement applications. SRR negative refractive index capacity was increased by approximately 4.5 GHz with the optimization work.