ANTENNA WITH METAMATERIAL DESIGN SURIA BINTI HALIM UNIVERSITI TEKNOLOGI MALAYSIA

Transcription

1 ANTENNA WITH METAMATERIAL DESIGN SURIA BINTI HALIM UNIVERSITI TEKNOLOGI MALAYSIA

2 iii To my beloved husband, Hairul Azydy Muhammad Yusuf for his love, support and understanding To my lovely son, Muhammad Irfan Raziq (born on 4 th May 2007) for the 9 months of wonderful experienced and lots to come

3 iv ACKNOWLEDGEMENTS I would like to thank the project s supervisor Dr. Mohamad Kamal A. Rahim for his guidance, time and supervision. His ideas, advise and constructive comments have contributed greatly in the overall project progression and in the writing of this report. This acknowledgements also for all the individuals who assist me in their own ways throughout the project s completion.

4 v ABSTRACT Metamaterial exhibiting negative permittivity and negative permeability in certain frequency range or known as left-handed material (LHM), provides another alternative to the existing right-hand rule. With this theory, it offers a new dimension to the antenna applications as well as optic. The negative refractive index and the convergence of the electromagnetic waves when passing through the metamaterial is good for optical applications. However, this project looks into the effect of metamaterial structure to the conventional antenna and concentrate on proving the existence of the negative index material within certain frequency regions. Also, the relationship between different varies dimensions used affect the frequency response is being emphasized in order to understand further the metamaterial structure and its properties. Knowing that, the structure is optimized to get the left-handed properties in X-band frequency which is around 8GHz-12GHz. Although, the metamaterial structure giving a limited negative range within the X-band, it does agree to the metamaterial theory with the co-existence of both negative permittivity and negative permeability. The theoretical calculation give a reference value to work with, while the simulation via HFSS simulation tools is used to optimized and confirmed to the theoretical result. Then the simulation also being performed on the antenna with metamaterial structure and the effect is observed and analyzed where we can see a frequency shift occurred.

5 vi ABSTRAK Metamaterial menunjukkan permitiviti dan permeabiliti negatif dalam julat frekuensi tertentu. Ia juga dikenali sebagai left-handed material (LHM), yang memberikan alternatif lain kepada peraturan tangan kanan sedia ada. Indeks pembiasan negatif dan penumpuan gelombang electromagnet selepas melepasi metamaterial adalah berguna untuk aplikasi optik. Walau bagaimana pun, projek ini melihat kesan struktur metamaterial ke atas antena konvensional dan tumpuan diberikan untuk menunjukkan kewujudan material berindeks negatif dalam kawasan frekuensi tertentu. Hubungkait antara pelbagai variasi dimensi struktur metamaterial dan frekuensi ditekankan dalam projek ini untuk lebih pemahaman terhadap struktur metamaterial dan sifat-sifatnya. Dengan pengetahuan yang diperolehi, struktur metamaterial dioptimumkan untuk memberikan sifat tangan-kiri (left hand rule) dalam frekuensi julat-x (X-band) iaitu sekitar 8Ghz -12Ghz. Walaupun struktur metamaterial memberikan nilai frekuensi negatif yang terhad di dalam julat-x, ia tetap mematuhi teori metamaterial dengan kewujudan kedua-dua pemitiviti negatif dan permeabiliti negative. Pengiraan secara teori memberikan nilai rujukan, manakala simulasi menggunakan alat simulasi HFSS membenarkan struktur dioptimumkan dan keputusan teori dipastikan. Proses simulasi juga dilakukan ke atas antena dengan struktur metamaterial dan kesannya diperhatikan dan dianalisa di mana terdapatnya perubahan ke atas nilai frekuensi.

6 vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDMENTS ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS LIST OF SYMBOLS ii iii iv v vi vii x xi xiv xv 1 INTRODUCTION Introduction to Metamaterial Objective of the Project Scope of the Project Summary 4 2 LITERATURE REVIEW Brief Theory Negative Index Refraction Refraction and Snell s Law Single-Ring SRR and Double-Ring SRR 14

7 viii 2.3 Different Metamaterial Structure Metamaterial as Antenna Substrate to Enhance Directivity Summary 31 3 DESIGN METHODOLOGY Methodology Overview Metamaterial Structure Calculation of the Metamaterial Design Structure Calculation of Patch Antenna Simulation of the Metamaterial Unit Cell Simulation of the Metamaterial Array Simulation of the Patch Antenna Simulation of the Patch Antenna with Metamaterial Structure Summary SIMULATION RESULT AND ANALYSIS Metamaterial Unit Cell s Dimension Variation LHM/ Negative Index Medium Properties of the Metamaterial Unit Cell LHM/ Negative Index Medium Properties of the Metamaterial 2x3 Array S parameter of the Patch Antenna with and without the Metamaterial Structure Summary 57 5 CONCLUSION AND FUTURE WORKS 58 REFERENCES 60 APPENDIX A - 65

8 ix LIST OF TABLES TABLE NO. TITLE PAGE 2.1 Comparison among different metamaterial structure Effect of dimension variations on the frequency region Summary Relation of Unit Cell Dimension and Frequency Response 48

9 x LIST OF FIGURES FIGURE NO. TITLE PAGE 2.1 Electromagnetic waves Permittivity, ε - permeability,μ and refractive index (n) diagram Wave incident on a positive index material Wave incident on a negative index material The angle of incidence of the prism Conventional material the wave refracted towards the surface normal Left-handed material the wave refracted away from the surface normal Refracted rays in conventional material Refracted rays in Left-handed material Single-ring SRRs Transmission versus Frequency for single-ring SRRs Magnetic permeability for the single-ring SRRs Single-ring and Double-ring SRRs Transmission versus Frequency for double-ring and its isolated outer and inner rings Different metamaterial structure Retrieval results for 1-D Split-Ring structure Retrieval results for Symmetrical-Ring structure Retrieval results for Omega structure Retrieval results for S structure 20

10 xi 2.20 Full size rod structure Slab of metamaterial in a waveguide One cell rod structure in a waveguide Retrieval results for rod medium Radiated power and normalized radiation from simulation for rod The structure of metamaterial cover with patch antenna S11 of conventional type and metamaterial type patch antenna Radiation pattern under different distances of gaps Radiation directivity of metamaterial-cover patch antenna change with different distances between layers Schemetic representation of the structure Experimental and theoretical transmission of the slab of metamaterial for a normal incidence Emission diagram of the antenna Methodology Flow SRR structure Strip wire structure Metamaterial structure Square patch antenna structure The boundary conditions & waveports for metamaterial structure The 2 x 3 array of metamaterial structure Patch antenna structure Patch antenna with metamaterial structure Metamaterial unit cell The magnitude of the simulated S parameters for unit cell The phase of the simulated S parameters for unit cell The retrieved index of the unit cell The retrieved impedance of the unit cell 51

11 xii 4.6 The permittivity of the unit cell The permeability of the unit cell : Field pattern of metamaterial structure (E field) The magnitude and phase of the simulated S paramers for 2x3 array The retrieved material parameters for 2x3 array S 11 parameter of the patch antenna S 11 parameter of the patch antenna with metamaterial structure 56

12 xiii LIST OF ABBREVIATIONS HFSS - High Frequency Simulator System LH - Left -Handed LHM - Left-Handed Material PEC - Perfect Electric Conductor PMC - Perfect Magnetic Conductor RHM - Right-Handed Material SRR - Split Ring Resonator

13 xiv LIST OF SYMBOLS A - antenna aperture c - free space velocity of the light D - aperture diameter f - frequency F - filling factor g - gap h - height l - length n - refractive index s - separation w - width z - impedance ε - permittivity μ. - permeability ω - resonance frequency θ - angle λ - wavelength

14 CHAPTER 1 INTRODUCTION This chapter consists of the introduction to the metamaterial which includes the definition of the metamaterial, the early theory to the negative index of refraction, and the structure that shows the left-handed properties. Then, follows by the objective and scope of the project which reflect the overall project s content. 1.1 Introduction to Metamaterial Metamaterials are artificial materials synthesized by embedding specific inclusions, for example, periodic structures, in host media. Some of these materials demonstrate the property of either negative permittivity or permeability. If both happen at the same time, then the composite exhibits an effective negative index of refraction and is referred to as left-handed metamaterials. The name was given because the electric field, magnetic field and the wave vector formed a left-handed system. According to Valerie Browning and Stu Wolf of Defense Advanced Research Project Agency (DARPA), metamaterial can be defined as a new class of ordered composites that exhibit exceptional properties not readily observed in nature. These properties arise from qualitatively new response functions that are not observed in the

15 2 constituent materials and is the result from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneties. The electric and magnetic properties of materials are determined by two important material parameters, dielectric permittivity, ε and magnetic permeability, μ. Together the permeability and the permittivity, determine the response of the material to the electromagnetic radiation. Generally, ε and μ are both positive in ordinary materials. While ε could be negative in some materials (for instance, ε posses negative values below the plasma frequency of metals), no natural materials with negative μ are known. However, for certain structures, which are called left-handed materials (LHM), both the effective permittivity, ε eff and permeability, μ eff possess negative values. In such materials the index of refraction, n, is less than zero, and therefore, phase and group velocity of an electromagnetic wave can propagate in opposite directions such that the direction of propagation is reversed with respect to the direction of energy flow [1]. The idea of metamaterial or negative index of refraction was first proposed theoretically in 1968 by V.G.Veselago. This metamaterial exhibits a negative permittivity and permeability or also known as left handed material (LHM). Veselago also predicted that the LHMs exhibit anti-parallel nature in electromagnetic wave propagation and Poynting vectors. This is opposed the conventional materials which normally carry electromagnetic wave energy in the same direction as they propagate. With this theory, it provides another alternative and open the possibility for wider exploration in the area that previously cannot be reached using the right hand rules properties. The negative permittivity is easily obtained by an array of metallic wires and was theorized in It was shown that the structure is having a plasma frequency in the microwave regime. Because of its low plasma frequency, this structure can produce an effective negative permittivity at microwave frequencies while suffering relatively small losses. JB Pendry also theorized the structure of negative permeability which is

16 3 established in 1999 with split ring resonator (SRR) structure [20]. The first negative index medium was developed when both of these structures were combined and it was shown that the negative index of refraction is existed in the region where both the real parts of the electric permittivity and magnetic permeability were simultaneously negative. Typically, in a structure composed of SRRs and strip wires 1.2 Objective Of The Project Conventional antenna often limits the application of the antenna since they are governed by the right-hand rule which determine how electromagnetic wave should behave. Metamaterial offers an alternative solution to widen the antenna applications using the left-hand rule. The unique properties of metamaterial enable the enhancement of the conventional antenna, thus open more opportunities for better antenna design. This project will emphasize on obtaining the metamaterial structure with optimized parameters for negative index behaviour in which both permittivity and permeability co-exist simultaneously in the required frequency region. The main objectives of this project are: i) To design and simulate the metamaterial structure ii) To incorporate metamaterial structure in the antenna design 1.3 Scope Of The Project The scope of the project will includes the study of metamaterial which will be emphasized on the negative refractive index or left-handed material (LHM) and the metamaterial structure which cover the conventional LHM. Another is to design the metamaterial structure by using the theoretical method to find the optimized structure, to compare the design parameter and to see the effect of varies structure dimensions on the

17 4 frequency response. Finally to perform a simulation on the designed structure using High Frequency Simulator System (HFSS) and analyze the result obtained. 1.4 Summary The introduction of metamaterials described on the early finding of the metamaterials from the theory to the realization of the metamaterial properties and structures. Knowing the fundamental concept and information of the metamaterial, the objective and scope are defined to ensure that the overall studies are within the required field.

18 CHAPTER 2 LITERATURE REVIEW This chapter consists of brief theory of metamaterial which includes the properties of metamaterial in electromagnetic field, the behavior of negative index of refraction, and the other prominent properties of metamaterial that is refraction and the Snell s Law. Besides, there are also discussion based on few literatures in metamaterial areas performed by other researchers. The discussion look into the SRR structure and how its effect the left-handed properties of metamaterial where the emphasized are done on the single-ring SRR versus double-ring SRR as well as different structure of the SRRs. Also, includes here is a discussion on the metamaterial as antenna substrate to enhance directivity, which includes the interaction of metamaterial with a patch antenna and the effect of metamaterial structure on the conventional antenna in terms of its performance such as directivity. 2.1 Brief Theory Metamaterial exhibits negative electrical permittivity and/ or negative permeability. These two properties determine how a material will interact with electromagnetic radiation including microwave, radiowave, x-rays and all other electromagnetic wavelength. When both permittivity and permeability are multaneously

19 6 negative, its then having a negative refractive index or left-handed material. This relationship is shown by the following Maxwell s equation for refractive index: n = ± μ ε (2.1) Electromagnetic waves are governed by Maxwell's equations, which show that these waves contain both electric and magnetic fields as shown in Figure 2.1. Electromagnetic waves consist of in-phase, oscillating electric and magnetic fields. Plane waves, as shown here, have electric and magnetic fields that are polarized at right angles to each other. The field directions in a plane wave also form right angles with respect to their direction of travel (the propagation direction). When an electromagnetic wave enters in a material, the fields of the wave interact with the electrons and other charges of the atoms and molecules that compose the material, causing them to move about. For example, this interaction alters the motion of the wave-changing its speed or wavelength. Figure 2.1: Electromagnetic waves Knowing that the permittivity and permeability are the only relevant material parameters for electromagnetic waves, we can imagine a 'material parameter space' into which all materials can be placed. This is illustrated in Figure 2.2.

20 7 Figure 2.2: Permittivity, ε - permeability,μ and refractive index (n) diagram [4] Region I is where the permittivity and permeability are both positive. Since most known materials have this property, this region of material parameter space has been the most explored. However, the larger part of the map-three quarters, in fact has been much less explored. This is because materials are just not so easily available in these regions. In fact, materials that lie in the region III, where the permittivity and permeability are both less than zero, do not appear in nature at all [4]. While nature appears to have limitations in terms of the material properties that are found, artificially structured metamaterials are not limited in the same way. The hope, then, is that more of the material parameter space can be made accessible with metamaterials. An important step towards this goal was made in 2000, when a metamaterial was demonstrated to have a permittivity and permeability both less than zero.

21 Negative Index Refraction All transparent or translucent materials that is known of possess positive refractive index or a refractive index that is greater than zero, in nature. However, as proposed by Veselago and realized by Pendry, a negative refractive index is made possible. Maxwell's equations relate the permittivity and the permeability to the refractive index as follows in equation 2.1: The sign of the index is usually taken as positive. However, Veselago showed that if a medium has both negative permittivity and negative permeability, this convention must be reversed, thus the negative sign of the square root is chosen to indicate the negative refractive index. This negative value can be explain as follows; as an example, it is often said that the velocity of a wave in a material is given by c/n, where c is the speed of light in vacuum. The implication of a negative index, then, is that the wave travels backwards, as shown in below figure. An electromagnetic wave can be depicted as a sinusoidally varying function that travels to the right or to the left as a function of time. Figure 2.3 shows that a wave is incident on a positive index material (the reflected wave has been ignored). The greater index of the second medium implies that the wavelength decreases (by a factor of 1/n); however, to maintain the same phase at the interface as a function of time, the speed of the wave must also be reduced, again by a factor of 1/n. Figure 2.3: Wave incident on a positive index material

22 9 When the refractive index is negative, the speed of the wave, given by c/n is negative and the wave travels backwards toward the source as shown in Figure 2.4. Yet, it would reasonably expect that since energy is incident on the material from the left, the energy in the material should likewise travel to the right, which is away from the interface. To resolve this, Veselago showed that there are more ways to define the velocity of a wave. The definition c/n is well known as the phase velocity and determines the rate at which the peaks (or zeros) of a wave pass a given point in time. But this is not most relevant definition of a wave's velocity as we can also define the group, energy, signal and front velocities, and these generally differ from the phase velocity. Therefore, in left-handed metamaterial, wave propagates in the opposite direction to the energy flows. Figure 2.4: Wave incident on a negative index material Refraction and Snell's Law One of the most fundamental of optical effects is refraction, or the bending of light as it crosses the interface between two materials. Refraction is the basic principle behind lenses and other optical elements that focus, steer, guide or otherwise manipulate light. Highly sophisticated and complex optical devices are developed by carefully

23 10 shaping materials so that light is refracted in desired ways (think of a camera lens or a microscope objective). The underlying principle of refraction can be easily understood and applies to all electromagnetic waves and not just visible light. Every material, including air, has an index-of-refraction (or refractive index). When an electromagnetic wave traverses the interface from a material with refractive index n1 to another material with refractive index n2, the change in its trajectory can be determined from the ratio of refractive indices n2/n1 by the use of Snell's Law. (2.2) To apply Snell's Law, consider an interface between two materials and an imaginary line that runs perpendicular to the interface (the surface normal). The angles in Snell's law are measured away from the surface normal. If the refractive indices of the two materials are not equal, the angle of the transmitted beam will differ from the angle of the incident beam. The beam is then bent at the interface. A common way to determine the refractive index of a material is to form a prism out of the material, shine a beam of light through it and observe the deflection of the beam on the other side. Light enters the prism through one of the interfaces at direct incidence, striking the opposite interface at an oblique angle. Figure 2.5 shows what happens to the beam when the material has the same index as the surrounding medium, or has an index that is greater than the surrounding medium but either positive or negative. The figure also shown the dashed line, which represents the surface normal, which is perpendicular to the interface between the prism and the surrounding material. The angle of the prism defines the angle of incidence of the beam to the interface.

24 11 Figure 2.5 : The angle of incidence of the prism A measurement of the angle of the exit beam from the surface normal provides a measurement of the refractive index of the prism. Figure 2.6 shows the refracted wave for the conventional material, where the waves are refracted toward the surface normal. Snell's Law shows that a material with a negative refractive index, not a material that exists in nature would refract a beam to negative angles, as shown in Figure 2.7, where the refracted wave is away from the surface normal. Figure 2.6: Conventional material - the wave refracted towards the surface normal

25 12 Figure 2.7: Left-handed material - the wave refracted away from the surface normal Figure 2.8 and 2.9 shows how the spreading patterns of the waves on entering and exiting the conventional and LHM material respectively. For conventional material, the refracted waves are spreading away on entering and exiting the medium. For LHM, the waves are refracted in such a way as to produce a focus inside the material and then another just outside. The radiation pattern is more a beamlike, which leads to the creation of highly directional antennas and also may allow more antennas to be placed in closely packed space. Figure 2.8: Refracted rays in conventional material

26 13 Figure 2.9: Refracted rays in Left-handed material The startling properties of negative refractive index metamaterials: i) Snell s Law (n1 sin θ1 = n2 sin θ2) still applies but rays are refracted away from the normal on entering the material. ii) The Doppler Shift is reversed that is a light source moving toward an observer appears to reduce its frequency. iii) Cherenkov radiation points the other way. Cherenkov radiation is the light emitted when a charged particle passes through a medium under certain conditions, in normal material the emitted light is in a forward direction whereas in LHM, light is emitted in the reverse direction. iv) The group velocity is anti-parallel to phase velocity

27 Single Ring SRR and Double Ring SRR According to studies by Kafesaki, M. et.al. (2005), magnetic resonance with negative permeability,μ can be obtain using single or double-ring SRR. A single-ring SRR also behaves as a magnetic resonator. Figure 2.10 shows the square and circular shape for single-ring SRR placed in air. The linear SRR size of the square is 1.8mm and the outer diameter of the circular SRR also 1.8mm with similar computational cell and materials characteristics as of square SRR. Figure 2.10: Single-ring SRRs [11] The transmission for both single-ring SRR structures is plotted in figure 2.11, which shows that both the square and circular sing ring SRRs give a dip in the transmission coefficient which is associated with a negative permeability regime. The frequency of this dip, that is the magnetic resonance frequency, ω m, is a little lower for the square SRR that for the circular SRR. The inductance in the single-ring resonator is provided by its square or circular metallic loop, while the capacitance is given by the gap of the ring.[11].

28 15 Figure 2.11: Transmission versus Frequency for single-ring SRRs [11] The second dip in the transmission of figure 2.11 at ω = ω o corresponds to the electric cut-wire-like response of the SRR [13] i.e to a resonance in its electrical permittivity, ε. Since the ring exhibits both a magnetic and electric resonance which also associated with a μ < 0 and ε < 0 regime, respectively, theoretically it might be possible to achieve a LH transmission regime using only an array of SRRs, by tuning the magnetic resonance into the negative permittivity band provided by its own electric cutwire response. Figure 2.12 shows the magnetic permeability as a function of frequency for the single-ring SRR, at frequencies around the magnetic resonance frequency. Figure 2.12: Magnetic permeability for the single-ring SRRs [11]

29 16 From the result shown in figure 2.12 which compared the transmission properties and the retrieval values of the permeability, it is noted that there is no qualitative difference between the square and circular single-ring SRR. However, with the same linear dimension, metal characteristics and gaps, in general the circular SRR shows higher v alues of ω m and ω o which is due to the smaller area and the smaller side length. For ease of calculation, the square ring is used to compare the transmission parameter between the single-ring and double-ring SRRs. Figure 2.13 shows the double-ring SRR as well as single-ring SRR as discussed previously. Figure 2.14(a) shows the transmission through the double-ring SRR and figure2.14(b) shows the transmission through only its outer or its inner ring SRR. It can be seen that the lower magnetic resonance frequency of the double ring as represented by the first dip (figure2.149(a)), is essentially that of the outer ring, but with a relatively small downwards shift. This shift is due to the additional capacitance between the rings [11]. The second dip(figure 2.14(a)), corresponds essentially to the magnetic resonance of the inner ring with a small upwards shift. The strength of this resonance is sometimes very small, showing that the magnetic response of the inner ring is screened by the presence of the outer ring [11]. Figure 2.13: Single-ring and Double-ring SRRs

30 17 Figure 2.14: Transmission versus Frequency for double-ring and its isolated outer and inner rings [11] From the result, the advantage of the double-ring SRR as compared to the singlering SRR, is that the magnetic resonance frequency of the double ring occurs at a relatively lower frequency. This leads to a higher probability for the magnetic response to lie in the ε < 0 regime when combined with strip wires in the metamaterial structure. Another advantage is that, the array of double-ring SRRs possesses a stronger magnetic resonance, which might lead to a more robust LH peak for the metamaterial structure. 2.3 Different Metamaterial Structure Wu, B. I. et. al. (2005) also perform a comparative study of different metamaterial structure as antenna substrate, which includes 1-D Split Ring structure, Symmetrical Ring structure, Omega structure and S structure. These structures are all left-handed materials where there will be a region where n is negative and the index of refraction is zero would occur at the frequencies where either permittivity or permeability is zero. These structures are illustrated in figure 2.15.

31 : Different metamaterial structure [31] The result obtained for each structure is represented in figure 2.16 for 1-D Split ring structure, figure 2.17 for Symmetrical-Ring structure, figure 2.18 for Omega structure and figure 2.19 for S-structure.

32 19 Figure 2.16: Retrieval results for 1-D Split-Ring structure [31] Figure 2.17 : Retrieval results for Symmetrical-Ring structure [31]

33 20 Figure 2.18 : Retrieval results for Omega structure [31] Figure 2.19 : Retrieval results for S structure [31]

34 21 The result can be summarized as shown in table 2.1 is meant for frequency between 8GHz to 18GHz., where it shows the frequency bandwidth each structure exhibit the left-handed properties, the clean of retrieval, also the ease of tunability for directive antenna. From table 2.1, it is shown that the Symmetrical-Ring structure provide better directional beam and it s easier tune its permeability since it rings is symmetrical. Thus, the Symmetrical-Ring structure is more suitable as antenna substrate compared to others for directive antenna applications. Table 2.1: Comparison among different metamaterial structure [31] 2.4 Metamaterial as Antenna Substrate to Enhance Directivity A study by Wu, B. I. et al (2005), shows the effect of metamaterial on directivity where the simulations are done on the radiation of a dipole antenna embedded in metamaterial substrates. The structure used in the design is composed of a periodic collection of rods, or both rods and rings. Then the S-parameters in the waveguide are analyzed and being compared to their equivalent plasma or resonant structure. The study only adopted the numerical simulation and theoretical approach in designing a metmaterial structure that is good for antenna substrate. The radiation effect is being approximated based on simulation on a slice of metamaterial in a parallel plate waveguide. The radiation setup used the rod medium structure as shown in Figure 2.20, where each rod is a cylindrical PEC structure with a radius of 0.2mm, and the length of

35 22 250mm. The period is 5.8mm and 6.3mm in the x- and y-direction respectively with 6 layers of rods in y-direction and 40 repetition in the x-direction. For radiation, a 50Ω S- parameter discrete port of 1mm in length is placed at the center of the structure. The slab of metamaterial in PEC parallel plate waveguide as shown in Figure 2.21 is used to approximate the full size structure as to cope with the simulation limitation in memory and time. Figure 2.20 : Full size rod structure [31] To study the metamaterial properties in a waveguide, a unit cell is identified from the full size structure and placed in the waveguide. This is shown in Figure 2.22 where the rod is modeled with PEC material, and the background as air. The top and bottom surface has PEC boundary conditions, the left and right has PMC boundary condition, whereas the front and back as open boundary condition.

36 23 Figure 2.21 : Slab of metamaterial in a waveguide. [31] Figure 2.22 : One cell rod structure in a waveguide [31] Figure 2.23 shows the retrieval results for rod mediums, where an electric plasma frequency of 13.5Ghz is observed. Then, the far field radiation will be concentrated around 13.5GHz, since the index of refraction will be close to zero in that region and may produced a beam sharpening effect. The rod medium only give a permittivity value, but for metamaterial the permeability value also need to be considered.

37 24 Figure 2.23 : Retrieval results for rod medium [31] The radiation resulted from simulation shows that, the most directive beam is centered at around 13.7GHz and the high power beam is centered at around 14.4GHz for full size structure and around 13.6GHz and 13.9GHz directive and high power beam respectively for slab, as shown in figure These value even though is different from expected value but still within the working region.

38 25 Figure 2.24: Radiated power and normalized radiation from simulation for rod [31] In a studies by Hu Jun et.al (2005), where the designed of metamaterial is composed of perfect conductor with a square lattice and whose period is equal to 35.4 mm (in the x-axis and y-axis directions). The grids spacing in the z-axis direction is 43 mm. The edge of the square holes of the perfect conductor grids is mm. The metamaterial-cover patch antenna is composed of an ordinary patch antenna and two metamaterial layers each composed of 9 9 units as shown in figure 2.25

39 26 Figure 2.25: The structure of metamaterial cover with patch antenna [10] Given the structure of ordinary patch antenna and the structure of metamaterial layer, there are three key factors to adjust: the working frequency, the number of the layers and the distance between the layers (the grid s spacing in the z-axis direction). The working frequency of ordinary patch antenna is GHz;. The substrate is 2 mm thick, with relative dielectric coefficient equal to 2.2. The patch antenna size is 36.8 mm 45.9 mm and the feed is a 1.2 mm diameter metal cylinder, 6.65 mm to the center of the patch along the x-axis direction. Figure 2.26 compares S11 between ordinary patch antenna and metamaterial cover patch antenna. Obviously the working frequency moves to 2.57GHz and the scope of impedance is not changed much as being observed and compared the chosen frequency of the two types of antenna. Figure 2.26: S11 of conventional type and metamaterial type patch antenna [10]

40 27 Radiation patterns of metamaterial-cover patch antenna under different distances of gaps and ordinary patch antenna as shown in figure The abscissa represents angle between the normal of the cover and the radiation direction. Whereas figure 2.28 shows the radiation directivity of metamaterial-cover patch antenna change with different distances between layers Figure 2.27: Radiation pattern under different distances of gaps [10] Figure 2.28: Radiation directivity of metamaterial-cover patch antenna change with different distances between layers [10]

41 28 The ordinary patch antenna s directivity is 7.7 db; after adding metamaterial, the patch antenna s directivity is increased to db. Theoretically, the maximum directivity of an aperture antenna is 2 Dmax = 4πA λ 0 ; where, A = l2=318.6 mm mm, λ = c 0 /f 0 = mm, so Dmax = db. The directivity of the patch antenna with metamaterial designed as specified above has almost approached the theoretical limit of the antenna with the same size and the same working frequency. Thus it can be conclude that antenna with metamaterial design results in increased in antenna gain doubled that of the conventional antenna for similar range of working frequency. Stephen Enoch et al.(2002), whose concentrate on the study of metamaterial for directive emission in their paper, shows that the specific properties of metallic composite material can modify the emission of an embedded source. Also shown is the energy radiated by a source embedded in a slab material will be concentrated in a narrow cone in the surrounding media under a proper condition. The matematerial used is the simplest class of metamaterial which is a metallic mesh of thin wires with wires in the three directions of space. The metamaterial is composed of copper grids made using the conventional printed circuits technology of electronics and slices of foam whose permittivity is closed to 1 (ε = 1.08 at 14.6 GHz). The schematic structure is shown in figure 2.29.

42 29 Figure 2.29: Schematic representation of the structure [7] The structure used is composed of six identical grids with a square lattice embedded in foam essentially for its mechanical properties with the following parameters: - a square lattice whose period is equal to 5.8mm (in the x- and y-axis directions) - the grids spacing in the z-axis direction is 6.3mm and are separated with foam - the edge of the square grids is 226mm - the metamaterial is placed on ametallic ground plane and is excited by a monopole antenna between the 3 rd and the 4 th grids. Figure 2.30 shows the transmission of the slab of metamaterial for a normal incidence for experimental (solid line) and theoretical (dashed line) approach. Whereas, figure 2.31 show the emission diagram of the antenna in db scale (upper figure) and linear scale (lower figure) in the H plane (solid line) and the E plane (dashed line), which shows the emission of the antenna of the structure for the optimal frequency (f= GHz chosen to obtain the best directivity). The result shows that the emission of the structure is concentrated in a narrow lobe around the normal of the structure and moreover is linearly polarized.

43 30 Figure 2.30: Experimental and theoretical transmission of the slab of metamaterial for a normal incidence [7] Figure 2.31: Emission diagram of the antenna [7]

44 31 From the above studies, it can be concluded that metamaterial as antenna substrate offering an improvement in terms of antenna directivity due to its negative permittivity and permeability properties. Different approaches can be used in getting the directivity enhancement, however similar result to the theory should be expected upon performing certain optimization on the structure to suite the required application. 2.5 Summary With reference to the literature review discussed, it is shown that the SRR structure is an important discovery that leads to the negative permeability value that contribute to the left-handed properties. The conventional geometry of SRR either square or circular does not have so much effect on the left-handed properties but is govern by the dimension/ parameter of the structure. Whereas the double-ring SRR leads to a high probability of getting the negative regions compared to the single-ring thus is preferable when designing the metamaterial structure. Also, discussed is the used of metamaterial structure to enhance antenna directivity using different approaches. The structure of metamaterial also important in determining the effect on antenna directivity as well as the frequency range where the left-handed properties is applicable. With the optimized structure and parameters, metamaterial as antenna substrate is a great alternative to improve the antenna performance to suite many other applications.

45 CHAPTER 3 DESIGN METHODOLOGY This chapter consists of the design methodology used for this project which includes the description on the selected metamaterial structure, the design calculation of the metamaterial structure and the patch antenna. This is follows by the simulation performed using simulation tool on the metamaterial unit cell, metamaterial array, patch antenna as well as metamaterial array on the patch antenna. 3.1 Methodology Overview The methodology adopted in this design includes the numerical approach in which the basic parameters are first being calculated using the corresponding formula. The designed structure is then being simulated using a simulation tool and the simulation results are being compared to the calculation and theoretical result. To meet the theoretical expectation, the design is being optimized accordingly and is re-simulated. Then the analysis is being performed based on the overall results. The methodology described here is illustrated in Figure 3.1. The simulation performed also have a limitation in terms of memory and time, thus simple array structure is used to represent to approximate the result of antenna with metamaterial structure which is being described further in the following sub-sections.

46 33 Figure 3.1 : Methodology Flow 3.2 Metamaterial Structure Metamaterial or LHM is a composite, whose properties are not determined by the fundamental physical properties of their constituents but by the shape and distribution of specific patterns included in them. The structure can be designed in many way, however the fundamental concept and theory of the structure and its properties is very important since it will determine the ability to produce the LHM behavior in the required frequency band. The design start with the metamaterial structure which is conventionally composed of SRR and thin wire grids or strip wires. The periodic SRR structure provides negative effective permeability, whereas the periodic strip wire is responsible for the negative effective permittivity. When both structures are combined together, they may produced a negative index material property over a certain frequency range. The split ring resonator (SRR) is designed to meet the limitations that the experimental setup required due to the use of the waveguide. It was printed on a FR4 Epoxy substrate with dielectric constant of 4.4. The dimensions of the substrate and the SRR are adjusted accordingly in order to get the desired working frequency range. The

47 34 SRR consists of two metallic micro strip rings with a slit (or gap) which may be different in shape such as circular or square rings. There are several parameters that need to be tuned including width and height of the micro strips, distance between the rings, size of the gap, material properties of the rings, substrate and surrounding medium in order to get the desired negative permeability property at certain frequency range. The SRR structure is shown in Figure 3.2. The strip wire simply a thin wire deposited on the substrate and will give rise to the negative permittivity of the structure. The strip wire structure is shown in Figure 3.3. The length, width and the position of the strip wire on the substrate with respect to the SRR will have an affect to the negative index material property of the metamaterial. Figure 3.2: SRR structure

48 35 Figure 3.3 : Strip wire structure The conventional metamaterial structure discussed in this project is comprises of SRR and strip wire printed on the opposite sides of the substrate as shown in Figure.3.4. The transmission through that configurations has been simulated and measured experimentally and it is shown that at frequencies where the expected negative permittivity and permeability to simultaneously occur, there is a transmission peak observed, thus it has been concluded that a negative index of refraction exists. Figure 3.4 : Metamaterial Structure

49 Calculation of the Metamaterial Design Structure Using conventional LHM, it is composed of the rings and the rods. The ring is split ring resonator (SRR) which based on open ring ( C shape) with axis along the propagation direction that could provide a negative permeability. It was predicted to exhibit the resonant magnetic response to the electromagnetic wave, polarized with H parallel to the axis of the SRR [16]. Then the periodic array of SRR is characterized by the effective magnetic permeability μ eff = 1 Ff 2 / (f 2 f m 2 + i γ m f ) (3.1) In (3.1), f m is the resonance frequency which depends on the SRR structure (Figure 3.2(a)) as (2πf m ) 2 = 3L x c 2 / [π ln (2s/w 1 ) r 3 ]. F is the filling factor of the SRR within 1 unit cell and γ m is the damping factor 2πγ m = 2L x ρ/r or also known as losses of the system, where ρ is the resistivity of the metal and c is the free space velocity of light. Formula (3.1) assures that the real part of μ eff is negative at an interval Δf m around the resonance frequency [16] Whereas the rods consist of thin metallic wires where its being aligned along propagation direction which could provide a metamaterial with negative permittivity. The thin metallic wires, acts as a high pass filter for the electromagnetic wave polarized with E parallel to the wires. It leads to a plasma type effective permittivity. ε eff = 1 f e 2 / (f 2 + i γ e f ) (3.2)

50 37 2 In (3.2), f e is the electronic plasma frequency with f e = c 2 / [2πa 2 ln (a/r)] which predict that the effective permittivity is negative for f < f e. By combining both SRR and metallic wires structures, a LHM structure can be created. Here, the resulting structure would possess negative effective refraction index in the resonance frequency interval Δf m The calculation of the S parameters can be obtain using the following formula (3.3) (3.4) Whereas the calculation of the retrieved material parameters such as the index, impedance as well as the permittivity and permeability can be obtain using the following formula Refractive index, n (3.5) Impedance, z (3.6) Permittivity and permeability (3.7)

51 38 The parameters also being adjusted or optimized accordingly by substituting different values of metamaterial dimensions in the calculation formula above to get the desired frequency range and to study on the effect of various dimension on the frequency behavior. 3.4 Calculation of Patch Antenna The antenna used in this project is a square patch printed on a ground microwave substrate as shown in Figure 3.5. The patch antenna having attractive features such as low profile, light weight, easy to fabricate and conformity to mounting post. However the disadvantage of the patch antenna includes the narrow bandwidth and low gain. Figure 3.5 : Square patch antenna structure

52 39 In order to obtain the patch antenna with desired working frequency, the following formula is use to obtain the suitable parameter. The width (w) of the patch can be calculated as w = 2 f c ( ε + 1) r 2 (3.8) With c is the free space velocity of light, f is the frequency of operation, ε r is the dielectric constant and h is the height of the dielectric substrate. The effective dielectric constant (ε reff ) can be determined by ε reff ε r + 1 εr 1 = h w 1 2 (3.9) The actual length of patch (L) is calculated by L = Leff 2ΔL (3.10) Whereas, the effective length of the patch (L eff ) and the length extension (ΔL) can be determine respectively using L eff = 2 f c ε reff (3.11)

53 40 ΔL = 0.412h ( ε + 0.3) reff W h W ( ε 0.258) reff h (3.12) Finally, the ground plane parameters of the patch antenna can be calculated as Lg = 6h + L Wg = 6h + W (3.13) 3.5 Simulation of the Metamaterial Unit Cell The simulation of metamaterial structure is performed using Ansoft High Frequency Simulator System (HFSS). For simulation, the perfect electric conductor (PEC) boundary conditions were employed on the z-faces of the unit cell in order for the electric field to be polarized along the strips and excite its negative permittivity behavior. The perfect magnetic conductor (PMC) boundary conditions were used on the y-faces of the unit cell so that the negative permeability behavior of SRR would be excited. The waveport 1 and 2 are assigned along each of the substrate line on the x-faces. This is illustrated in Figure 3.6

54 41 Figure 3.6 : The boundary conditions & waveports for metamaterial structure (a) PEC boundary, (b) PMC boundary, (c) Waveports The simulations are performed on the metamaterial unit cell which is the basis of the design, on the metamaterial unit cell arrays, patch antenna as well as metamaterial arrays on the patch antenna. In order to obtain the metamaterial structure that exhibit the left-handed (LHM) properties in the desired working frequency region, metamaterial unit cell with different dimensions are simulated to see the effect of the variations on the frequency region and the LHM properties. Besides the dimensions of the metamaterial unit cell, SRR and strip wire dimensions are varies, the other parameters such as substrate type which provides the dielectric constant and the substrate thickness are kept constant. The parametric studies on the influence of the dielectric constant,ε r substrate thickness and the thickness of the SRR and strip wire components is described by M.Kafesaki et.al(2005). It can be summarize that the increase of the dielectric constant by using different type of substrate resulted in the reduction of both the electric and magnetic resonance frequencies of the SRR. Detailed quantitative analysis showed that 2 the dependence of magnetic response on the dielectric constant is ω m 1/ ε r. However, the systematic TMM studies concerning the dependence of the left-hand (LH) peak on the dielectric constant shows that the peak frequency is inversely proportional to

55 42 the square root of the dielectric constant. Thus increasing the dielectric constant cused the LH peak to moved to the lower frequencies. The studies also discussed on the effect of the wire position relative to the SRR, in which it shows that the optimum position of strip wire should be on the opposite sides of the substrate, just behind the SRR gaps. This position give a robust LH transmission. This can be explained by considering on the way the fields generated by the SRRs and strip wires interaction. When the SRR and strip wire are on opposite sides of the substrate, the behavior of each component is not significantly affected by the presence of the other since there is a little overlap between their magnetic fields. On the other hand, the studies shows that the LH peak becomes much broader as the SRR and wires are closer together. If the thickness of the substrate is reduced or in another words, the SRR and strip wire are brought closer together, it will enhance the strength of the total resonance, thus will increase the negative value of the effective permeability as well as the effective permittivity due to the increase in the plasma frequency. Thus reducing the thickness of the substrate allows the behavior of the structure to make transition from RHM to LHM behavior [6]. This is because of the stronger interaction among the SRR magnetic resonance as the broadening of the negative permeability regime due to the increasing amplitude of the approaching SRR. 3.6 Simulation of the Metamaterial Array After obtaining the unit cell structure with the optimized relevant component dimensions, the array of unit cell is designed for the target working frequency in the X- band. Using the optimized unit cell structure, it is then being duplicated to form 2x 3 array as shown in Figure 3.7. The unit cell is positioned closed together with zero sparations between each unit cell to give rise to the periodic structure of the

56 43 metamaterial. The simulation result of the array structure is then being analyzed to look for any variation as compared to the single unit cell structure. Figure 3.7 : The 2x3 array of metamaterial structure. The 2 x 3 array is used since it provide the maximum number of unit cells for this case, that can be simulated using the HFSS simulation tools due to the memory limitation. Besides, the arrangement is also made to ensure the metamaterial array can cope minimally with the next designed patched antenna working in the same frequency band. Thus, the metamaterial array structure present here is to shows on any effect of the metamaterial structure on the conventional patch antenna without emphasizing any particular properties of interest. Studies by Liang et.al (2006), shows that the number of unit cell used in the metamaterial array structure give rise to the better directive properties as can be demonstrated by the radiation pattern of the elements.

57 Simulation of the Patch Antenna The simulation of the patch antenna only to ensure that the structure used provides the working frequency within the desired band as specified. The basic dimensions and parameters of the patch antenna is based on the calculation result. Thus the optimization of the patch antenna structure is deemed necessary in the simulation process to ensure that the resulted gain is optimum within the required frequency band. The structure of the patch antenna used in the simulation is shown in Figure 3.8. Figure 3.8 : Patch antenna structure 3.8 Simulation of the Patch Antenna with Metamaterial Structure To shows the effect of the metamaterial structure on the conventional patch antenna, the matematerial array structure is placed on top of the patch antenna as shown in Figure 3.9. The simulation performed only to see any variation resulted on the gain or the frequency band of the new structure compared to the patch antenna alone.

58 45 Figure 3.9 : Patch antenna with metamaterial structure 3.9 Summary Using the conventional metamaterial structure, the design calculation is performed to obtain the desired parameters follows by the simulation process to rectify the result. Having obtaining the required parameters for the metamaterial unit cell and patch antenna in the desired working frequency, the unit cell is replicated to obtain the metamaterial array and is used to see the effect of the metamaterial structure on the patch antenna.

59 CHAPTER 4 SIMULATION RESULT AND ANALYSIS This chapter consists of the simulation result and analysis of the result which being performed on the metamaterial unit cell with different dimensions, the simulation result that emphasize on the subjects of the LHM/ Negative Index Medium Properties of the Metamaterial Unit Cell, LHM/ Negative Index Medium Properties of the Metamaterial 2x3 Array and S parameter of the Patch Antenna with and without the Metamaterial Structure as well as the analysis on each subject. 4.1 Metamaterial Unit Cell s Dimension Variation Simulation result for metamaterial unit cell dimension variation is listed in Table 4.1. The target negative frequency regions are in the S-band and X-band respectively. The dimensions that are made varies include the length of the unit cell which is also represent the length of the substrate (d) as well as the length of the strip wire, the width on the SRR (w1), the width of strip wire (w2), the ring separation (s) and the SRR gap (g). For better visualization, these dimensions are being illustrate in figure 4.1. The dielectric constant used is 4.4, the substrate thickness is 0.25mm and the SRR and strip wire components which made up of copper element have a thickness of mm

60 47 Figure 4.1: Metamaterial unit cell Table 4.1: Effect of dimension variations on the frequency region Unit cell dimensions (mm) d w1 w2 s g Negative Frequency regions (GHz) Unit Unit Unit ~2.0 Unit ~2.5 From Table 4.1, it shows that unit cell size, d plays an important role in determining the frequency band in which the negative properties will lies. Table 4.2 shows the summary relation of the dimension variations with respect to the magnetic and electric responses that contribute to the value of negative frequency regions. Noted that, by varying the dimensions in order to decrease the overall frequency response from higher to lower frequency also result in the reduction of the resonance strength.

61 48 Table 4.2: Summary Relation of Unit Cell Dimension and Frequency Response Unit cell dimension Magnetic Response, ω m SRR width (w1) - Strip wire width (w2) - Ring separation (s) - SRR gap (g) - Unit size/ wire length (d) Electric Response(plasma frequency), ω p The variations as summarize in Table 4.2 can be explain using the fact that the SRR acts as a LC circuit, with the ring acts as inductor and the open section acts as capacitor. The transmission is affected by the SRR width as well as the combination of changing both width and separation of SRR. SRR width affects the inductance, L of the loop, in which smaller width means larger inductance, thus smaller magnetic response. The ring separation on the other hand affects the capacitance between the rings, which is also a component of total capacitance of the SRR. Therefore, reduction of s results in a decrease of the magnetic resonance frequency. This is expected, as reduction of s is equivalent to increase of the inter-ring capacitance (noted that ω m LC and for a parallel plane capacitor with separation of plates s, C 1/s) [18]. As for the SRR gaps, the effect to the magnetic response is quite minimal. The reduction of the gaps size, does reduce the magnetic response however still much less than the influence shows by the variation in the ring separation. The continuous strip wire provides the electric response of the LHM. The simulation result shows that the plasma frequency decreases as the width of the strip wire decreases. However, with the presence of SRR, the response becomes lower. This is due to the fact that the SRR also respond electrically like a system of cut wires, exhibits a resonance at frequency ω o, which can be demonstrated by closing the SRRs,

62 49 thus destroying the their magnetic response.[15]. However, since the variation caused by SRR is highly dependence on the relative position and distance of the resonance frequency and cut-off plasma frequency, we can make the effect negligible on the electrical response of the LHM. Thus each component can be used to control the LHM properties independently in such a way that the used of SRR to control the magnetic response and the strip wire to control the electrical response. 4.2 LHM/ Negative Index Medium Properties of the Metamaterial Unit Cell Optimizing the dimensions of the metamaterial structure provides a good guideline or reference as to select the optimized design for the desired frequency band for required applications. In this case, the unit 1 dimensions is used to shows the existence of the LHM properties in the X-band frequency. The simulation results shown for the S-parameters and the retrieved material parameters of the metamaterial unit cell. Figure 4.2 and 4.3 show the magnitude and phase of the computed S parameter which is S 11 and S 21. The dip in the phase of S 21, indicates the presence of a negative index band. Figure 4.4 shows the retrieved index of the structure which confirms the existence of the negative index band which lies between roughly 8.8GHz to 9.5GHz. Whereas Figure 4.5 shows the retrieved impedance that roughly lies in the frequency that is matched to that of negative index frequency. Figure 4.6 and 4.7 show the permittivity and permeability parameters respectively. The negative permittivity roughly lies between 8.9GHz to 9.5GHz and the negative permeability roughly lies between 9.25GHz to 9.5GHz. Thus, it is shows that, the LHM properties exist within 9.25GHz to 9.5GHz regions, that is when both the permittivity and permeability are simultaneously negative.

63 50 Figure 4.2 : The magnitude of the simulated S parameters for unit cell Figure 4.3 : The phase of the simulated S parameters for unit cell

64 51 Figure 4.4 : The retrieved index of the unit cell Figure 4.5 : The retrieved impedance of the unit cell

65 52 Figure 4.6 : The permittivity of the unit cell Figure 4.7 : The permeability of the unit cell

66 53 The electric field pattern of the metamaterial unit cell structure is shown in figure 4.8. Here, at the magnetic resonance, the electric field has its maximum mainly at the SRR outer ring gap and in the region between the rings. While along the direction perpendicular to the SRR plane, it is not very much extended. Figure 4.8 : Field pattern of metamaterial structure (E field) 4.3 LHM/ Negative Index Medium Properties of the Metamaterial 2x3 Array Figure 4.8 shows the magnitude and phase of the simulated S parameters. As for the unit cell structure, the dip in the phase of S 21 indicates the presence of a negative index band. Figure 4.9 shows the retrieved index, permittivity and permeability values which show the existence of negative properties in the frequency regions of around 8.0GHz and between 10.6GHz to 11.1Ghz.

67 54 Figure 4.9 : The magnitude and phase of the simulated S paramers for 2x3 array Figure 4.10 : The retrieved material parameters for 2x3 array For array of metamaterial structure, the difference in behavior of the single unit cell and array of unit cells is caused by the interactions between nearest neighbour SRRs. In a unit cell structure, the resonance region is due to an individual SRR which result in a single peak. Whereas on the array structure, the resonance regions are a result of both the individual SRR resonances and the interactions between nearest neighbor

68 55 SRRs. Thus there is additional peaks in the phase plot which caused their LHM regions to differ from a unit cell structure. 4.4 S parameter of the Patch Antenna with and without the Metamaterial Structure Figure 4.10 shows the S 11 parameter of the designed patch antenna with return loss value of dB at frequency of 9.0GHz which is within the desired X band frequency. Figure 4.11 shows the new S 11 parameter of designed antenna with metamaterial array structure. There is a shift in the frequency regions as well as the downshift in the S 11 value. The frequency is now shift to 8.80GHz and 10.4GHz with S 11 value of -4.3dB and -7.5dB respectively. Figure 4.11 : S 11 parameter of the patch antenna

69 56 Figure 4.12 : S 11 parameter of the patch antenna with metamaterial structure The simulation results indicate that the metamaterial structure has an affect to the conventional patch antenna by shifting the frequency regions to different value as well as affecting the S 11 parameters. As far as current simulations performed, it is shown that the metamaterial structure will be able to reduced the size of the patch antenna working in the high frequency regions. As known, the size of the patch antenna need to be increased in order to get a higher frequency band, however with metamaterial structure, the frequency band can now be shifted to a higher value. However, since there is a limitation for the metamaterial array as discussed in section 3, the result obtained for the patch antenna with metamaterial structure cannot be conclude without further studies being performed to see the actual effect of the metamaterial structure on the patch antenna. Nevertheless, with reference to other researches on this area, metamaterial structure is shown to have the capability to enhance the performance of conventional antenna in terms of its gain and directivity.

70 Summary Different dimensions of the conventional metamaterial structure lead to frequency variation of the negative index region. These dimensions affect the lefthanded behavior produce by the designed structure with reference to the structure basic properties. The simulation result also shown that the negative index region is obtained within certain frequency range with limited left-handed peaks for both metmaterial unit cell and metamaterial array. Having some constraint in the simulation process, we only can see the effect of metamaterial structure on the patch antenna in general.

71 CHAPTER 5 CONCLUSION AND FUTURE WORKS In the designing of the metamaterial structure, the parameters and dimensions of each component plays an important role in determining the LHM properties and the frequency regions in which the negative index lies. In most cases, it is very difficult to obtain both negative permittivity and permeability simultaneously, however there can exist separately over a different frequency regions. Since the influence of these parameters are quite significant, and the fact that the negative index only exists over a certain frequency range, a careful and high accuracy designed is expected. However, further works can be carries to see the influence of using different metamaterial structure on the LHM properties, instead of the conventional square or circular SRR. Varies other geometries may also be used to see how the LHM properties will react and how the frequency band will be affected. The other parameters that is not discussed in details in this project can also being carry out in the future works such as the usage of cheaper substrate and metamaterial components for cost reduction. With varies parameters influential, it is also possible to look at the potential of the used of metamaterial as antenna based instead of as an additional structure for conventional antenna

72 59 The size of metamaterial unit greatly determine the frequency band over which the negative region will lies. Since it is shown that the miniature size of metamaterial leads to the higher frequency band with stronger left-handed peak as compared to the larger size with weaker or low left-handed peak, metamaterial is more suitable for higher frequency applications. Further works can be performed in order to obtain a good LHM properties working in the lower frequency range especially in ISM band for wireless LAN applications for example. This is an interesting area to be explore since the success in obtaining the metamaterial structure with both negative permeability and permittivity at lower frequency will improve the current wireless LAN applications by providing better gain, directivity as well as may leads to the ability to reduce the size of current conventional antenna for these applications. Also since the effect of the metamaterial structure on the conventional antenna cannot be conclude in this project, it is proposed that further works to be done to see the improvement of antenna performance by using larger metamaterial array structure, the effect to the antenna performance if using a few layer of the metamaterial structure on the conventional antenna as well as the effect of changing the position of the metamaterial structure on the conventional antenna.

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78 APPENDIX A Double Negative Metamaterial

79 66

80 67

81 Effective Medium Parameter 68

82 69

83 70

84 71