Metamaterials: Negative Refractive Index - Assignment Example

Metamaterials (Negative Refractive Index) April 2008 Table Of Contents Introduction 3 Chapter 1 Metamaterials 4-5 Chapter 2 Electromagnetic Waves 6-8 Chapter 3 Negative Refractive Index 9-10 Chapter 4 Split Resonator 12-22 Bibliography 23-24 Introduction This essay provides insight into metamaterials, electromagnetic waves, negative refractive index, split resonators and how to build a metamaterial with a negative refractive index. This article discussed the basics of negative index materials and how to build them. The applications of negative index metamaterials include phase compensators, superlenses (sub-diffraction limited near field lenses) and subwavelength resonant cavities. The missiles could be developed using metamaterials, which are invisible. Chapter 1 Metamaterials Any material is made from the 116 elements palette also called periodic table. For instance, pick a small quantity of sulfur, some carbon, a small piece of dysprosium and a new substance - voilà. Suppose if we add some additional colors to the palette, what will happen? Here, comes in the new field - metamaterials. The metamaterials allows forming artificial atoms, which can be merged to create substances having innovative properties. Hence, engineers could fashion metamaterials, which concentrate images of extraordinary resolution, refract light in the backward direction, or even can form as a basis for a concealing device. Engineers can use metamaterials to create innovative devices with novel properties and freed from the limitations of building blocks in the nature. Professor Xiang Zhang, who is working at Nanoscale Science and Engineering Center & Department of Mechanical Engineering of UC Berkeley, is a leading player in the emerging metamaterials field. He expressed interest to develop artificial materials having astonishing properties. He and his colleagues illustrated the acoustic metamaterial fabrication for the first time in the world. Now let us find out what exactly is a metamaterial. Take a large quantity of concrete with Manhattan’s size, which is an ordinary material formed using almost a uniform substance. Now take the case of actual Manhattan, which is made by arranging concrete into the buildings array on a lattice of city blocks, which is a metamaterial. The city structure has a complicated substructure with its skyscrapers when compared with the concrete slab, though both have analogous compositions. Now put copper in concrete’s place and “wires and coils” in the place of buildings and shrink the total by a factor of one billion (imagine microns instead of kilometers), we get the metamaterial basics. The size and arrangement of wires and coils is critical for metamaterial’s structure. If a sound wave or light wave goes through a structures arrangement that are very much small when compared with its wavelength, the light/sound wave understands the material as having different properties when compared with constituent materials. The wave would see the material as an innovative material and could not recognize the separate substructures in it. Metamaterial engineers can work on large-scale, easily modified components when compared with going for naturally arranged atoms. The structures are developed using copper coils that are in micron size to operate at microwaves. This array’s properties are tuned in such a way that the coils resonate naturally at a frequency near to the incoming wave’s frequency. In fact, electromagnetic metamaterial is developed to offer electromagnetic response surpassing natural structures. It could be either a disordered or an ordered structure such as aperiodic, quasiperiodic, periodic and fractal. The properties of a metamaterial are obtained from its structure instead of from its composition. The metamaterial that holds unusual properties can be identified using the metamaterial sticker from other composite materials. Mr Rodger M. Walser, who is working at the University of Texas at Austin, provided the name ‘metamaterial’ in the year 1999. The metamaterials, which are manmade macroscopic composites with a three dimensional and periodic cellular construction, are developed to exhibit two or more results to a particular excitation. The metamaterials are artificial materials and are not naturally available materials. Mr W.E. Kock had developed the first metamaterial in the later part of 1940 using metallic delay lenses and metal lens antennas. Electromagnetic metamaterials finds applications in photonics and optics. In fact, electromagnetic metamaterials finds a special place in electromagnetism. They offer promising applications in numerous microwave and optical applications including new varieties of modulators, antenna radomes, microwave couplers, beam steerers, lenses and band pass filters. 1 Chapter 2 Electromagnetic Waves The magnetic and electric fields are produced by the alternating current. The electric field wave and the magnetic field wave travel in a perpendicular direction to each other. The magnetic and electric fields can be separated at extremely lower frequencies. However, electric field and magnetic field cannot be separated at higher frequencies and hence the name “electromagnetic fields” or “electromagnetic waves”. The characteristics of an electromagnetic wave include wavelength, frequency, amplitude and velocity. The definitions of each of these parameters are given below: Wavelength: It is the length between crests of a single cycle as indicated in the figure below. It is denoted by the symbol  (lambda). Amplitude: It is the distance between the midpoint of a wave to its trough or crest. Frequency: It is denoted by the symbol ‘f’. It is defined as the number of peaks passing a point in a time of one second. It is in fact the inverse of time. Formula: f = 1/t where t is the time. Suppose t = 0.5 seconds, then frequency is f=1/0.5=2 Hz (Hertz) The unit for frequency is Hertz (cycles/second). Period: It is the time passed between successive peaks passing a certain point. It is denoted by the letter t. The time t is calculated by the formula t = 1/f where f is the frequency. Velocity: It is denoted by the symbol v. The distance covered in a certain period of time is called velocity. The formula for velocity is v=f, where f = frequency and  = wavelength. A typical electromagnetic wave is depicted below: Electromagnetic waves, which are oscillations, transmit through free space at a light velocity (Vc). Vc = 299,792,500 +/- 300 m/s. It is approximated as 3 x 108 m/s in vacuum. The electromagnetic (EM) waves travel in a way perpendicular to the propagation direction. Hence, the EM waves are transverse whereas water waves travel in the propagation direction i.e. longitudinal waves. The behavior of EM waves could be predicted in all conditions including refraction, reflection and diffraction. The electromagnetic waves propagate evenly in all the directions from a given source, as there is no presence of obstacles in free space. Electromagnetic waves travel at a constant velocity. Electromagnetic waves accomplish energy transmission through a vacuum. The electromagnetic fields disturbance causes electromagnetic radiation. The applications of electromagnetic waves include transmission of short/FM/long wavelength radio waves; telephone/television/wireless signals as well as energies. They also facilitate energy transmission in various forms including VIS (visible light), IR (infrared radiation), X-rays, ultraviolet and gamma rays. Hence, every part of the EM spectrum plays vital role in our daily life. Now days, the widely used mobile communication is made possible through the use of electromagnetic waves. The microwaves are used for transmission between ground station and vice versa. The ship-to-ship, ship to satellite communication is made possible using electromagnetic waves. 2 Chapter 3 Negative Refractive Index /Development Techniques A properly built metamaterial could be used to accomplish a negative refractive index. If an electromagnetic wave is transmitted to higher index medium from a lower index medium, say from air to water, the EM wave turns towards a line, which is 900 to the surface. If the light passes through a negative index substance, it twists to the opposite direction, though it returned from a perpendicular line. It is this property that allows development of superlenses with high resolution when compared with common lenses. Zhang’s lab shifted its attention to ultrasound from electromagnetic waves and developed an acoustic metamaterial for the first time in the world. The musical instrument, which we used to play, carries sound waves having the wavelength higher than the buttons on it. In a similar fashion, we would develop structures either to control or manipulate the ultrasound’s resonating frequencies using small resonator cavities or tiny elements. The main aim for electromagnetic waves is to achieve a negative refraction index. Zhang’s group accomplished a negative modulus for acoustic waves in the metamaterial. The material’s elastic modulus decides the compression property i.e. how much the material gets compressed on pushing it. The material expands instead of compressing when the modulus is negative. This condition becomes true when the material is pushed at a 33 KHz frequency. The negative modulus is not usually found in natural materials since it is a distinct property. The acoustic devices developed using metamaterials are compact and small when compared with the present acoustic devices, as the latter must be bigger than wave’s wavelength. Zhang’s group staged a decision to modify the linear array into 2 or 3 dimensional metamaterial that could offer several useful applications including sonar systems and medical ultrasound imaging. They could develop a superlens to overcome diffraction limit by taking the advantage of negative modulus. Mr Victor Veselago, a Russian Physicist, first dreamt about a metamaterial. He just thought how a material would perform if its permeability and permittivity are negative. The permeability and permittivity factors determine the interaction of a material with magnetic and electric fields. However, such materials are unavailable in the nature. The engineers recently created the metamaterials. Developing a metamaterial for use in sound means finding the acoustic analogues to permeability and permittivity instead of finding ways to construct a material in that both are negative. The acoustic analogues mentioned here is elastic constant and mass density of a material. A group of physicists working at a Chinese Wuhan University described a method to develop such a material. The metamaterial they proposed develop is somewhat strange. The metamaterial comprise an array of gold spheres, which are coated with rubber, together with spheres of water spheres consisting of air bubbles and all included in an epoxy resin. Mr Yigun Ding and his colleagues devised a method for making the two main numbers negtaive at a particluar frequency and at the same time. Prior to this development, they could make only one aspect negtaive at a time. A long established fact is that water spheres periodic array consisting of air bubbles could exhibit negative elastic constant at some frequencies. Recently, physicists found that soft rubber coated periodic arrays of hard spheres inlcuded in a hard plastic could show an effective negative mass density at certain frequencies. Now someone can try to develop a metamaterial having a negative index of refraction. Of course, this could happen in the near future. It is possible to make lenses that are better than earlier ones for ultrasound machines, provided acoustic metamaterials could achieve the same for sound as they could accomplish for light. If this can be done, even Cloaks could be built using metamaterial to conceal submarines from sonar systems. So some companies could come forward and take up this chore. A metamaterial, which is a zinc blende structure comprising of fcc collection of water spheres containing air bubbles (BWSs) and another fcc array consisting of gold spheres coated with rubber (RGSc) embedded in an epoxy matrix, possesses mass density and negative bulk modulus simultaneously. The mass density and negative bulk modulus are developed simultaneously from the concurremy nonpolar resonances. The metamaterial’s poisson ratio would be negative at resonance frequency. 3 Chapter 4 Split Resonators A material having a negative index of refraction is called a metamaterial and split ring resonator is part of it. If an electromagnetic material is passed to a denser optical material from a less dense optical material, it refracts as it gives a part of its energy to the electrons situated in the denser optical material. The magnetic field and electric field are two constituents of an electromagnetic wave. The electrons moves forth and back owing to electric field and in a circular motion in view of magnetic field. Rotating currents are induced in the rings when magnetic flux penetrates metal rings (SRRs) causing electrons to oscillate at a frequency, which is called resonant frequency. The dimensions and structure of the SSRs’ determines the resonant frequency. The material works as a metamaterial if the electromagnetic material having a frequency greaten than that of a resonant frequency travels through it. A method for nanofabrication of planar split ring resonators for one-dimensional metamaterials with negative refractive index in the infrared range (5-10 m) is discussed here: Complementary double split ring and double split ring resonators (CSRR and SRR) having circular and square geometries were used for fabrication as these are the basic building blocks to accomplish magnetic permeability and negative effective dielectric permittivity. Curvilinear and straight-line segments having a line width of 80-120 nm were fabricated using scanning probe nanolithography having a z-scanner movement. The demarcated geometries in 20 nm thin silver layers were sputter deposited on a photoresist positive substrate that was spin coated on polycarbonate slabs and on single polished crystal silicon wafers. Atomic force microscopy characterizes the structure’s morphology with repeatability of 60-150 nm that depends on the feature complexity and process conditions. The depth of nanolithographic groove in various samples varied from 4 nm to 80 nm. Electromagnetic materials having a negative refractive index (NRM) could be classified as synthetic subwavelength structures that were developed to achieve negative values of negative value of the magnetic permeability and effective dielectric permittivity simultaneously in a specified wavelength. NRMs are sometimes known as left hand materials as the Poynting vector’s direction in a negative index metamaterial is reverse to wavevector’s direction. The vectors of magnetic and electric fields as well as the wavevectors create a left oriented set. These materials are also called Veselago media, backward media anddouble negative materials. Veselago has first described about the NRMs. However, Pendry proposed practical implementation methods after rediscovering the same. Smith et al had first realized experimental NRMs. Several innovative applications were proposed with NRM. Perfect lenses or Superlenses are most popular among them. Superlenses allow resolutions further than the diffraction limit as they focus 2D image’s all Fourier components such as evanescent modes. Another application of NRM includes subwavelength resonant structure. A resonator with smaller dimensions when compared with operating wavelength is called subwavelength resonator. Various solutions including different microwave transmission lines, filters, resonators, materials having magnetic properties at THz frequencies; electrically small, high gain antennas for the microwave, active optical elements that depend on nonlinear phenomena and antireflection structures have been developed from these. Split ring resonators (SRR) for negative magnetic permeability and thin metallic wires having negative effective dielectric permittivity were the first building blocks that act as NRMs. SRRs were also called meta atoms or particles of NRM. SRR is a leading building block for achieving μ < 0, though numerous methods have been proposed to fabricate NRM with the help of transmission line method. The proposed complementary split ring resonator structure in November 2004 endows a negative dielectric permittivity. Hence, this becomes a first particle substitute to transmission line and thin wire structures. Fabrication of such structures for use in the optical range is quite difficult as the NRM building block’s dimensions must be subwavelength. The features of smallest investigational SRRs were about 5 mm that offers a response in the infrared. The double split ring resonator (SRR), the basic building block for NRM, has highly conductive structure that holds high capacitance between the two rings in order to compensate inductance. SRR’s operating principle instigated from its complex electromagnetic resonant capacitive/inductive response portrayed by its LC resonant equivalent circuit. The application of a time varying magnetic field perpendicular to the ring’s surface induces currents that generates magnetic field, which may either enhance or oppose the incident field, thereby creating a negative or positive effective permeability. The complementary geometry of an SRR is a complementary split ring (CSRR) (Babinet law) and also the unit cell of metasurfaces/metameterial that endows a negative ε. Figure 1. Double split ring geometries suitable for the optical range are shown in the above figure. White areas indicate nanolithographic cuts whereas shaded areas represent metal surface. Bottom and top right are complementary SRR. Bottom and top left are ordinary SRR. Bottom row uses liner line segments whereas top utilizes circular segments. Complementary structures are shown in the right column. The formulae for effective permittivity and permeability in an NRM unit cell is given below: , The thickness of the split ring resonators when the rings are kept in vacuum (top left of the above figure) is neglected. Hence, the following equation is achieved: where d is the gap between the rings, a is the unit cell length and σ is the electrical conductance. The following equation gives the resonant frequency (for which µeff ): The following equation gives the magnetic plasma frequency (for which µeff 0): For a ring line width w and a dielectric with ε: Figure 2. The above figure indicates magnetic plasma wavelength and resonant wavelength for a series of unit cell dimensions for a double split ring resonator. The unit cell dimensions necessary to achieve optical wavelength range could be computed easily using equations 2 – 5. The selected ratio of unit cell to the SRR radius was about 0.4 for a circular structure split ring. The structure response of various inter-ring spacing values d was computed. Figure 2 above shows the plasma frequency calculation results. The unit cell dimensions based on that should be smaller by 5-10 times when compared with the operating wavelength, which depends on the selected gap in the SRR. Structures that feature 1.5 - 4 m could be developed with nanolithographic lines of the order 0.1 m to achieve target wavelengths of 5-10 m in the mid-infrared range. A CSRR structure reveals dual behavior to that of equivalent SRR based on the Babinet principle. Hence, the equations 2-5 that were used to compute the negative permeability as well as resonant frequency of an SRR could be utilized straight to obtain resonant frequency and effective permeability of a CSRR. This task was accomplished both experimentally and theoretically. Hence, the whole theory discussed above for SRR is applicable to CSR also just by replacing μeff with εeff. However, the resonant frequency as well as ranges of CSRR’s negative permittivities is similar to that corresponding SRR. The high frequency scalability of forms described in the equations 2 – 4 is another issue to be taken into account. The metal layers thickness for the CSRR/SRR should be greater when compared with the skin depth. Typical value for silver at 100 THz is 20 nm. Additional inductance comes into the picture when wavelengths approach the optical range to determine the plasma frequency. Such inductance is called interial inductance, which is an outcome of currents and the effective electron mass through almost a purely ballistic SRR. The interial inductance exists for the scaled down dimensions whereas the effect of negative permittivity/permeability vanishes completely. The original SRR design modified with the addition of more capacitive gaps, in order to overcome this problem. CSRR and double SRR structures were shown in the bottom row of Figure 1. In order to balance the interial inductance, additional capacitive gaps were introduced in these structures. The geometries indicated in the upper row can also changed in the same way. Experiment: Double polished silicon wafers were used for the preparation of a sample. The spin-coated wafers using a positive photoresist having a thickness of 400 nm were dried. In order to deposit a silver layer of 20 nm thickness above the photoresist, RF sputtering method was employed. Prior to the nanolithography, atomic force microscopy characterizes the surface morphology. The silver surface has a flatness of better than 2 nm. Uncoated polycarbonate samples having 10-30 nm flatness were also utilized in the experiments. In order to get NRM building blocks, the surface of the samples was subjected to nanolithography process under normal room temperature and humidity conditions. A scanning probe nanolithography with a Veeco Autoprobe CR-Research atomic force microscope utilized to accomplish this task. To ensure proper operation, shock free and antivibration conditions are necessary. Anti-vibration tables having active oscillation dumping was used to achieve this chore. However, this method also sometimes failed to offer disturbance free operation. The three modes of operation possible using the Autoprobe CP-Research AFM include the voltage pulse mode, in which direct oxide formation on the silicon or any other semiconductor; z-scanner movement or scratching mode; and the constant load mode or set point nanolithography. Z-scanner method is utilized among all the three modes. For this operation, a silicon nitride microcantilever tip was utilized. In order to achieve perfect pressing of the needle tip against the surface of the sample, the position of the scanner was setup between 0.9 m and 0.7 m. Various factors including the force applied, the needle tip shape, needle tip speed and the sample surface material decide the width and depth of the nanolithographic lines obtained. Figure 3. Dimensions and profiles of nanolithographic lines a) Line profiles of a polycarbonate substrate (top) and silver over a photoresist (bottom); and b) Three dimensional AFM micrograph of a single nanolithographic line in a polycarbonate The z-scanner nanolithography leaves upturned material as it is on its edges and digs a groove actually in the substrate. Figure 4. AFM profile for square double split ring resonator structure made using SPM nanolithography in silver over a photoresist The above figure shows square segment based SRR structure. The diagonal of the whole structure is 2.5 m whereas its inner square diagonal is 1 m. Each ring in this structure is splitted into 4 segments. The displacement of the z-scanner was about 0.7m. The width of the nanolithographic line was 60 nm. Some lines were displaced by 60-150 nm in the obtained structure when compared with the designed values. Figure 5. Two different double CSRR structures’ AFM profiles developed using SPM nanolithography in silver over photoresist The above figure shows two complementary split ring resonators having curvilinear segments but varying in the capacitive gap widths. CSRRs outer diameter was about 2.2 m whereas the diameter of the inner ring was 1 m. The larger z-displacement resulted in broader nanolithographiclines, say about 80 nm. The process duration for single straight line CSRR or SRR segments was just many seconds whereas for each curvilinear structure it lasted for 2-3 minutes. This is mainly due to drawing of circle up to 360 linear segments. Also, each of the nanolithographic procedure needs full surface scanning after and before the process. The fabrication of additional complex patterns that holds more elements requires more time. Gradual shifting of patterns fabricated with regard to the nanofabrication of CSRR and SRR geometries is another problem noticed when compared with the designed ones. It results in minor curving of the actually straight segments. Another problem noticed in the patterns was a kink at the end and at the beginning of each line. It may be due to piezo actuated micropositioner operation. Also the selected silver substrates could easily be created using gallium nitride needle tip. 4 Metamaterials could be used to improve the performance of antennae. The introduction of metamaterials would improve antenna’s radiating power. It is possible to achieve high directivity, electrically small antenna and adjustable operational frequency by using negative permeability materials. A backward to forward scanning ability is accomplished by using left handed (LH) and right handed (RH) combination in a composite transmission line. Isaacs invented antennae consisting of single negative materials, which resonantly linked to external radiation. The resonant antenna coupling makes antenna sensitive to radiation, though the radiation wavelength is much bigger when compared with the antenna size. Hence, one can make electrically small antenna to operate at microwave frequencies with the use of such a resonator. The main aim is to make such an antenna. Figure 6. a) Split ring resonator (SRR) schematic b) SRR inserted monopole antenna c) Coaxial cable d) Measured S11 for the monopole SRR composite and monopole source. The geometrical parameters of the SRR shown in Figure 6 are r=2.5 mm, R=3.6 mm, t=0.9 mm and w=0.2 mm. The parameters of the chosen standard FR-4 substrate having a thickness of 1.6 mm include a loss tangent of 0.008 at 3 GHz and relative permittivity of 3.85 at 4 GHz. The fabrication of SRR is accomplished through etching of deposited 30-µm thick copper. The SRR is excited with a monopole antenna (Figure 6 b), which consist of a coaxial cable, radiating wire part and ground plane, which is made of aluminum. The characteristics of the SSI 0413 coaxial cable include a shield thickness of 0.48 mm, Teflon thickness of 1.08 mm, inner wire radius of 0.409 mm and insulator coating thickness of 0.48 mm. The dielectric constant of the Teflon cable was 2.2. Hence, the cable can safely broadcast the TEM mode waves up to a frequency of 65 GHz. The 0.5 mm thick and square shaped ground plane is connected to the shield using a conducting paste. The antenna was developed to operate at 3.52 GHz based on the geometrical parameters of SRR. It has a corresponding wavelength (λ) of 85.17 mm. The wire length above the ground plane was 8.32 mm. The wire length for the monopole antenna was 1/4 of the operation wavelength. This monopole efficiently worked at a frequency of 7.8 GHz and feed wavelength of 33.28 mm. Hence operation frequency of the monopole is higher than the SRR resonance frequency. SRR is kept near to the monopole antenna’s radiating wire. The SRR and the wire part act as a composite radiating structure at an operating frequency of 3.52 GHz. The characteristic impedance of the wire SRR composite and the coaxial cable becomes closer. The structure efficiently radiates when the magnitude of the surface currents on the SRR rises. 5 Bibliography Zhengyou, et al, March 2007, Development of a metamaterial, available at http://link.aps.org/abstract/PRL/v99/e093904 Fang, N. et al, Nature Materials 5, 452-456 (2006). 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