Determination of Transmission and Reflection Parameters by Analysis of Square Loop Metasurface

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1 Determination of Transmission and Reflection Parameters by Analysis of Square Loop Metasurface Anamika Sethi #1, Rajni *2 #Research Scholar, ECE Department, MRSPTU, INDIA *Associate Professor, ECE Department, MRSPTU, INDIA Abstract In this present work, the transmission and reflection coefficients of the square loop metasurface structure are determined and analyzed by varying the different geometrical parameters of the structure. Initially, the block of 3X 3 square loop cells has been placed centrally in a waveguide and appropriate boundary conditions and excitations are applied. The simulation is carried out with a FEM based electromagnetic solver High Frequency Structure Simulator (HFSS). The simulation results show that reflection coefficient relies on the different geometrical parameters and hence the value of reflection coefficient can be controlled from these parameters. Keywords Square Loop, Metasurface, Reflection coefficient, Transmission coefficient. I. INTRODUCTION Metamaterials (MTM) are those exotic impertinent materials that have the ability to display some unnatural properties. Numerous components comprising of different materials are united and their arrangement is done periodically at smaller wavelengths so as to design a MTM. These unnatural and artificially prepared materials derive their properties from their structures as well as the arrangement of the materials [1]. MTMs are new materials that display unnatural qualitative response functions and have the ability to exhibit negative permeability ( and negative permittivity (. With respect to permeability and permittivity, MTM s can be categorized into four types: Double negative medium, Epsilon negative medium, Mu negative medium and Double positive medium [2]. This category of the materials can be artificially synthesized so that the permeability and permittivity values can be altered with the changing requirements of the system [3, 4]. The two dimensional equivalent of metamaterial known as metasurface, is the surface dispersal of wholes and electrically minute scatterers. Because of their exceptional behaviour and enhanced performance [5], these materials have attracted a lot of researchers to instigate their research in a variety of applications which include miniaturization of antenna [6], with enhanced directivity [7], beam-width control and beam scanning [8]. For every naturally occurring material, the values of permeability and permittivity are positive, but a remarkable discovery was made by Veselago, in 1968 by introduction of first DNG medium which simultaneously exhibited negative permeability and permittivity [9]. This theoretical assumption of Veselago was acknowledged by Pendry three decades later, by proposing thin-wired periodical structure that exhibited negative effective permittivity [10]. Subsequently, the use of an array of split ring resonators was made to achieve negative value for magnetic permeability [11]. The confirmation of the existence of double negative mediums, which exhibited properties like negative refractive index, was done experimentally by Pendry and Smith [12-15]. Substantial work has been carried out to obtain simultaneous negative values for both permeability and permittivity in visible frequency ranges, terahertz, microwave and infrared range [16-19]. This paper presents a metasurface structure of square loop cells in a waveguide, which is modelled and simulated using Finite Element Method (FEM) based Ansoft HFSS software. The transmission characteristics of the model are plotted and analysed by varying the different parameters of the structure. This paper is organized in four sections. Section 1 discusses the introduction and previously done work. Section 2 describes the proposed design of square loop structure and simulation methodology of square loop cells with suitable boundary conditions and excitations. Section 3 presents the numerically analysed results and discussions. Section 4 concludes the paper. II. DESIGN PARAMETERS AND SIMULATION METHODOLOGY OF STRUCTURE IN WAVEGUIDE The proposed double negative medium comprising of 3 X 3 square loops is depicted in Fig. 1(a), and the geometry of a single unit cell of square loop is shown in Fig. 1(b). The metasurface structure of square loops is designed at the top of a Rogers RO4350 substrate, with the value of permittivity equals to 3.66 and has a dielectric constant of ISSN: Page 161

2 and a thickness of mm. Table 1 enlists the geometrical dimensions of the proposed metasurface of square loops. The square loop unit cell has its outer dimension equal to 6 mm and its inner cut dimension equal to 2 mm. The square loop metasurface structure has a substrate on its other side. two ports and Perfect Electric conductor (PEC) and Perfect Magnetic Conductor (PMC) are applied as boundary conditions. The two wave ports are assigned along each of the substrate line on the x- faces from x to x direction. After applying the boundary conditions the structure is simulated. Fig. 2 illustrates the design of metasurface in a waveguide and also depicts its boundary conditions. III. RESULTS AND DISCUSSIONS A full wave simulation of the square loop metasurface in a waveguide is performed with electromagnetic solver. The metasurface structure is simulated after applying suitable boundary conditions and excitations. The transmission and reflection parameters are plotted in order to validate the performance of the proposed metasurface structure. Fig. 1. Geometry of (a) 3X3 cell structure, (b) Unit cell TABLE I. Dimension of LHM unit cell structure Sr. No. Parameter Unit (mm) 1 Side of outer square (L) 2 Side of inner square 2 3 Gap between two square loops(g) A. Transmission and Reflection Parameters The ratio of the amplitude of the complex transmitted wave and incident wave at a point of discontinuity in the transmission line is termed as transmission coefficient (S 21 ) and the ratio of complex amplitude of the reflected wave and the transmitted wave is termed as reflection coefficient (S 11 ). The reflection coefficient and transmission coefficient characteristics of the square loop metasurface with respect to frequency are shown in Fig. 3. It can be observed from the plot that there is a strong reflection at db below 0 db at GHz. This reveals that the square loop metasurface resonates at GHz. 4 Thickness of substrate (T) Fig.2. Boundary conditions of the square loop metasurface The metasurface structure is designed and simulated using EM software. The proposed square loop structure is put in a waveguide consisting of Fig. 3. Reflection Coefficient (S 11) and Transmission Coefficient (S 21) of Square loop metasurface B. Reliance of performance of antenna on its parameters The geometrical parameters of the square loop metasurface structure, such as the side of the outer ISSN: Page 162

3 square, side of the inner square and the gap between two unit cells, affect the performance characteristics of the antenna significantly. So, the values of these parameters are varied and its effect on the performance of antenna is analysed. 1) Effect on variation in side of outer square: Initially, the side of the outer square of the unit cell is taken as 6 mm. Then to check its reliance on the performance of antenna, its value is increased from 6 mm to 8 mm with a step of 1 mm and the reflection coefficient is plotted in Fig. 4. It can be observed from the plot that there is a reflection of db below zero at GHz for the value of L equal to 6 mm. With the increase in the value of the side of the outer square, the resonance of the antenna shifts to lower frequencies. 2) Effect on variation in side of inner square: Initially, the side of the inner square cut of the unit cell is taken as 2 mm. Subsequently, its value is decreased by one step and increased by one step; each of 1 mm. The reflection coefficient is plotted in Fig. 5 below. It can be observed from the plot that the antenna resonates at approximately 5 GHz for all the different values of C. This reveals that the change in value of C, does not affect the performance of antenna. 3) Effect on variation of gap between two unit cells: At first, the gap between two unit cells was taken as 0.35 mm. Then its value was increased to 0.5 mm and finally to 1 mm. The reflection coefficient for all the values of G is plotted in Fig. 6. It can be observed from the plot that there is a strong reflection of db below zero at GHz. With the increase in the gap between two unit cells, the resonance of the antenna shifts to lower frequencies. 4) Effect on variation in thickness of substrate: Initially, the thickness of the substrate is taken as mm. Then its value is increased up to 3.5 mm with a step of 1 mm and the reflection coefficient is plotted in Fig. 7. The plot reveals that there is a strong reflection of db below zero at GHz for T = mm. As the thickness of the substrate is increased, the resonance of the antenna shifts to lower frequencies. Fig. 4. Reflection Coefficient for different values of L Fig. 5. Reflection Coefficient for different values of C ISSN: Page 163

4 Fig. 6. Reflection Coefficient for different values of G Fig. 7. Reflection coefficient for different values of T The effect of the variation of different geometrical reflection coefficient is enlisted in Table 2 below: parameters of the square loop metasurface on the Table II. Parametric analysis Sr. No. Parameter Value (mm) Resonant Frequency( GHz) S 11 (db) 1 Side of outer square (L) Side of inner square (C) 3 Gap between two unit cells (G) 4 Thickness of substrate (T) ISSN: Page 164

5 IV. CONCLUSIONS It can be summarized from Table 2 that the different parameters of the square loop metasurface effects the reflection coefficient. As can be observed from the table that the variation in the side of the outer square affect the resonant frequency significantly, whereas the side of the inner square does not have much effect on the resonant frequency. With the increase in the value of different parameters, the resonant frequency shifts to lower side. Hence it can be concluded that the reflection coefficient of a metasurface can be controlled by altering the geometrical dimensions of the structure. [17] J.B. Pendry, D. Schurig and D.R. Smith, Controlling electromagnetic fields, Science, vol. 312, pp , [18] D.R. Smith, J.B. Pendry, and M.C.K. Wiltshire, Metamaterials and negative refractive index, Science, vol. 305, pp , [19] T.J. Yen, W.J. Padilla, N. Fang, D.C. Vier, D.R. Smith, J.B. Pendry, D.N. Basov and X. Zhang, Terahertz magnetic response from artificial materials, Science, vol.303, pp , REFERENCES [1] A. Sethi, and Rajni, Reconfigurability in Antennas by Incorporation of Metasurface, International Journal of Engineering trends and Technology, vol. 32(1), pp , [2] Rajni and A. Marwaha, Resonance Characteristics and Effective Parameters of New Left Hand Metamaterial, Telkomnika Indonesian Journal of Electrical Engineering, vol. 15(3), pp , [3] A. Lai, T. Itoh and C. Caloz, Composite right/left-handed transmission line metamaterials, IEEE Microwave Magazine, vol. 5(3), pp , [4] N. Engheta and R. Ziolkowski, Physics and Engineering Exploration, New York: Wiley Interscience, [5] Rajni, G. Singh and A. Marwaha, Modeling of Split Ring Resonators loaded microstrip line with different orientations, International Journal of Electrical and Computer Engineering, vol.5(6), pp , [6] A. Sanada, M. Kimura, I. Awai, C. Caloz and T. Itoh, T, A planar zeroth order resonator antenna using lefthanded transmission line, Proceedings 34 th European Microwave Conference. pp , [7] S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, A metamaterial for directive emission, Physical Review Letters, vol. 89(21), , [8] S. Lim, C. Caloz, and T. Itoh, Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth, IEEE Transactions on Microwave Theory and Techniques, vol. 53(1), pp , [9] V.G. Veselago, The electrodynamics of substances with simultaneously negative values of ε, and μ, Soviet Physics- USPEKHI, vol. 10(4), pp , [10] J.B. Pendry, A.J. Holden, D.J. Robbins and W.J. Stewarts, Low Frequency Plasmons for Thin-Wire Structure, Journal of Phyics: Condened Matter, vol. 10, pp , [11] J. Holden, J, D.J. Robbins, and W.J. Stewart, Magnetism from conductors and enhanced non-linear phenomena, IEEE Transactions on Microwave Theory and Technology, vol. 47, pp , [12] J.B. Pendry and D.R. Smith, Negative refraction makes a perfect lens, Physics Review Letters, vol. 85, pp , [13] R. Liu, C. Ji, J.J. Mock, J.Y. Chin, T.J. Cui and D.R. Smith, Broadband ground-plane cloak, Science, vol. 323, pp , [14] U. Leonhardt, Optical conformal mapping,. Science, vol. 312, pp , [15] Rajni and A. Marwaha, Magnetic Resonance of spiral resonators, International Journal of applied engineering Research, vol. 10(13), pp , [16] J.B. Pendry, A chiral route to negative refraction, Science, vol. 306, pp , ISSN: Page 165