Negative index metamaterial array configuration, which was constructed of copper
split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3 by 20×20 unit cells with overall dimensions of 10×100×100 mm.
[1][2]
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior.[3][4][5]
The primary research in metamaterials investigates materials with negative refractive index.[6][7][8] 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,[6] acoustic and seismic metamaterials are also areas of active research.[9][10]
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.[10][11][12][13][14]
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.[4]
Metamaterials have become a new subdiscipline within physics and electromagnetism (especially optics and photonics).[15][16][17]
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.[3][5][6]
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.[5][6]
For microwave radiation, the structures need only be on the order of several milimeters. 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.[5][6]
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.[18]
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.[citation needed]
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.[citation needed]
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.[19][20][21][22][23][24]
In 2007, one researcher[25] 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.[25]
A comparison of refraction in a left-handed metamaterial to that in a normal material
The greatest potential of metamaterials is the possibility to create a structure with a negative refractive index, since this property is not found in any non-synthetic material. 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 ε at visible wavelengths. A material having either (but not both) ε or µ negative is opaque to electromagnetic radiation (see surface plasmon for more details).
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 Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle n =\pm\sqrt{\epsilon_r\mu_r} . 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.
Video representing negative refraction of light at uniform planar interface.
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.[26] Metamaterials with negative n have numerous interesting properties:
- Snell's law (n1sinθ1 = n2sinθ2), but as n2 is negative, the rays will be refracted on the same side of the normal on entering the material.
- Cherenkov radiation points the other way.
- The time-averaged Poynting vector is antiparallel to phase velocity. However, for waves (energy) to propagate, a -µ must be paired with a -ε in order to satisfy the wave number dependence on the material parameters Failed to parse (Missing texvc executable; please see math/README to configure.): k = \omega\sqrt{\mu \epsilon}
.
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.[4]
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.[4][27]
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:[3][4][28]
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.[3]
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.[4]
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.[3][14]
To date, materials exhibiting a negative index of refraction have only been demonstrated as artificially constructed materials.[3][27][29]
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.[27]
- Epsilon negative media (ENG) – εr is negative while µr is positive.[3][27] Many plasmas exhibit this characteristic. For example noble metals such as gold or silver will exhibit this characteristic in the infrared and visible spectrums.
- Mu-negative media (MNG) – εr is positive while µr is negative.[3][27] A material, which called gyrotropic or gyromagnetic exhibits this characteristic. A gyrotropic material is a medium that has been altered by the presence of a quasistatic magnetic field. This results in the magneto-optic effect. A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a material, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect). Two gyrotropic materials with reversed rotation directions of the two principal polarizations are called optical isomers.
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.[30][31]
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.[32]
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.[33]
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.[34] Each unit of the prescribed periodic structure acts like large scale atoms.[3][34]
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.[3][4]
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."[3] 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.[3][4]
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.[3]
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[35]), are referred to as bi-anisotropic.[36][37] 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.[4]
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.[4]
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.[38] [39] This is because the refractive index of the medium has distinct values for the left and right, given by
Failed to parse (Missing texvc executable; please see math/README to configure.): n = \sqrt{\epsilon_r\mu_r} \pm \kappa
It can be seen that a negative index will occur for one polarization if κ > √εrµr. In this case, it is not necessary that either or both εr and µr be negative for backward wave propagation.[4]
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 before the start 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.[40][41]
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.[14][42][43] Applying metamaterials to increase performance of antennas has garnered much interest.[14] Demonstrations have shown that metamaterials could enhance the radiated power of an antenna.[14][44] Materials which can attain negative permeability could possibly allow for properties such as an electrically small antenna size, high directivity, and tunable operational frequency.[14]
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.[45]
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.[46][47]
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.[48][49][50][51][52][53]
These are 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." [54] They are also called Mechanical Metamaterials.
| Continuum mechanics |
 |
|
|
|
|
|
|
|
|
|
|
|
|
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.[9]
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).
Seismic metamaterials, are metamaterials which are designed to counteract the adverse effects of seismic waves on man-made structures, which exist on or near the surface of the earth.[10][55][56]
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.
Negative refraction is the name for an electromagnetic phenomenon where light rays are refracted at an interface in the reverse sense to that normally expected.
Left-handed materials were first described theoretically by Victor Veselago in 1967.[21]
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.[3] 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 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.[3]
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:[11]
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).[57]
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.[58]
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.[59][60]
-
-
-
- Academic journals
-
-
-
- Metamaterials books
- ^ Shelby, R. A.; Smith D.R.; Shultz S.; Nemat-Nasser S.C. (2001). "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial". Applied Physics Letters 78 (4): 489. Bibcode 2001ApPhL..78..489S. DOI:10.1063/1.1343489. http://people.ee.duke.edu/~drsmith/pubs_smith_group/Shelby_APL_(2001).pdf. [dead link]
- ^ Smith, D. R.; Padilla, WJ; Vier, DC; Nemat-Nasser, SC; Schultz, S (2000). "Composite Medium with Simultaneously Negative Permeability and Permittivity". Physical Review Letters 84 (18): 4184–7. Bibcode 2000PhRvL..84.4184S. DOI:10.1103/PhysRevLett.84.4184. PMID 10990641. http://people.ee.duke.edu/~drsmith/pubs_smith_group/Smith_PRL_84_4184_(2000).pdf.
- ^ a b c d e f g h i j k l m n o Engheta, Nader; Richard W. Ziolkowski (2006-06). Metamaterials: Physics and Engineering Explorations. Wiley & Sons. pp. xv, 3–30, 37, 143–150, 215–234, 240–256. ISBN 978-0-471-76102-0. http://books.google.com/?id=51e0UkEuBP4C.
- ^ a b c d e f g h i j k Zouhdi, Saïd; Ari Sihvola, Alexey P. Vinogradov (2008-12). Metamaterials and Plasmonics: Fundamentals, Modelling, Applications. New York: Springer-Verlag. pp. 3–10, Chap. 3, 106. ISBN 978-1-4020-9406-4. http://books.google.com/?id=OqRi4s_EskoC&pg=PA6.
- ^ a b c d Smith, David R. (2006-06-10). "What are Electromagnetic Metamaterials?". Novel Electromagnetic Materials. The research group of D.R. Smith. http://people.ee.duke.edu/~drsmith/about_metamaterials.html. Retrieved 2009-08-19.
- ^ a b c d e Shelby, RA; Smith, DR; Schultz, S; Smith D.R; Shultz S. (2001). "Experimental Verification of a Negative Index of Refraction". Science 292 (5514): 77–9. Bibcode 2001Sci...292...77S. DOI:10.1126/science.1058847. PMID 11292865.
- ^ Pendry, John B. (2004). "Negative Refraction". Contemporary Physics (Princeton University Press) 45 (3): 191–202. Bibcode 2004ConPh..45..191P. DOI:10.1080/00107510410001667434. ISBN 0-691-12347-0. http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/NegRef_submit.pdf. Retrieved 2009-08-26.
- ^ Veselago, V. G. (1968). "The electrodynamics of substances with simultaneously negative values of [permittivity] and [permeability]". Soviet Physics Uspekhi 10 (4): 509–514. Bibcode 1968SvPhU..10..509V. DOI:10.1070/PU1968v010n04ABEH003699.
- ^ a b Guenneau, Sébastien; Alexander Movchan, Gunnar Pétursson, and S. Anantha Ramakrishna (2007). "Acoustic metamaterials for sound focusing and confinement" (free download pdf). New Journal of Physics 9 (399): 1367–2630. Bibcode 2007NJPh....9..399G. DOI:10.1088/1367-2630/9/11/399.
- ^ a b c Brun, M.; S. Guenneau, and A.B. Movchan (2009-02-09). "Achieving control of in-plane elastic waves". Appl. Phys. Lett. 94 (61903): 1–7. arXiv:0812.0912. Bibcode 2009ApPhL..94f1903B. DOI:10.1063/1.3068491.
- ^ a b Smith, David R; Research group (2005-01-16). "Novel Electromagnetic Materials program". http://people.ee.duke.edu/~drsmith/collaborators.htm. Retrieved 2009-08-17.
- ^ Rainsford, Tamath J.; Samuel P. Mickan, and Derek Abbott (9 March 2005). "T-ray sensing applications: review of global developments". Proc. SPIE (Conference Location: Sydney, Australia 2004-12-13: The International Society for Optical Engineering) 5649 Smart Structures, Devices, and Systems II (Poster session): 826–838. DOI:10.1117/12.607746.
- ^ Cotton, Micheal G. (2003-12). "Applied Electromagnetics". 2003 Technical Progress Report (NITA – ITS) (Boulder, CO, USA: NITA – Institute for Telecommunication Sciences) Telecommunications Theory (3): 4–5. http://www.its.bldrdoc.gov/pub/ntia-rpt/tpr/2003/telecommunications_theory-03.pdf. Retrieved 2009-09-14.
- ^ a b c d e f Alici, Kamil Boratay; Özbay, Ekmel (2007). "Radiation properties of a split ring resonator and monopole composite". Physica status solidi (b) 244 (4): 1192. Bibcode 2007PSSBR.244.1192A. DOI:10.1002/pssb.200674505.
- ^ Hapgood, Fred; Grant, Andrew (From the April 2009 issue; published online 2009-03-10). "Metamaterial Revolution: The New Science of Making Anything Disappear" (Magazine article access for free. Four page article.). Discover Magazine: p. page 2. http://discovermagazine.com/2009/apr/10-metamaterial-revolution-new-science-making-anything-disappear. Retrieved 2010-03-04.
- ^ McDonald, Kim (2000-03-21). "UCSD Physicists Develop a New Class of Composite Material with 'Reverse' Physical Properties Never Before Seen". UCSD Science and Engineering. http://ucsdnews.ucsd.edu/newsrel/science/mccomposite.htm. Retrieved 2010-12-17.
- ^ Pendry, John B.; Smith, David R. (2006). "The Quest for the Superlens" (Free PDF downlaod). Scientific American 295: 60. DOI:10.1038/scientificamerican0706-60. http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/sciam-pendry-4a.pdf.
- ^ Sievenpiper, Dan et al. (1999-11). "High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band" (Free PDF download. Cited by 1,078). IEEE Transactions on Microwave Theory and Techniques 47 (11): 2059. Bibcode 1999ITMTT..47.2059S. DOI:10.1109/22.798001. http://www.rsl.ku.edu/~eecs501/Hi-Z_surfaces/Sievenpiper1999TMTTpp2059-2074.pdf. Retrieved 2009-11-11.
- ^ Kock, W. E. (1946). "Metal-Lens Antennas". IRE Proc. 34 (11): 828. DOI:10.1109/JRPROC.1946.232264.
- ^ Kock, W.E. (1948). "Metallic Delay Lenses". Bell. Sys. Tech. Jour. 27: 58–82.
- ^ a b Veselago, V. G. (1968 (Russian text 1967)). "The electrodynamics of substances with simultaneously negative values of ε and μ". Sov. Phys. Usp. 10 (4): 509–14. Bibcode 1968SvPhU..10..509V. DOI:10.1070/PU1968v010n04ABEH003699. http://ufn.ru/en/articles/1968/4/a/.
- ^ Caloz, C.; Chang, C.-C. and Itoh, T. (2001). "Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations". J. Appl. Phys. 90 (11): 11. Bibcode 2001JAP....90.5483C. DOI:10.1063/1.1408261. http://xlab.me.berkeley.edu/MURI/publications/publications_9.pdf.
- ^ Eleftheriades, G.V.; Iyer A.K.; and Kremer, P.C. (2002). "Planar Negative Refractive Index Media Using Periodically L-C Loaded Transmission Lines". IEEE Transactions on Microwave Theory and Techniques 50 (12): 2702–2712. Bibcode 2002ITMTT..50.2702E. DOI:10.1109/TMTT.2002.805197.
- ^ Caloz, C. and Itoh, T. (2002). "Application of the Transmission Line Theory of Left-handed (LH) Materials to the Realization of a Microstrip 'LH line'". IEEE Antennas and Propagation Society International Symposium 2: 412. DOI:10.1109/APS.2002.1016111. ISBN 0-7803-7330-8.
- ^ a b DOE / Ames Laboratory (2007-01-04). "Metamaterials found to work for visible light" (Costas Soukoulis discusses some metamaterials). HTML. http://eurekalert.org/pub_releases/2007-01/dl-mft010407.php?light. Retrieved 2009-11-07.
- ^ R. A. Depine and A. Lakhtakia (2004). "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity". Microwave and Optical Technology Letters 41 (4): 315. DOI:10.1002/mop.20127.
- ^ a b c d e Eleftheriades, George V.; Keith G. Balmain (2005). Negative-refraction metamaterials: fundamental principles and applications. Wiley, John & Sons. p. 340. ISBN 978-0-471-60146-3. http://books.google.com/?id=a4MiyF5_N7MC&pg=PA379.
- ^ Pendry, John B.; and David R. Smith (2004-06). "Reversing Light: Negative Refraction". Physics Today (American Institute of Physics) 57 (June 37): 2 of 9 (originally page 38 of pp. 37–45). http://esperia.iesl.forth.gr/~ppm/DALHM/publications/papers/PhysicsTodayv57p37.pdf. Retrieved 2009-09-27.
- ^ Alù, Andrea and; Nader Engheta (2004-01). "Guided Modes in a Waveguide Filled With a Pair of Single-Negative (SNG), Double-Negative (DNG), and/or Double-Positive (DPS) Layers" (Free PDF download. Cited by 123). IEEE Transactions on Microwave Theory and Techniques 52 (1): 199. Bibcode 2004ITMTT..52..199A. DOI:10.1109/TMTT.2003.821274. http://repository.upenn.edu/cgi/viewcontent.cgi?article=1001&context=ese_papers. Retrieved 2010-01-03.
- ^ Engheta, Nader; Richard W. Ziolkowski (2006-06) (added this reference on 2009-12-14.). Metamaterials: physics and engineering explorations. Wiley & Sons. pp. 211–221. ISBN 978-0-471-76102-0. http://books.google.com/?id=51e0UkEuBP4C.
- ^ Valentine, J et al. (2008). "Three-dimensional optical metamaterial with a negative refractive index". Nature 455 (7211): 376–9. Bibcode 2008Natur.455..376V. DOI:10.1038/nature07247. PMID 18690249.
- ^ Pendry, JB (2009-04-11). "Metamaterials Generate Novel Electromagnetic Properties" (This is a seminar – lecture series lasting one semster – fall 2009.). UC Berkeley Atomic Physics Seminar 290F Main. http://ultracold.physics.berkeley.edu/seminar/pmwiki/Main/MetamaterialsGenerateNovelElectromagneticProperties. Retrieved 2009-12-14.
- ^ Chappell, William leads the IDEA laboratory at Purdue University (2005). "Metamaterials". research in various technologies. https://engineering.purdue.edu/IDEAS/Metamaterials.html. Retrieved 2009-11-23.
- ^ a b Edited by Soukoulis, C. M. (2001-05). Photonic Crystals and Light Localization in the 21st Century (Proceedings of the NATO Advanced Study Institute on Photonic Crytals and Light Localization, Crete, Greece, June 18–30, 2000 ed.). London: Springer London, Limited. pp. xi. ISBN 0-7923-6948-3. http://books.google.com/?id=y8O7cfQl9ogC&pg=PP1.
- ^ Marques, Ricardo; Medina, Francisco; Rafii-El-Idrissi, Rachid (2002-04-04). "Role of bianisotropy in negative permeability and left-handed metamaterials" (Free PDF download of this article is linked to this reference.). Physical Review B 65 (14): 144440–1. Bibcode 2002PhRvB..65n4440M. DOI:10.1103/PhysRevB.65.144440. http://centro.us.es/gmicronda/Miembros/Ricardo/1-Role-of-bianisotropy.pdf. Retrieved 2009-10-20.
- ^ Rill, M. S. et al. (2008-12-22). "Negative-index bianisotropic photonic metamaterial fabricated by direct laser writing and silver shadow evaporation". Optics Letters 34 (1): 19–21. DOI:10.1364/OL.34.000019. PMID 19109626. http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-34-1-19.
- ^ Kriegler, C. E. et al. (submitted 2009-03-31 to be published 2010-04). "Bianisotropic photonic metamaterials" (download free PDF article.). IEEE journal of selected topics in quantum electronics 999 (2): 1–15. DOI:10.1109/JSTQE.2009.2020809. http://esperia.iesl.forth.gr/~ppm/PHOME/publications/IEEE_10_1109_2009.pdf. Retrieved 2009-10-20.
- ^ Wang, Bingnan et al. (2009-11). "Chiral metamaterials: simulations and experiments". J. Opt. A: Pure Appl. Opt. 11 (11): 114003 (10pp). Bibcode 2009JOptA..11k4003W. DOI:10.1088/1464-4258/11/11/114003. http://www.iop.org/EJ/article/1464-4258/11/11/114003/joa9_11_114003.pdf?request-id=61616caa-78a3-48cf-b811-b98a69c5c590. Retrieved 2009-12-24.
- ^ S. Tretyakov, A. Sihvola and L. Jylhä (2005). "Backward-wave regime and negative refraction in chiral composites". Photonics and Nanostructures – Fundamentals and Applications 3 (2–3): 107. arXiv:cond-mat/0509287. Bibcode 2005PhNan...3..107T. DOI:10.1016/j.photonics.2005.09.008.
- ^ <Please add first missing authors to populate metadata.> (2008-18). "Photonic Metamaterials". Encyclopedia of Laser Physics and Technology. I & II. Wiley-VCH Verlag. pp. 1. http://www.rp-photonics.com/photonic_metamaterials.html. Retrieved 2009-10-01.
- ^ Capolino, Filippo (2009-10). Applications of Metamaterials. Taylor & Francis, Inc.. pp. 29–1, 25–14, 22–1. ISBN 978-1-4200-5423-1. http://books.google.com/?id=8M0IqvcsHisC&pg=PT640. Retrieved 2009-10-01.
- ^ Enoch, Stefan; Tayeb, GéRard; Sabouroux, Pierre; Guérin, Nicolas; Vincent, Patrick (2002). "A Metamaterial for Directive Emission". Physical Review Letters 89 (21): 213902. Bibcode 2002PhRvL..89u3902E. DOI:10.1103/PhysRevLett.89.213902. PMID 12443413.
- ^ Siddiqui, O.F.; Mo Mojahedi; Eleftheriades, G.V. (2003). "Periodically loaded transmission line with effective negative refractive index and negative group velocity". IEEE Transactions on Antennas and Propagation 51 (10): 2619. Bibcode 2003ITAP...51.2619S. DOI:10.1109/TAP.2003.817556.
- ^ Wu, B.-I.; W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk and J. A. Kong (2005). "A Study of Using Metamaterials as Antenna Substrate to Ehance Gain". Progress in Electromagnetics Research (MIT, Cambridge, MA, USA: EMW Publishing) 51: 295–328. DOI:10.2528/PIER04070701. http://ceta.mit.edu/PIER/pier51/17.0407071.Wu.WPCGK.pdf. Retrieved 2009-09-23.
- ^ Capolino, Filippo (2009-10). "32". Theory and Phenomena of Metamaterials. Taylor & Francis. pp. 32–1. ISBN 978-1-4200-5425-5. http://books.google.com/?id=0PMnYo8hva8C&pg=PT546.
- ^ Pendry, J. B. (2000). "Negative Refraction Makes a Perfect Lens". Physical Review Letters 85 (18): 3966–9. Bibcode 2000PhRvL..85.3966P. DOI:10.1103/PhysRevLett.85.3966. PMID 11041972.
- ^ Fang, N.; Lee, H; Sun, C; Zhang, X (2005). "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens". Science 308 (5721): 534–7. Bibcode 2005Sci...308..534F. DOI:10.1126/science.1108759. PMID 15845849.
- ^ "First Demonstration of a Working Invisibility Cloak". Office of News & Communications Duke University. http://www.dukenews.duke.edu/2006/10/cloakdemo.html. Retrieved 2009-05-05.
- ^ Schurig, D. et al. (2006). "Metamaterial Electromagnetic Cloak at Microwave Frequencies". Science 314 (5801): 977–80. Bibcode 2006Sci...314..977S. DOI:10.1126/science.1133628. PMID 17053110.
- ^ "Experts test cloaking technology". BBC News. 2006-10-19. http://news.bbc.co.uk/1/hi/sci/tech/6064620.stm. Retrieved 2008-08-05.
- ^ "Engineers see progress in creating 'invisibility cloak'". http://www.purdue.edu/uns/x/2007a/070402ShalaevCloaking.html.
- ^ A. Alu and N. Engheta (2005). "Achieving transparency with plasmonic and metamaterial coatings". Phys. Rev. E 72: 016623. arXiv:cond-mat/0502336. Bibcode 2005PhRvE..72a6623A. DOI:10.1103/PhysRevE.72.016623.
- ^ Richard Merritt, "Next Generation Cloaking Device Demonstrated: Metamaterial renders object 'invisible'"
- ^ Page, John (2011). "Metamaterials: Neither solid nor liquid". Nature Materials 10 (8): 565–6. Bibcode 2011NatMa..10..565P. DOI:10.1038/nmat3084. PMID 21778996.
- ^ Johnson, R. Colin (2009-07-23). "Metamaterial cloak could render buildings 'invisible' to earthquakes". EETimes.com. http://www.eetimes.com/showArticle.jhtml?articleID=218600378. Retrieved 2009-09-09.
- ^ Barras, Colin (2009-06-26). "Invisibility cloak could hide buildings from quakes". New Scientist: p. 1. http://www.newscientist.com/article/dn17378-invisibility-cloak-could-hide-buildings-from-quakes.html#. Retrieved 2009-10-20.
- ^ MURI metamaterials, UC Berkely (2009). "Scalable and Reconfigurable Electromagnetic Metamaterials and Devices" (Link to web site). http://xlab.me.berkeley.edu/MURI/MURI.html. Retrieved 2009-12-08.
- ^ U.S. Department of Defense, Office of the Assistant Secretary of Defense (Public Affairs) (2009-05-08). "DoD Awards $260 Million in University Research Funding". DoD. http://www.defense.gov/releases/release.aspx?releaseid=12657. Retrieved 2009-12-08.
- ^ Tretyakov, Prof. Sergei; President of the Association; Dr. Vladmir Podlozny; Secretary General (2009-12-13). "Metamorphose" (See the "About" section of this web site for information about this organization.). Metamaterials research and development. © 2009 Metamorphose VI. http://www.metamorphose-vi.org/. Retrieved 2009-12-13.
- ^ de Baas, A. F.; and J. L. Vallés (2007-02-11). "Success stories in the Materials domain". Metamorphose (European Commission Directorate-General for Research. Directorate G – Industrial technologies. Unit G3 ‘Value – added Materials’.) Networks of Excellence Key for the future of EU research: 19. http://ec.europa.eu/research/industrial_technologies/pdf/noes-122007_en.pdf. Retrieved 2009-12-13.
-
-
- Educational pages on metamaterials:
-
-
- Internet portals:
-
-
- More articles and presentations:
