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Metamaterials are artificial materials engineered to have properties that may not be found in nature. They are assemblies of multiple individual elements fashioned from conventional microscopic materials such as metals or plastics, but the materials are usually arranged in periodic patterns. Metamaterials gain their properties not from their composition, but from their exactingly-designed structures. Their precise shape, geometry, size, orientation and arrangement can affect the waves of light or sound in an unconventional manner, creating material properties which are unachievable with conventional materials. These metamaterials achieve desired effects by incorporating structural elements of sub-wavelength sizes, i.e. features that are actually smaller than the wavelength of the waves they affect.
The primary research in metamaterials investigates materials with negative refractive index. Negative refractive index materials appear to permit the creation of superlenses which can have a spatial resolution below that of the wavelength. In other work, a form of 'invisibility' has been demonstrated at least over a narrow wave band with gradient-index materials. Although the first metamaterials were electromagnetic, acoustic and seismic metamaterials are also areas of active research.
Potential applications of metamaterials are diverse and include remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, public safety, radomes, high-frequency battlefield communication and lenses for high-gain antennas, improving ultrasonic sensors, and even shielding structures from earthquakes.
The research in metamaterials is interdisciplinary and involves such fields as electrical engineering, electromagnetics, solid state physics, microwave and antennae engineering, optoelectronics, classic optics, material sciences, semiconductor engineering, nanoscience and others.
They show promise for optical and microwave applications such as new types of beam steerers, modulators, band-pass filters, lenses, microwave couplers, and antenna systems. Furthermore, the lower density of materials means that components, devices, and systems can be lightweight and small, while at the same time enhancing system and component performance.
Metamaterials consist of periodic structures. An electromagnetic metamaterial affects electromagnetic waves by having structural features smaller than the wavelength of the respective electromagnetic wave. In addition, if a metamaterial is to behave as a homogeneous material accurately described by an effective refractive index, its features must be much smaller than the wavelength. To date, subwavelength structures have shown only a few questionable results at visible wavelengths.
For microwave radiation, the structures need only be on the order of several millimeters. Microwave frequency metamaterials are usually synthetic, constructed as arrays of electrically conductive elements (such as loops of wire) which have suitable inductive and capacitive characteristics. These are known as split-ring resonators.
Photonic metamaterials, at the scale of nanometers, are being studied in order to manipulate light at optical frequencies. Plasmonic metamaterials utilize surface plasmons, which are packets of electrical charges that collectively oscillate at the surfaces of metals at optical frequencies.
Another structure which can exhibit subwavelength characteristics are frequency selective surfaces (FSS) known as Artificial Magnetic Conductors (AMC) or alternately called High Impedance Surfaces (HIS). These also have inductive and capacitive characteristics, which are directly related to its subwavelength structure.
Photonic crystals and frequency-selective surfaces such as diffraction gratings, dielectric mirrors, and optical coatings do have apparent similarities to subwavelength structured metamaterials. However, these are usually considered distinct from subwavelength structures, as their features are structured for the wavelength at which they function, and thus cannot be approximated as a homogeneous material.
However, novel-material structures such as photonic crystals are effective with the visible light spectrum. The middle of the visible spectrum has a wavelength of approximately 560 nm (for sunlight), the photonic crystal structures are generally half this size or smaller, that is <280 nm.
Winston E. Kock developed materials that had similar characteristics to metamaterials in the late 1940s. Materials, which exhibited reversed physical characteristics were first described theoretically by Victor Veselago in 1967. A little over 30 years later, in the year 2000, Smith et al. reported the experimental demonstration of functioning electromagnetic metamaterials by horizontally stacking, periodically, split-ring resonators and thin wire structures. Later, a method was provided in 2002 to realize negative index metamaterials using artificial lumped-element loaded transmission lines in microstrip technology. At microwave frequencies, the first real invisibility cloak was realized in 2006. However, only a very small object was imperfectly hidden.
In 2007, one researcher stated that for metamaterial applications to be realized, several goals must be achieved. Reducing energy loss, which is a major limiting factor, keep developing three-dimensional isotropic materials instead of planar structures, then finding ways to mass-produce.
The greatest potential of metamaterials is the possibility to create a structure with a negative refractive index, since this property is usually not found in any natural materials. Almost all materials encountered in optics, such as glass or water, have positive values for both permittivity ε and permeability µ. However, many metals (such as silver and gold) have negative permittivity at shorter wavelengths. A material having either (but not both) ε or µ negative is often opaque to electromagnetic radiation (see surface plasmon for more details). However, anisotropic materials with only negative permittivity can produce negative refraction due to chirality.
Although the optical properties of a transparent material are fully specified by the parameters εr and µr, refractive index n is often used in practice, which can be determined from . All known non-metamaterial transparent materials possess positive εr and µr. By convention the positive square root is used for n.
However, some engineered metamaterials have εr < 0 and µr < 0. Because the product εrµr is positive, n is real. Under such circumstances, it is necessary to take the negative square root for n. Physicist Victor Veselago proved that such substances can transmit light.
The foregoing considerations are simplistic for actual materials, which must have complex-valued εr and µr. The real parts of both εr and µr do not have to be negative for a passive material to display negative refraction. Metamaterials with negative n have numerous interesting properties:
For plane waves propagating in electromagnetic metamaterials, the electric field, magnetic field and wave vector follow a left-hand rule. This is a reversal of direction when compared to the behavior of conventional optical materials.
Negative refractive index is an important characteristic in metamaterial design and fabrication. As reverse-refraction media, these occur when both permittivity ε and permeability µ are negative. Furthermore, this condition occurs mathematically from the vector triplet E, H and k.
In ordinary, everyday materials – solid, liquid, or gas; transparent or opaque; conductor or insulator – the conventional refractive index dominates. This means that permittivity and permeability are both positive resulting in an ordinary index of refraction. However, metamaterials have the capability to exhibit a state where both permittivity and permeability are negative, resulting in an extraordinary, index of negative refraction.
Various types of composite material, both electromagnetic and other types are being studied by various research groups worldwide (see all sections and references below). Electromagnetic metamaterials are represented by different classes, as follows:
In negative index metamaterials (NIM), both permittivity and permeability are negative resulting in a negative index of refraction. Hence, because of the double negative parameters these are also known as Double Negative Metamaterials or double negative materials (DNG). Other terminologies for NIMs are "left-handed media", "media with a negative refractive index", and "backward-wave media", along with other nomenclatures.
In optical materials, if both permittivity ε and permeability µ are positive this results in propagation in the forward direction. If both ε and µ are negative, a backward wave is produced. If ε and µ have different polarities, then this does not result in wave propagation. Mathematically, quadrant II and quadrant IV have coordinates (0,0) in a coordinate plane where ε is the horizontal axis, and µ is the vertical axis.
In 1968 Victor Veselago published a paper theorizing plane wave propagation in a material whose permittivity and permeability were assumed to be simultaneously negative. In such a material, he showed that the phase velocity would be anti-parallel to the direction of Poynting vector. This is contrary to wave propagation in natural occurring materials. In the years 2000 and 2001, papers were published about the first demonstrations of an artificial material that produced a negative index of refraction. By 2007, research experiments which involved negative refractive index had been conducted by many groups.
In single negative (SNG) metamaterials either relative permittivity (εr) or relative permeability (µr) are negative, but not both. These are ENG metamaterials and MNG metamaterials discussed below. Interesting experiments have been conducted by combining two SNG layers into one metamaterial. These effectively create another form of DNG metamaterial. A slab of ENG material and slab of MNG material have been joined to conduct wave reflection experiments. This resulted in the exhibition of properties such as resonances, anomalous tunneling, transparency, and zero reflection. Like negative index materials, SNGs are innately dispersive, so their εr, µr, and refraction index n, will alter with changes in frequency.
Electromagnetic bandgap metamaterials control the propagation of light. This is accomplished with either a class of metamaterial known as photonic crystals (PC), or another class known as left-handed materials (LHM) Both are a novel class of artificially engineered structure, and both control and manipulate the propagation of electromagnetic waves (light). PCs can prohibit light propagation altogether. However, both the PC and LHM are capable of allowing it to propagate in certain, designed directions, and both can be designed to have electromagnetic bandgaps at desired frequencies.
In addition, metamaterials such as Photonic crystals (PC) are complex, periodic, materials and are considered to be electromagnetic bandgap material. However, a PC is at first distinguished from sub-wavelength structures, such as tunable metamaterials, because the PC derives its properties from its band gap characteristics. In addition the PC operates at the wavelength of light, compared to other metamaterials which operate as a sub-wavelength structure. Furthermore, the complex response of photonic crystals functions by diffracting light. In contrast, a permittivity and permeability defines metamaterials (also a complex response), which is derived from their sub-wavelength structure and diffraction must be eliminated.
The PC is also a material in which periodic inclusions inhibit wave propagation due to destructive interference from scattering from the periodic repetition. The photonic bandgap property of PCs makes them the EM analog of the electronic semi-conductor crystals.
Intended material fabrication of EBGs has the goal of creating periodic, dielectric structures, with low loss, and that are of high quality. An EBG affects the properties of the photon in the same way semiconductor materials affect the properties of the electron. So, it happens that the PC is the perfect bandgap material, because it allows no propagation of light. Each unit of the prescribed periodic structure acts like large scale atoms.
Electromagnetic bandgap structured (EBG) metamaterials are designed to prevent the propagation of an allocated bandwidth of frequencies, for certain arrival angles and polarizations. With EBG materials new methods utilize the properties of various dielectrics to achieve better performance. A variety of geometries and structures have been proposed to fabricate the special EBG metamaterial properties. However, in practice it is impossible to build a flawless EBG device. Factors such as advances in ideas, research, testing and development, along with the prospects of significant technological solutions, have driven the development of EBG applied science.
Commercial production of dielectric EBG devices has lagged, because commercial rewards are not readily apparent. However, start-up companies are cropping up solely focused on exploiting EBG metamaterials. These metamaterials have been manufactured for frequencies ranging from a few gigahertz (GHz) up to several terahertz (THz). In other words, applications have achieved fabricated media for radio frequency, microwave and mid-infrared regions. "It now appears that EBG concepts can, in many cases act as improved replacements for conventional solutions to electromagnetic problems." Applicable developments include an EBG transmission line, fabricated utilizing the special properties of metamaterials, EBG woodpiles made of square dielectric bars, and several different types of low gain antennas.
An EBG is a result of a metamaterial that functions in the regime where the period is an appreciable amount of the wavelength, and constructive and destructive interference occur.
Double positive mediums (DPS) do occur in nature such as naturally occurring dielectrics. Permittivity and magnetic permeability are both positive and wave propagation is in the forward direction. Artificial materials have been fabricated which have DPS, ENG, and MNG properties combined.
Categorizing metamaterials into double or single negative, or double positive, is normally done based on the assumption that the metamaterial has independent electric and magnetic responses described by the parameters ε and µ. However in many examples of electromagnetic metamaterials, the electric field causes magnetic polarization, and the magnetic field induces an electrical polarization, i.e., magnetoelectric coupling. Such media are denoted as being bi-isotropic. Media which exhibit magneto-electric coupling, and which are also anisotropic (which is the case for many commonly used metamaterial structures), are referred to as bi-anisotropic. are denoted as bi-anisotropic.
Intrinsic to magnetoelectric coupling of bi-isotropic media, are four material parameters interacting with the electric (E) and magnetic (H) field strengths, and electric (D) and magnetic (B) flux densities. These four material parameters are ε, µ, κ and χ or permittivity, permeability, strength of chirality, and the Tellegen parameter respectively. Furthermore, in this type of media, the material parameters do not vary with changes along a rotated coordinate system of measurements. In this way they are also defined as invariant or scalar.
The intrinsic magnetoelectric parameters, κ and χ, affect the phase of the wave. Furthermore, the effect of the chirality parameter is to split the refractive index. In isotropic media this results in wave propagation only if ε and µ have the same sign. In bi-isotropic media with χ assumed to be zero, and κ a non-zero value, different results are shown. Both a backward wave and a forward wave can occur. Alternatively, two forward waves or two backward waves can occur, depending on the strength of the chirality parameter.
When a metamaterial is constructed from chiral elements then it is considered to be a chiral metamaterial, and the effective parameter k will be non-zero. This is a potential source of confusion as within the metamaterial literature there are two conflicting uses of the terms left and right-handed. The first refers to one of the two circularly polarized waves which are the propagating modes in chiral media. The second relates to the triplet of electric field, magnetic field and Poynting vector which arise in negative refractive index media, which in most cases are not chiral.
Some of the earliest structures which may be considered metamaterials date back to Jagadish Chandra Bose who in 1898 researched substances with chiral properties and to studies by Karl Ferdinand Lindman on wave interaction with metallic helices as artificial chiral media in the early twentieth century. In the 1950s and 1960s, artificial dielectrics were studied for lightweight microwave antennas. Microwave radar absorbers moved into the research arena in the 1980s and 1990s as applications for artificial chiral media.
Wave propagation properties in chiral metamaterials demonstrate that negative refraction can be realized in chiral metamaterials with a strong chirality, with neither negative ε nor μ as a requirement.  This is because the refractive index of the medium has distinct values for the left and right, given by
It can be seen that a negative index will occur for one polarization if κ > √. In this case, it is not necessary that either or both εr and µr be negative for backward wave propagation.
History of metamaterials shares a common history with artificial dielectrics in microwave engineering, as it developed just after World War II. However, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 19th century. The history of metamaterials is essentially a history of developing certain types of manufactured materials, which interact at radio frequency, microwave and later, optical frequencies.
Below are applications of metamaterials (or types of metamaterials), which are at different stages of research. Metamaterial antennas (see below) are commercially available. The listed applications are briefly summarized, and linked to their respective main article. The main articles describe each type in more detail.
Terahertz radiation lies at the far end of the infrared band, just after the end of the microwave band.
Terahertz metamaterials are metamaterials which interact at terahertz frequencies. For research or applications of the terahertz range for metamaterials and other materials, the frequency range is usually defined as 0.1 to 10 THz. This corresponds to the millimeter and submillimeter wavelengths between 3 mm (EHF band) and 0.03 mm (long-wavelength edge of far-infrared light).
A Photonic metamaterial is an artificially fabricated, sub-wavelength, periodic structure, designed to interact with optical frequencies (mid-infrared). The sub-wavelength period distinguishes the photonic metamaterial from photonic band gap structures.
A tunable metamaterial is a metamaterial which has the capability to arbitrarily adjust frequency changes in the refractive index at will. A tunable metamaterial encompasses the development of expanding beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials.
Plasmonic metamaterials are negative index metamaterials that exploit surface plasmons, which are produced from the interaction of light with metal-dielectric materials. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating electromagnetic waves known as surface plasmon polaritons
Metamaterial antennas are a class of antennas which use metamaterials to improve the performance of the antenna systems. Applying metamaterials to increase performance of antennas has garnered much interest. Demonstrations have shown that metamaterials could enhance the radiated power of an antenna. Materials which can attain negative permeability could possibly allow for properties such as an electrically small antenna size, high directivity, and tunable operational frequency.
Link to section: Frequency selective surface (FSS) based metamaterials
FSS based metamaterials have become an alternative to the fixed frequency metamaterial. The former allow for optional changes of frequencies in a single medium (metamaterial), rather than the restrictive limitations of a fixed frequency response. Other applications are also being explored.
Metamaterials may also be fabricated which include some form of nonlinear media – materials which have properties which change with the power of the incident wave. Nonlinear media are essential for nonlinear optics. However most optical materials have a relatively weak nonlinear response, meaning that their properties only change by a small amount for large changes in the intensity of the electromagnetic field. Nonlinear metamaterials can overcome this limitation, since the local electromagnetic fields of the inclusions in the metamaterial can be much larger than the average value of the field. In addition, exotic properties such as a negative refractive index, open up opportunities to tailor the phase matching conditions, which must be satisfied in any nonlinear optical structure.
A metamaterial absorber manipulates the loss components of the complex effective parameters, permittivity and magnetic permeability of metamaterials, to create a high electromagnetic absorber. Loss components are often noted in applications of negative refractive index (photonic metamaterials, antenna systems metamaterials) or transformation optics (metamaterial cloaking, celestial mechanics), but often not utilized in these applications.
A superlens uses metamaterials to achieve resolution beyond the capabilities of ordinary lenses (beyond the diffraction limit). The diffraction limit is inherent in conventional optical devices or lenses.
Metamaterials are a basis for attempting to build a practical cloaking device. The proof of principle of a working invisibility cloak was demonstrated on October 19, 2006. Work continues to develop a practical cloaking device. Various theoretical models have been proposed and are being studied. A working, practical cloak is not yet available.
These are a type of metamaterial that uses different parameters to achieve a negative index of refraction in materials that are not electromagnetic. Furthermore, "a new design for elastic metamaterials that can behave either as liquids or solids over a limited frequency range may enable new applications based on the control of acoustic, elastic and seismic waves."  They are also called Mechanical Metamaterials.
Acoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research in electromagnetic metamaterials. Furthermore, with acoustic metamaterials, sonic waves can now be extended to the negative refraction domain.
Control of the various forms of sound waves is mostly accomplished through the bulk modulus β, mass density ρ, and Chirality. The bulk modulus and density are analogies of the electromagnetic parameters, permittivity and permeability, in electromagnetic metamaterials. Related to this is the mechanics of sound wave propagation in a lattice structure. Also materials have mass, and intrinsic degrees of stiffness. Together, these form a resonant system, and the mechanical (sonic) resonance may be excited by appropriate sonic frequencies (for example pulses at audio frequencies).
Artificial dielectrics came into use with the radar microwave technologies developed between the 1940s and 1970s. The term "artificial dielectrics" came into use because these are macroscopic analogues of naturally occurring dielectrics.
A split-ring resonator (SRR) is an artificially engineered material that delivers strong magnetic coupling for metamaterials. Also, see image at the beginning of this article.
METATOYS (METAmaTerial fOr raYs) differ from metamaterials in that instead of being composed of sub-wavelength structures, they are composed of structures larger than the wavelength of light, such as small arrays of prisms and lenses. A key difference between METATOYs and metamaterials is that METATOYs can operate over a broad band of frequencies, whereas metamaterials are usually severely limited in this respect.
John Pendry was the first to theorize a practical way to make a left-handed metamaterial. Left-handed in this context means a material in which the right-hand rule is not followed, allowing an electromagnetic wave to convey energy (have a group velocity) in the lode against its phase velocity. Pendry's initial idea was that metallic wires aligned along the direction of propagation could provide a metamaterial with negative permittivity (ε < 0). Note however that natural materials (such as ferroelectrics) were already known to exist with negative permittivity; the challenge was to construct a material which also showed negative permeability (µ < 0). In 1999 Pendry demonstrated that a split ring (C shape) with its axis placed along the direction of wave propagation could provide a negative permeability. In the same paper, he showed that a periodic array of wires and ring could give rise to a negative refractive index. A related negative-permeability particle, which was also proposed by Pendry, is the Swiss roll.
The analogy is as follows: All materials are made of atoms, which are dipoles. These dipoles modify the light velocity by a factor n (the refractive index). The ring and wire units play the role of atomic dipoles: the wire acts as a ferroelectric atom, while the ring acts as an inductor L and the open section as a capacitor C. The ring as a whole therefore acts as an LC circuit. When the electromagnetic field passes through the ring, an induced current is created and the generated field is perpendicular to the magnetic field of the light. The magnetic resonance results in a negative permeability; the index is negative as well. (The lens is not truly flat, since the capacitance of the structure imposes a slope for the electric induction.)
In peer reviewed journal articles (see References), there are several (mathematical) material models which describe frequency response in DNGs. One of these is the Lorentz model. This describes electron motion in terms of a driven-damped, harmonic oscillator. When the acceleration component of the Lorentz mathematical model is small compared to the other components of the equation, then the Debye relaxation model is applied. When the restoring force component is negligible, and the coupling coefficient is generally the plasma frequency, then the Drude model is applied. There are other component distinctions that call for the use of one of these models, depending on its polarity, or purpose.
For metamaterial consisting of three-dimensional composite of metal/non-metallic inclusions periodically/randomly embedded in a low permittivity matrix, it's usually modeled by analytical methods including mixing formulas and scattering-matrix based methods. In these methods, the particle is modeled by either an electric dipole, which is parallel to the applied electric field, or a pair of crossed electric and magnetic dipoles, which are parallel to the electric and magnetic fields, respectively, of the applied EM wave. These dipoles are the leading terms in the multipole series, and the only existing ones for a homogeneous sphere, whose polarizability can be easily obtained from the Mie scattering coefficients. In general, this procedure is known as the "point-dipole approximation", which is a good approximation for metamaterials consisting of composites of electrically small spheres. Such an approximation restricts the application of these methods to composites of spheres, however. Merits of these methods include low calculation cost and mathematical simplicity. 
The number of groups studying metamaterials is continuously increasing. For example, Duke University has initiated an umbrella organization researching metamaterials under the banner "Novel Electromagnetic Materials" and became a leading metamaterials research center. The center is a part of an international team, which also includes California Institute of Technology, Harvard University, UCLA, Max Planck Institute of Germany, and the FOM Institute of the Netherlands. In addition, there are currently six groups connected to this umbrella organization, which are conducting intense metamaterial research:
MURI stands for Multidisciplinary University Research Initiative. Tens of Universities and a few government organizations participate in the MURI program. A MURI Metamaterials web page can be found at UC Berkeley. A few other Universities which participate in MURI are UC Los Angeles, UC San Diego, Massachusetts Institute of Technology, and Imperial College in London, UK. The sponsors are Office of Naval Research (ONR) and the Defense Advanced Research Project Agency (DARPA).
The MURI program supports research by teams of research investigators that intersect more than one traditional science and engineering discipline in order to accelerate both research progress and transition of research results to application. Most MURI efforts involve researchers from multiple academic institutions and academic departments. Based on the proposals selected in the fiscal 2009, a total of 69 academic institutions are expected to participate in 41 research efforts.
The Virtual Institute for Artificial Electromagnetic Materials and Metamaterials ”Metamorphose VI AISBL” is a non-profit international association whose purposes are the research, the study and the promotion of artificial electromagnetic materials and metamaterials. Some of their stated main tasks are to spread excellence in this field, in particular, by organizing scientific conferences and creating specialized journals in this field; create and manage research programs in this field; activate and manage training programs (including PhD and training programs for students and industrial partners); and transfer new technology in this field to the European Industry.
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