Last updated
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 20x20 unit cells with overall dimensions of 10 mm x 100 mm x 100 mm (0.39 in x 3.94 in x 3.94 in). Split-ring resonator array 10K sq nm.jpg
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 mm × 100 mm × 100 mm (0.39  in × 3.94 in × 3.94 in).

A metamaterial (from the Greek word μετά meta, meaning "beyond" and the Latin word materia, meaning "matter" or "material") is a material engineered to have a property that is not found in naturally occurring materials. [3] They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

Ancient Greek Version of the Greek language used from roughly the 9th century BCE to the 6th century CE

The ancient Greek language includes the forms of Greek used in Ancient Greece and the ancient world from around the 9th century BCE to the 6th century CE. It is often roughly divided into the Archaic period, Classical period, and Hellenistic period. It is antedated in the second millennium BCE by Mycenaean Greek and succeeded by Medieval Greek.

Meta is a prefix used in English to indicate a concept that is an abstraction behind another concept, used to complete or add to the latter.

Latin Indo-European language of the Italic family

Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets and ultimately from the Phoenician alphabet.


Appropriately designed metamaterials can affect waves of electromagnetic radiation or sound in a manner not observed in bulk materials. [4] [5] [6] Those that exhibit a negative index of refraction for particular wavelengths have attracted significant research. [7] [8] [9] These materials are known as negative-index metamaterials.

Electromagnetic radiation form of energy emitted and absorbed by charged particles, which exhibits wave-like behavior as it travels through space

In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

Sound mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing; pressure wave, generated by vibrating structure

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.

Negative-index metamaterial

Negative-index metamaterial or negative-index material (NIM) is a metamaterial whose refractive index for an electromagnetic wave has a negative value over some frequency range.

Potential applications of metamaterials are diverse and include optical filters, medical devices, remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, crowd control, radomes, high-frequency battlefield communication and lenses for high-gain antennas, improving ultrasonic sensors, and even shielding structures from earthquakes. [10] [11] [12] [13] Metamaterials offer the potential to create superlenses. Such a lens could allow imaging below the diffraction limit that is the minimum resolution that can be achieved by conventional glass lenses. A form of 'invisibility' was demonstrated using gradient-index materials. Acoustic and seismic metamaterials are also research areas. [10] [14]

Optical filter device that selectively transmits light of certain wavelengths

An optical filter is a device that selectively transmits light of different wavelengths, usually implemented as a glass plane or plastic device in the optical path, which are either dyed in the bulk or have interference coatings. The optical properties of filters are completely described by their frequency response, which specifies how the magnitude and phase of each frequency component of an incoming signal is modified by the filter.

Medical device Equipment designed to aid in the diagnosis, monitoring or treatment of medical conditions

A medical device is any device intended to be used for medical purposes. Thus what differentiates a medical device from an everyday device is its intended use. Medical devices benefit patients by helping health care providers diagnose and treat patients and helping patients overcome sickness or disease, improving their quality of life. Significant potential for hazards are inherent when using a device for medical purposes and thus medical devices must be proved safe and effective with reasonable assurance before regulating governments allow marketing of the device in their country. As a general rule, as the associated risk of the device increases the amount of testing required to establish safety and efficacy also increases. Further, as associated risk increases the potential benefit to the patient must also increase.

Aerospace engineering branch of engineering

Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is similar, but deals with the electronics side of aerospace engineering.

Metamaterial research is interdisciplinary and involves such fields as electrical engineering, electromagnetics, classical optics, solid state physics, microwave and antenna engineering, optoelectronics, material sciences, nanoscience and semiconductor engineering. [5]

Electrical engineering Field of engineering that deals with electricity

Electrical engineering is a technical discipline concerned with the study, design and application of equipment, devices and systems which use electricity, electronics, and electromagnetism. It emerged as an identified activity in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electrical power generation, distribution and use.

Electromagnetism Branch of science concerned with the phenomena of electricity and magnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions in nature, together with the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Optics The branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.


Explorations of artificial materials for manipulating electromagnetic waves began at the end of the 19th century. Some of the earliest structures that may be considered metamaterials were studied by Jagadish Chandra Bose, who in 1898 researched substances with chiral properties. Karl Ferdinand Lindman studied wave interaction with metallic helices as artificial chiral media in the early twentieth century.

Jagadish Chandra Bose Bengali polymath, physicist, biologist, botanist and archaeologist

Sir Jagadish Chandra Bose (;, IPA: [dʒɔɡodiʃ tʃɔndro bosu]; 30 November 1858 – 23 November 1937), also spelled Jagdish and Jagadis, was a polymath, physicist, biologist, biophysicist, botanist and archaeologist, and an early writer of science fiction. He pioneered the investigation of radio and microwave optics, made significant contributions to plant science, and laid the foundations of experimental science in the Indian subcontinent. IEEE named him one of the fathers of radio science. Bose is considered the father of Bengali science fiction, and also invented the crescograph, a device for measuring the growth of plants. A crater on the moon has been named in his honour.

Dispersion (optics) Dependence of phase velocity on frequency

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

Chirality (chemistry) geometric property of some molecules and ions

Chirality is a geometric property of some molecules and ions. A chiral molecule/ion is non-superposable on its mirror image. The presence of an asymmetric carbon center is one of several structural features that induce chirality in organic and inorganic molecules. The term chirality is derived from the Ancient Greek word for hand, χείρ (cheir).

Winston E. Kock developed materials that had similar characteristics to metamaterials in the late 1940s. In the 1950s and 1960s, artificial dielectrics were studied for lightweight microwave antennas. Microwave radar absorbers were researched in the 1980s and 1990s as applications for artificial chiral media. [5]

Winston E. Kock American electrical engineer

Winston Kock (1909–1982) was the first Director of NASA Electronics Research Center in Cambridge, Massachusetts, from September 1, 1964, to October 1, 1966. The Center was created for multidisciplinary scientific research, its proximity to certain colleges, its proximity to a local U.S. Air Force research facility, and was perceived as part of the nation's cold war effort.

Dielectric electrically poorly conducting or non-conducting, non-metallic substance of which charge carriers are generally not free to move

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

Microwave antenna

A microwave antenna is a physical transmission device used to broadcast microwave transmissions between two or more locations. In addition to broadcasting, antennas are also used in radar, radio astronomy and electronic warfare.

Negative-index materials were first described theoretically by Victor Veselago in 1967. [15] He proved that such materials could transmit light. He showed that the phase velocity could be made anti-parallel to the direction of Poynting vector. This is contrary to wave propagation in naturally occurring materials. [9]

John Pendry was the first to identify a practical way to make a left-handed metamaterial, a material in which the right-hand rule is not followed. [15] Such a material allows an electromagnetic wave to convey energy (have a group velocity) against its phase velocity. Pendry's idea was that metallic wires aligned along the direction of a wave could provide negative permittivity (dielectric function ε < 0). Natural materials (such as ferroelectrics) display negative permittivity; the challenge was achieving 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 do so. In the same paper, he showed that a periodic array of wires and rings could give rise to a negative refractive index. Pendry also proposed a related negative-permeability design, the Swiss roll.

In 2000, Smith et al. reported the experimental demonstration of functioning electromagnetic metamaterials by horizontally stacking, periodically, split-ring resonators and thin wire structures. A method was provided in 2002 to realize negative-index metamaterials using artificial lumped-element loaded transmission lines in microstrip technology. In 2003, complex (both real and imaginary parts of) negative refractive index [16] and imaging by flat lens [17] using left handed metamaterials were demonstrated. By 2007, experiments that involved negative refractive index had been conducted by many groups. [4] [13] At microwave frequencies, the first, imperfect invisibility cloak was realized in 2006. [18] [19] [20] [21] [22]

Electromagnetic metamaterials

An electromagnetic metamaterial affects electromagnetic waves that impinge on or interact with its structural features, which are smaller than the wavelength. To behave as a homogeneous material accurately described by an effective refractive index, its features must be much smaller than the wavelength.[ citation needed ]

For microwave radiation, the features are on the order of millimeters. Microwave frequency metamaterials are usually constructed as arrays of electrically conductive elements (such as loops of wire) that have suitable inductive and capacitive characteristics. One microwave metamaterial uses the split-ring resonator. [6] [7]

Photonic metamaterials, nanometer scale, manipulate light at optical frequencies. To date, subwavelength structures have shown only a few, questionable, results at visible wavelengths. [6] [7] Photonic crystals and frequency-selective surfaces such as diffraction gratings, dielectric mirrors and optical coatings exhibit 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, material structures such as photonic crystals are effective in the visible light spectrum. The middle of the visible spectrum has a wavelength of approximately 560 nm (for sunlight). Photonic crystal structures are generally half this size or smaller, that is <280 nm. [ citation needed ]

Plasmonic metamaterials utilize surface plasmons, which are packets of electrical charge that collectively oscillate at the surfaces of metals at optical frequencies.

Frequency selective surfaces (FSS) can exhibit subwavelength characteristics and are known variously as artificial magnetic conductors (AMC) or High Impedance Surfaces (HIS). FSS display inductive and capacitive characteristics that are directly related to their subwavelength structure. [23]

Negative refractive index

A comparison of refraction in a left-handed metamaterial to that in a normal material Metarefraction.svg
A comparison of refraction in a left-handed metamaterial to that in a normal material

Almost all materials encountered in optics, such as glass or water, have positive values for both permittivity ε and permeability µ. However, metals such as silver and gold have negative permittivity at shorter wavelengths. A material such as a surface plasmon that has either (but not both) ε or µ negative is often opaque to electromagnetic radiation. However, anisotropic materials with only negative permittivity can produce negative refraction due to chirality.[ citation needed ]

Although the optical properties of a transparent material are fully specified by the parameters and , refractive index n is often used in practice, which can be determined from . All known non-metamaterial transparent materials possess positive and . By convention the positive square root is used for n.

However, some engineered metamaterials have and . Because the product is positive, n is real. Under such circumstances, it is necessary to take the negative square root for n.

Video representing negative refraction of light at uniform planar interface.

The foregoing considerations are simplistic for actual materials, which must have complex-valued and . The real parts of both and do not have to be negative for a passive material to display negative refraction. [24] [25] Metamaterials with negative n have numerous interesting properties: [5] [26]

Negative index of refraction derives mathematically from the vector triplet E, H and k. [5]

For plane waves propagating in electromagnetic metamaterials, the electric field, magnetic field and wave vector follow a left-hand rule, the reverse of the behavior of conventional optical materials.


Electromagnetic metamaterials are divided into different classes, as follows: [4] [15] [5] [27]

Negative index

In negative-index metamaterials (NIM), both permittivity and permeability are negative, resulting in a negative index of refraction. [15] These are also known as double negative metamaterials or double negative materials (DNG). Other terms for NIMs include "left-handed media", "media with a negative refractive index", and "backward-wave media". [4]

In optical materials, if both permittivity ε and permeability µ are positive, wave propagation travels in the forward direction. If both ε and µ are negative, a backward wave is produced. If ε and µ have different polarities, waves do not propagate.

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. [5]

To date, only metamaterials exhibit a negative index of refraction. [4] [26] [28]

Single negative

Single negative (SNG) metamaterials have either negative relative permittivity (εr) or negative relative permeability (µr), but not both. [15] They act as metamaterials when combined with a different, complementary SNG, jointly acting as a DNG.

Epsilon negative media (ENG) display a negative εr while µr is positive. [4] [26] [15] Many plasmas exhibit this characteristic. For example, noble metals such as gold or silver are ENG in the infrared and visible spectrums.

Mu-negative media (MNG) display a positive εr and negative µr. [4] [26] [15] Gyrotropic or gyromagnetic materials exhibit this characteristic. A gyrotropic material is one that has been altered by the presence of a quasistatic magnetic field, enabling a magneto-optic effect.[ citation needed ] A magneto-optic effect is a phenomenon in which an electromagnetic wave propagates through such a medium. In such a material, left- and right-rotating elliptical polarizations can propagate at different speeds. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the polarization plane can be rotated, forming a Faraday rotator. The results of such a reflection 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.

Joining a slab of ENG material and slab of MNG material resulted in 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, are a function of frequency. [26]


Electromagnetic bandgap metamaterials (EBG or EBM) control light propagation. This is accomplished either with photonic crystals (PC) or left-handed materials (LHM). PCs can prohibit light propagation altogether. Both classes can allow light to propagate in specific, designed directions and both can be designed with bandgaps at desired frequencies. [29] [30] The period size of EBGs is an appreciable fraction of the wavelength, creating constructive and destructive interference.

PC are distinguished from sub-wavelength structures, such as tunable metamaterials, because the PC derives its properties from its bandgap characteristics. PCs are sized to match the wavelength of light, versus other metamaterials that expose sub-wavelength structure. Furthermore, PCs function by diffracting light. In contrast, metamaterial does not use diffraction. [31]

PCs have periodic inclusions that inhibit wave propagation due to the inclusions' destructive interference from scattering. The photonic bandgap property of PCs makes them the electromagnetic analog of electronic semi-conductor crystals. [32]

EBGs have the goal of creating high quality, low loss, periodic, dielectric structures. An EBG affects photons in the same way semiconductor materials affect electrons. PCs are the perfect bandgap material, because they allow no light propagation. [33] Each unit of the prescribed periodic structure acts like one atom, albeit of a much larger size. [4] [33]

EBGs are designed to prevent the propagation of an allocated bandwidth of frequencies, for certain arrival angles and polarizations. Various geometries and structures have been proposed to fabricate EBG's special properties. In practice it is impossible to build a flawless EBG device. [4] [5]

EBGs have been manufactured for frequencies ranging from a few gigahertz (GHz) to a few terahertz (THz), radio, microwave and mid-infrared frequency regions. EBG application developments include a transmission line, woodpiles made of square dielectric bars and several different types of low gain antennas. [4] [5]

Double positive medium

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 combine DPS, ENG and MNG properties. [4] [15]

Bi-isotropic and bianisotropic

Categorizing metamaterials into double or single negative, or double positive, normally assumes that the metamaterial has independent electric and magnetic responses described by ε and µ. However, in many cases, the electric field causes magnetic polarization, while the magnetic field induces electrical polarization, known as magnetoelectric coupling. Such media are denoted as bi-isotropic. Media that exhibit magnetoelectric coupling and that are anisotropic (which is the case for many metamaterial structures [34] ), are referred to as bi-anisotropic. [35] [36]

Four material parameters are intrinsic to magnetoelectric coupling of bi-isotropic media. They are the electric (E) and magnetic (H) field strengths, and electric (D) and magnetic (B) flux densities. These parameters are ε, µ, κ and χ or permittivity, permeability, strength of chirality, and the Tellegen parameter respectively. In this type of media, material parameters do not vary with changes along a rotated coordinate system of measurements. In this sense they are invariant or scalar. [5]

The intrinsic magnetoelectric parameters, κ and χ, affect the phase of the wave. 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 appear. Either a backward wave or a forward wave can occur. Alternatively, two forward waves or two backward waves can occur, depending on the strength of the chirality parameter.

In the general case, the constitutive relations for bi-anisotropic materials read where and are the permittivity and the permeability tensors, respectively, whereas and are the two magneto-electric tensors. If the medium is reciprocal, permittivity and permeability are symmetric tensors, and , where is the chiral tensor describing chiral electromagnetic and reciprocal magneto-electric response. The chiral tensor can be expressed as , where is the trace of , I is the identity matrix, N is a symmetric trace-free tensor, and J is an antisymmetric tensor. Such decomposition allows us to classify the reciprocal bianisotropic response and we can identify the following three main classes: (i) chiral media (), (ii) pseudochiral media (), (iii) omega media (). Generally the chiral and/or bianisotropic electromagnetic response is a consequence of 3D geometrical chirality: 3D chiral metamaterials are composed by embedding 3D chiral structures in a host medium and they show chirality-related polarization effects such as optical activity and circular dichroism. The concept of 2D chirality also exists and a planar object is said to be chiral if it cannot be superposed onto its mirror image unless it is lifted from the plane. On the other hand, bianisotropic response can arise from geometrical achiral structures possessing neither 2D nor 3D intrinsic chirality. Plum et al. [37] investigated extrinsic chiral metamaterials where the magneto-electric coupling results from the geometric chirality of the whole structure and the effect is driven by the radiation wave vector contributing to the overall chiral asymmetry (extrinsic electromagnetic chiralilty). Rizza et al. [38] suggested 1D chiral metamaterials where the effective chiral tensor is not vanishing if the system is geometrically one-dimensional chiral (the mirror image of the entire structure cannot be superposed onto it by using translations without rotations).


Chiral metamaterials are constructed from chiral materials in which the effective parameter k is non-zero. This is a potential source of confusion as the metamaterial literature includes two conflicting uses of the terms left- and right-handed. The first refers to one of the two circularly polarized waves that are the propagating modes in chiral media. The second relates to the triplet of electric field, magnetic field and Poynting vector that arise in negative refractive index media, which in most cases are not chiral.

Wave propagation properties in chiral metamaterials demonstrate that negative refraction can be realized in metamaterials with a strong chirality and positive ε and μ. [39] [40] This is because the refractive index has distinct values for left and right, given by

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. [5]

FSS based

Frequency selective surface-based metamaterials block signals in one waveband and pass those at another waveband. They have become an alternative to fixed frequency metamaterials. They allow for optional changes of frequencies in a single medium, rather than the restrictive limitations of a fixed frequency response. [41]

Other types


These metamaterials use 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." [42] They are also called mechanical metamaterials.[ citation needed ]


Acoustic metamaterials control, direct and manipulate sound in the form of sonic, infrasonic or ultrasonic waves in gases, liquids and solids. As with electromagnetic waves, sonic waves can exhibit negative refraction. [14]

Control of sound waves is mostly accomplished through the bulk modulus β, mass density ρ and chirality. The bulk modulus and density are analogs of 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 audible pulses).


Structural metamaterials provide properties such as crushability and light weight. Using projection micro-stereolithography, microlattices can be created using forms much like trusses and girders. Materials four orders of magnitude stiffer than conventional aerogel, but with the same density have been created. Such materials can withstand a load of at least 160,000 times their own weight by over-constraining the materials. [43] [44]

A ceramic nanotruss metamaterial can be flattened and revert to its original state. [45]


Metamaterials may be fabricated that include some form of nonlinear media, whose properties change with the power of the incident wave. Nonlinear media are essential for nonlinear optics. Most optical materials have a relatively weak response, meaning that their properties change by only a small amount for large changes in the intensity of the electromagnetic field. The local electromagnetic fields of the inclusions in nonlinear metamaterials can be much larger than the average value of the field. Besides, remarkable nonlinear effects have been predicted and observed if the metamaterial effective dielectric permittivity is very small (epsilon-near-zero media). [46] [47] [48] In addition, exotic properties such as a negative refractive index, create opportunities to tailor the phase matching conditions that must be satisfied in any nonlinear optical structure.

Hall metamaterials

In 2009, Marc Briane and Graeme Milton [49] proved mathematically that one can in principle invert the sign of a 3 materials based composite in 3D made out of only positive or negative sign Hall coefficient materials. Later in 2015 Muamer Kadic et al. [50] showed that a simple perforation of isotropic material can lead to its change of sign of the Hall coefficient. This theoretical claim was finally experimentally demonstrated by Christian Kern et al. [51]

In 2015, it was also demonstrated by Christian Kern et al. that an anisotropic perforation of a single material can lead to a yet more unusual effect namely the parallel Hall effect. [52] This means that the induced electric field inside a conducting media is no longer orthogonal to the current and the magnetic field but is actually parallel to the latest.

Thermo-electric metamaterials

Frequency bands


Terahertz metamaterials interact at terahertz frequencies, usually defined as 0.1 to 10 THz. Terahertz radiation lies at the far end of the infrared band, just after the end of the microwave band. This corresponds to millimeter and submillimeter wavelengths between the 3 mm (EHF band) and 0.03 mm (long-wavelength edge of far-infrared light).


Photonic metamaterial interact with optical frequencies (mid-infrared). The sub-wavelength period distinguishes them from photonic band gap structures. [53] [54]


Tunable metamaterials allow arbitrary adjustments to frequency changes in the refractive index. A tunable metamaterial expands beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials.


Plasmonic metamaterials exploit surface plasmons, which are produced from the interaction of light with metal-dielectrics. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating electromagnetic waves known as surface plasmon polaritons.


Metamaterials are under consideration for many applications. [55] Metamaterial antennas are commercially available.

In 2007, one researcher stated that for metamaterial applications to be realized, energy loss must be reduced, materials must be extended into three-dimensional isotropic materials and production techniques must be industrialized. [56]


Metamaterial antennas are a class of antennas that use metamaterials to improve performance. [13] [15] [57] [58] Demonstrations showed that metamaterials could enhance an antenna's radiated power. [13] [59] Materials that can attain negative permeability allow for properties such as small antenna size, high directivity and tunable frequency. [13] [15]


A metamaterial absorber manipulates the loss components of metamaterials' permittivity and magnetic permeability, to absorb large amounts of electromagnetic radiation. This is a useful feature for photodetection [60] [61] and solar photovoltaic applications. [62] Loss components are also relevant in applications of negative refractive index (photonic metamaterials, antenna systems) or transformation optics (metamaterial cloaking, celestial mechanics), but often are not utilized in these applications.


A superlens is a two or three-dimensional device that uses metamaterials, usually with negative refraction properties, to achieve resolution beyond the diffraction limit (ideally, infinite resolution). Such a behaviour is enabled by the capability of double-negative materials to yield negative phase velocity. The diffraction limit is inherent in conventional optical devices or lenses. [63] [64]

Cloaking devices

Metamaterials are a potential basis for a practical cloaking device. The proof of principle was demonstrated on October 19, 2006. No practical cloaks are publicly known to exist. [65] [66] [67] [68] [69] [70]

RCS (Radar Cross Section) reducing metamaterials

Conventionally, the RCS has been reduced either by Radar absorbent material (RAM) or by purpose shaping of the targets such that the scattered energy can be redirected away from the source. While RAMs have narrow frequency band functionality, purpose shaping limits the aerodynamic performance of the target. More recently, metamaterials or metasurfaces are synthesized that can redirect the scattered energy away from the source using either array theory [71] [72] [73] or generalized Snell's law. [74] [75] This has led to aerodynamically favorable shapes for the targets with the reduced RCS.

Seismic protection

Seismic metamaterials counteract the adverse effects of seismic waves on man-made structures. [10] [76] [77]

Sound filtering

Metamaterials textured with nanoscale wrinkles could control sound or light signals, such as changing a material's color or improving ultrasound resolution. Uses include nondestructive material testing, medical diagnostics and sound suppression. The materials can be made through a high-precision, multi-layer deposition process. The thickness of each layer can be controlled within a fraction of a wavelength. The material is then compressed, creating precise wrinkles whose spacing can cause scattering of selected frequencies. [78] [79]

Theoretical models

All materials are made of atoms, which are dipoles. These dipoles modify light velocity by a factor n (the refractive index). In a split ring resonator the ring and wire units act as atomic dipoles: the wire acts as a ferroelectric atom, while the ring acts as an inductor L, while the open section acts as a capacitor C. The ring as a whole acts as an LC circuit. When the electromagnetic field passes through the ring, an induced current is created. The generated field is perpendicular to the light's magnetic field. The magnetic resonance results in a negative permeability; the refraction index is negative as well. (The lens is not truly flat, since the structure's capacitance imposes a slope for the electric induction.)

Several (mathematical) material models frequency response in DNGs. One of these is the Lorentz model, which describes electron motion in terms of a driven-damped, harmonic oscillator. The Debye relaxation model applies when the acceleration component of the Lorentz mathematical model is small compared to the other components of the equation. The Drude model applies when the restoring force component is negligible and the coupling coefficient is generally the plasma frequency. Other component distinctions call for the use of one of these models, depending on its polarity or purpose. [4]

Three-dimensional composites of metal/non-metallic inclusions periodically/randomly embedded in a low permittivity matrix are usually modeled by analytical methods, including mixing formulas and scattering-matrix based methods. The particle is modeled by either an electric dipole parallel to the electric field or a pair of crossed electric and magnetic dipoles parallel to the electric and magnetic fields, respectively, of the applied wave. These dipoles are the leading terms in the multipole series. They are 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. Merits of these methods include low calculation cost and mathematical simplicity. [80] [81]

Other first principles techniques for analyzing triply-periodic electromagnetic media may be found in Computing photonic band structure

Institutional networks


The Multidisciplinary University Research Initiative (MURI) encompasses dozens of Universities and a few government organizations. Participating universities include UC Berkeley, UC Los Angeles, UC San Diego, Massachusetts Institute of Technology, and Imperial College in London. The sponsors are Office of Naval Research and the Defense Advanced Research Project Agency. [82]

MURI supports research that intersects more than one traditional science and engineering discipline to accelerate both research and translation to applications. As of 2009, 69 academic institutions were expected to participate in 41 research efforts. [83]


The Virtual Institute for Artificial Electromagnetic Materials and Metamaterials "Metamorphose VI AISBL" is an international association to promote artificial electromagnetic materials and metamaterials. It organizes scientific conferences, supports specialized journals, creates and manages research programs, provides training programs (including PhD and training programs for industrial partners); and technology transfer to European Industry. [84] [85]

See also

Related Research Articles

Refractive index dimensionless number that describes how fast light propagates through the material

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light travels through the material. It is defined as

Relative permittivity

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the vacuum permittivity.

An optical medium is material through which electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an intrinsic impedance, given by

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. Such an effect can be obtained using a metamaterial which has been designed to achieve a negative value for both (electric) permittivity ε and (magnetic) permeability μ, as in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.

Victor Veselago Russian physicist

Victor Georgievich Veselago was a Soviet/Russian physicist. In 1967, he was the first to publish a theoretical analysis of materials with negative permittivity, ε, and permeability, μ.

A superlens, or super lens, is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is a feature of conventional lenses and microscopes that limits the fineness of their resolution. Many lens designs have been proposed that go beyond the diffraction limit in some way, but constraints and obstacles face each of them.

Split-ring resonator

A split-ring resonator (SRR) is an artificially produced structure common to metamaterials. Their purpose is to produce the desired magnetic susceptibility in various types of metamaterials up to 200 terahertz. These media create the necessary strong magnetic coupling to an applied electromagnetic field, not otherwise available in conventional materials. For example, an effect such as negative permeability is produced with a periodic array of split ring resonators.

Terahertz metamaterial

A terahertz metamaterial is a class of composite metamaterials designed to interact at terahertz (THz) frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz.

Metamaterial antenna

Metamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space. However, this class of antenna incorporates metamaterials, which are materials engineered with novel, often microscopic, structures to produce unusual physical properties. Antenna designs incorporating metamaterials can step-up the antenna's radiated power.

An acoustic metamaterial is a material designed to control, direct, and manipulate sound waves as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research in negative index material. Furthermore, with acoustic metamaterials, controlling sonic waves can now be extended to the negative refraction domain.

Tunable metamaterial

A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capability to determine whether the EM wave is transmitted, reflected, or absorbed. In general, the lattice structure of the tunable metamaterial is adjustable in real time, making it possible to reconfigure a metamaterial device during operation. It encompasses developments beyond the bandwidth limitations in left-handed materials by constructing various types of metamaterials. The ongoing research in this domain includes electromagnetic materials that are very meta which mean good and has a band gap metamaterials (EBG), also known as photonic band gap (PBG), and negative refractive index material (NIM).

Photonic metamaterial

A photonic metamaterial (PM), also known as an optical metamaterial, is a type of electromagnetic metamaterial, that interacts with light, covering terahertz (THz), infrared (IR) or visible wavelengths. The materials employ a periodic, cellular structure.

A seismic metamaterial, is a metamaterial that is designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth. Current designs of seismic metamaterials utilize configurations of boreholes, trees or proposed underground resonators to act as a large scale material. Experiments have observed both reflections and bandgap attenuation from artificially induced seismic waves. These are the first experiments to verify that seismic metamaterials can be measured for frequencies below 100 Hz, where damage from Rayleigh waves is the most harmful to artificial structures.

A nonlinear metamaterial is an artificially constructed material that can exhibit properties not found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and material permeability. The product of the permittivity and permeability results in the refractive index. Unlike natural materials, nonlinear metamaterials can produce a negative refractive index. These can also produce a more pronounced nonlinear response than naturally occurring materials.

Metamaterial cloaking

Metamaterial cloaking is the usage of metamaterials in an invisibility cloak. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the propagation and transmission of specified parts of the light spectrum and demonstrate the potential to render an object seemingly invisible. Metamaterial cloaking, based on transformation optics, describes the process of shielding something from view by controlling electromagnetic radiation. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.

A metamaterial absorber is a type of metamaterial intended to efficiently absorb electromagnetic radiation such as light. Furthermore, metamaterials are an advance in materials science. Hence, those metamaterials that are designed to be absorbers offer benefits over conventional absorbers such as further miniaturization, wider adaptability, and increased effectiveness. Intended applications for the metamaterial absorber include emitters, photodetectors, sensors, spatial light modulators, infrared camouflage, wireless communication, and use in solar photovoltaics and thermophotovoltaics.

History of metamaterials

The history of metamaterials begins with artificial dielectrics in microwave engineering as it developed just after World War II. Yet, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 19th century. Hence, 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.

In the physics of continuous media, spatial dispersion is a phenomenon where material parameters such as permittivity or conductivity have dependence on wavevector. Normally, such a dependence is assumed to be absent for simplicity, however spatial dispersion exists to varying degrees in all materials.

Sergei Tretyakov (scientist) Russian scientist

Sergei Tretyakov is a Russian-Finnish scientist, focused in electromagnetic field theory, complex media electromagnetics and microwave engineering. He is currently a professor at Department of Electronics and Nanoengineering, Aalto University, Finland. His main research area in recent years is metamaterials and metasurfaces from fundamentals to applications. He was the president of the European Virtual Institute for Artificial Electromagnetic Materials and Metamaterials and general chair of the Metamaterials Congresses from 2007 to 2013. He is a fellow/member of many scientific associations such as IEEE, URSI, the Electromagnetics Academy, and OSA. He is also an Honorary Doctor of Francisk Skorina Gomel State University.


  1. Shelby, R. A.; Smith D.R.; Shultz S.; Nemat-Nasser S.C. (2001). "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial" (PDF). Applied Physics Letters. 78 (4): 489. Bibcode:2001ApPhL..78..489S. doi:10.1063/1.1343489. Archived from the original (PDF) on June 18, 2010.
  2. Smith, D. R.; Padilla, WJ; Vier, DC; Nemat-Nasser, SC; Schultz, S (2000). "Composite Medium with Simultaneously Negative Permeability and Permittivity" (PDF). Physical Review Letters. 84 (18): 4184–87. Bibcode:2000PhRvL..84.4184S. doi:10.1103/PhysRevLett.84.4184. PMID   10990641. Archived from the original (PDF) on June 18, 2010.
  3. Kshetrimayum, R. S. (2004). "A Brief Intro to Metamaterials". IEEE Potentials. 23 (5): 44–46. doi:10.1109/mp.2005.1368916.
  4. 1 2 3 4 5 6 7 8 9 10 11 12 Engheta, Nader; Richard W. Ziolkowski (June 2006). Metamaterials: Physics and Engineering Explorations. Wiley & Sons. pp. xv, 3–30, 37, 143–50, 215–34, 240–56. ISBN   978-0-471-76102-0.
  5. 1 2 3 4 5 6 7 8 9 10 11 Zouhdi, Saïd; Ari Sihvola; Alexey P. Vinogradov (December 2008). Metamaterials and Plasmonics: Fundamentals, Modelling, Applications. New York: Springer-Verlag. pp. 3–10, Chap. 3, 106. ISBN   978-1-4020-9406-4.
  6. 1 2 3 Smith, David R. (2006-06-10). "What are Electromagnetic Metamaterials?". Novel Electromagnetic Materials. The research group of D.R. Smith. Archived from the original on July 20, 2009. Retrieved 2009-08-19.
  7. 1 2 3 Shelby, R. A.; Smith, D. R.; Schultz, S. (2001). "Experimental Verification of a Negative Index of Refraction". Science. 292 (5514): 77–79. Bibcode:2001Sci...292...77S. CiteSeerX . doi:10.1126/science.1058847. PMID   11292865.
  8. Pendry, John B. (2004). Negative Refraction (PDF). Contemporary Physics . 45. Princeton University Press. pp. 191–202. Bibcode:2004ConPh..45..191P. doi:10.1080/00107510410001667434. ISBN   978-0-691-12347-9 . Retrieved 2009-08-26.
  9. 1 2 Veselago, V. G. (1968). "The electrodynamics of substances with simultaneously negative values of ε and μ". Soviet Physics Uspekhi. 10 (4): 509–14. Bibcode:1968SvPhU..10..509V. doi:10.1070/PU1968v010n04ABEH003699.
  10. 1 2 3 Brun, M.; S. Guenneau; and A.B. Movchan (2009-02-09). "Achieving control of in-plane elastic waves". Appl. Phys. Lett. 94 (61903): 061903. arXiv: 0812.0912 . Bibcode:2009ApPhL..94f1903B. doi:10.1063/1.3068491.
  11. Rainsford, Tamath J.; D. Abbott; Abbott, Derek (9 March 2005). Al-Sarawi, Said F (ed.). "T-ray sensing applications: review of global developments". Proc. SPIE. Smart Structures, Devices, and Systems II. 5649 Smart Structures, Devices, and Systems II (Poster session): 826–38. Bibcode:2005SPIE.5649..826R. doi:10.1117/12.607746.
  12. Cotton, Micheal G. (December 2003). "Applied Electromagnetics" (PDF). 2003 Technical Progress Report (NITA – ITS). Telecommunications Theory (3): 4–5. Retrieved 2009-09-14.
  13. 1 2 3 4 5 Alici, Kamil Boratay; Özbay, Ekmel (2007). "Radiation properties of a split ring resonator and monopole composite". Physica Status Solidi B. 244 (4): 1192–96. Bibcode:2007PSSBR.244.1192A. doi:10.1002/pssb.200674505. hdl:11693/49278.
  14. 1 2 Guenneau, S. B.; Movchan, A.; Pétursson, G.; Anantha Ramakrishna, S. (2007). "Acoustic metamaterials for sound focusing and confinement". New Journal of Physics. 9 (11): 399. Bibcode:2007NJPh....9..399G. doi:10.1088/1367-2630/9/11/399.
  15. 1 2 3 4 5 6 7 8 9 10 Slyusar, V.I. (October 6–9, 2009). Metamaterials on antenna solutions (PDF). 7th International Conference on Antenna Theory and Techniques ICATT’09. Lviv, Ukraine. pp. 19–24.
  16. AIP News, Number 628 #1, March 13 Physics Today, May 2003, Press conference at APS March Meeting, Austin, Texas, March 4, 2003, New Scientist, v. 177, p. 24.
  17. Parimi, P. V.; Lu, W. T.; Vodo, P; Sridhar, S (2003). "Photonic crystals: Imaging by flat lens using negative refraction". Nature. 426 (6965): 404. Bibcode:2003Natur.426..404P. doi:10.1038/426404a. PMID   14647372.
  18. Kock, W. E. (1946). "Metal-Lens Antennas". IRE Proc. 34 (11): 828–36. doi:10.1109/JRPROC.1946.232264.
  19. Kock, W.E. (1948). "Metallic Delay Lenses". Bell. Sys. Tech. Jour. 27: 58–82. doi:10.1002/j.1538-7305.1948.tb01331.x.
  20. Caloz, C.; Chang, C.-C.; Itoh, T. (2001). "Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations" (PDF). J. Appl. Phys. 90 (11): 11. Bibcode:2001JAP....90.5483C. doi:10.1063/1.1408261.
  21. Eleftheriades, G.V.; Iyer A.K. & 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): 2702–12. Bibcode:2002ITMTT..50.2702E. doi:10.1109/TMTT.2002.805197.
  22. Caloz, C.; 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. p. 412. doi:10.1109/APS.2002.1016111. ISBN   978-0-7803-7330-3.
  23. Sievenpiper, Dan; et al. (November 1999). "High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band" (PDF). IEEE Transactions on Microwave Theory and Techniques . 47 (11): 2059–74. Bibcode:1999ITMTT..47.2059S. doi:10.1109/22.798001. Archived from the original (PDF) on July 19, 2011. Retrieved 2009-11-11.
  24. Depine, Ricardo A.; Lakhtakia, Akhlesh (2004). "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity". Microwave and Optical Technology Letters. 41 (4): 315–16. arXiv: physics/0311029 . doi:10.1002/mop.20127.
  25. Voznesenskaya, A. and Kabanova, D. (2012) "Analysis of Ray Tracing Through Optical Systems with Metamaterial Elements", Scientific and Technical Journal of Information Technologies, Mechanics and Optics, Volume 5, Number 12, p. 5.
  26. 1 2 3 4 5 Eleftheriades, George V.; Keith G. Balmain (2005). Negative-refraction metamaterials: fundamental principles and applications. Wiley. p. 340. ISBN   978-0-471-60146-3.
  27. Pendry, John B.; David R. Smith (June 2004). "Reversing Light: Negative Refraction" (PDF). Physics Today. 57 (June 37): 2 of 9 (originally page 38 of pp. 37–45). Bibcode:2004PhT....57f..37P. doi:10.1063/1.1784272 . Retrieved 2009-09-27.
  28. Alù, Andrea and; Nader Engheta (January 2004). "Guided Modes in a Waveguide Filled With a Pair of Single-Negative (SNG), Double-Negative (DNG), and/or Double-Positive (DPS) Layers" (PDF). IEEE Transactions on Microwave Theory and Techniques . 52 (1): 199–210. Bibcode:2004ITMTT..52..199A. doi:10.1109/TMTT.2003.821274 . Retrieved 2010-01-03.
  29. Engheta, Nader; Richard W. Ziolkowski (2006). Metamaterials: physics and engineering explorations (added this reference on 2009-12-14.). Wiley & Sons. pp. 211–21. ISBN   978-0-471-76102-0.
  30. Valentine, J.; Zhang, S.; Zentgraf, T.; Ulin-Avila, E.; Genov, D. A.; Bartal, G.; Zhang, X. (2008). "Three-dimensional optical metamaterial with a negative refractive index". Nature. 455 (7211): 376–79. Bibcode:2008Natur.455..376V. doi:10.1038/nature07247. PMID   18690249.
  31. Pendry, JB (2009-04-11). "Metamaterials Generate Novel Electromagnetic Properties". UC Berkeley Atomic Physics Seminar 290F. Archived from the original (Seminar – lecture series) on 2010-06-27. Retrieved 2009-12-14.
  32. Chappell, William leads the IDEA laboratory at Purdue University (2005). "Metamaterials". research in various technologies. Retrieved 2009-11-23.
  33. 1 2 Soukoulis, C. M., ed. (May 2001). Photonic Crystals and Light Localization in the 21st Century (Proceedings of the NATO Advanced Study Institute on Photonic Crystals and Light Localization, Crete, Greece, June 18–30, 2000 ed.). London: Springer London, Limited. pp. xi. ISBN   978-0-7923-6948-6.
  34. Marques, Ricardo; Medina, Francisco; Rafii-El-Idrissi, Rachid (2002-04-04). "Role of bianisotropy in negative permeability and left-handed metamaterials" (PDF). Physical Review B. 65 (14): 144440–41. Bibcode:2002PhRvB..65n4440M. doi:10.1103/PhysRevB.65.144440. hdl:11441/59428. Archived from the original (PDF) on 20 July 2011.
  35. 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. arXiv: 0809.2207 . Bibcode:2009OptL...34...19R. doi:10.1364/OL.34.000019. PMID   19109626.
  36. Kriegler, C. E.; et al. (2010). "Bianisotropic photonic metamaterials" (PDF). IEEE Journal of Selected Topics in Quantum Electronics. 999 (2): 1–15. Bibcode:2010IJSTQ..16..367K. doi:10.1109/JSTQE.2009.2020809.
  37. Plum, E.; Liu, X.-X.; Fedotov, V. A.; Chen, Y.; Tsai, D. P.; Zheludev, N. I. (2009). "Metamaterials: Optical Activity without Chirality" (PDF). Phys. Rev. Lett. 102 (11): 113902. Bibcode:2009PhRvL.102k3902P. doi:10.1103/physrevlett.102.113902. PMID   19392202.
  38. C. Rizza; Andrea Di Falco; Michael Scalora & Alessandro Ciattoni (2015). "One-Dimensional Chirality: Strong Optical Activity in Epsilon-Near-Zero Metamaterials". Phys. Rev. Lett. 115 (5): 057401. arXiv: 1503.00490 . Bibcode:2015PhRvL.115e7401R. doi:10.1103/PhysRevLett.115.057401. PMID   26274441.
  39. Wang, Bingnan; et al. (November 2009). "Chiral metamaterials: simulations and experiments" (PDF). J. Opt. Soc. Am. A. 11 (11): 114003. Bibcode:2009JOptA..11k4003W. doi:10.1088/1464-4258/11/11/114003 . Retrieved 2009-12-24.
  40. Tretyakov, S.; Sihvola, A.; Jylhä, L. (2005). "Backward-wave regime and negative refraction in chiral composites". Photonics and Nanostructures Fundamentals and Applications . 3 (2–3): 107–15. arXiv: cond-mat/0509287 . Bibcode:2005PhNan...3..107T. doi:10.1016/j.photonics.2005.09.008.
  41. Capolino, Filippo (2009). "Chapter 32". Theory and Phenomena of Metamaterials. Taylor & Francis. ISBN   978-1-4200-5425-5.
  42. Page, John (2011). "Metamaterials: Neither solid nor liquid". Nature Materials. 10 (8): 565–66. Bibcode:2011NatMa..10..565P. doi:10.1038/nmat3084. PMID   21778996.
  43. Szondy, David (June 22, 2014). "New materials developed that are as light as aerogel, yet 10,000 times stronger". Gizmag.
  44. Fang, Nicholas. "Projection Microstereolithography" (PDF). Department of Mechanical Science & Engineering, University of Illinois.
  45. Fesenmaier, Kimm (23 May 2014). "Miniature Truss Work". Caltech.
  46. Ciattoni, A.; Rizza, C.; Palange, E. (2010). "Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity". Phys. Rev. A. 81 (4): 043839. arXiv: 1002.3321 . Bibcode:2010PhRvA..81d3839C. doi:10.1103/PhysRevA.81.043839.
  47. Vincenti, M. A.; De Ceglia, D.; Ciattoni, A.; Scalora, M. (2011). "Singularity-driven second- and third-harmonic generation at epsilon-near-zero crossing points". Phys. Rev. A. 84 (6): 063826. arXiv: 1107.2354 . Bibcode:2011PhRvA..84f3826V. doi:10.1103/PhysRevA.84.063826.
  48. Capretti, Antonio; Wang, Yu; Engheta, Nader; Dal Negro, Luca (2015). "Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers". Opt. Lett. 40 (7): 1500–3. Bibcode:2015OptL...40.1500C. doi:10.1364/OL.40.001500. PMID   25831369.
  49. Briane, Marc; Milton, Graeme W. (28 November 2008). "Homogenization of the Three-dimensional Hall Effect and Change of Sign of the Hall Coefficient" (PDF). Archive for Rational Mechanics and Analysis. 193 (3): 715–736. doi:10.1007/s00205-008-0200-y.
  50. Kadic, Muamer; Schittny, Robert; Bückmann, Tiemo; Kern, Christian; Wegener, Martin (22 June 2015). "Hall-Effect Sign Inversion in a Realizable 3D Metamaterial". Physical Review X. 5 (2): 021030. arXiv: 1503.06118 . Bibcode:2015PhRvX...5b1030K. doi:10.1103/PhysRevX.5.021030.
  51. Kern, Christian; Kadic, Muamer; Wegener, Martin (2017). "Experimental Evidence for Sign Reversal of the Hall Coefficient in Three-Dimensional Metamaterials". Physical Review Letters. 118 (1): 016601. Bibcode:2017PhRvL.118a6601K. doi:10.1103/PhysRevLett.118.016601. PMID   28106428.
  52. Kern, Christian; Kadic, Muamer; Wegener, Martin (28 September 2015). "Parallel Hall effect from three-dimensional single-component metamaterials". Applied Physics Letters. 107 (13): 132103. arXiv: 1507.04128 . Bibcode:2015ApPhL.107m2103K. doi:10.1063/1.4932046.
  53. Paschotta, Rüdiger (2008–18). "Photonic Metamaterials". Encyclopedia of Laser Physics and Technology. I & II. Wiley-VCH Verlag. p. 1. Retrieved 2009-10-01.
  54. Capolino, Filippo (2009). Applications of Metamaterials. Taylor & Francis, Inc. pp. 29–1, 25–14, 22–1. ISBN   978-1-4200-5423-1 . Retrieved 2009-10-01.
  55. Oliveri, G.; Werner, D.H.; Massa, A. (2015). "Reconfigurable electromagnetics through metamaterials – A review". Proceedings of the IEEE . 103 (7): 1034–56. doi:10.1109/JPROC.2015.2394292.
  56. Costas Soukoulis (2007-01-04). "Metamaterials found to work for visible light". DOE /Ames Laboratory . Retrieved 2009-11-07.
  57. 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.
  58. 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): 2619–25. Bibcode:2003ITAP...51.2619S. doi:10.1109/TAP.2003.817556.
  59. Wu, B.-I.; W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk and J. A. Kong; Pacheco, Joe; Chen, Xudong; Grzegorczyk, Tomasz M.; Kong, Jin Au (2005). "A Study of Using Metamaterials as Antenna Substrate to Enhance Gain" (PDF). Progress in Electromagnetics Research. 51: 295–28. doi:10.2528/PIER04070701. Archived from the original (PDF) on September 6, 2006. Retrieved 2009-09-23.CS1 maint: multiple names: authors list (link)
  60. Li, W.; Valentine, J. (2014). "Metamaterial Perfect Absorber Based Hot Electron Photodetection". Nano Letters. 14 (6): 3510–14. Bibcode:2014NanoL..14.3510L. doi:10.1021/nl501090w. PMID   24837991.
  61. Yu, Peng; Wu, Jiang; Ashalley, Eric; Govorov, Alexander; Wang, Zhiming (2016). "Dual-band absorber for multispectral plasmon-enhanced infrared photodetection". Journal of Physics D: Applied Physics. 49 (36): 365101. Bibcode:2016JPhD...49J5101Y. doi:10.1088/0022-3727/49/36/365101. ISSN   0022-3727.
  62. Yu, Peng; Besteiro, Lucas V.; Huang, Yongjun; Wu, Jiang; Fu, Lan; Tan, Hark H.; Jagadish, Chennupati; Wiederrecht, Gary P.; Govorov, Alexander O. (2018). "Broadband Metamaterial Absorbers". Advanced Optical Materials: 1800995. doi:10.1002/adom.201800995@10.1002/(issn)2195-1071.halloffame. ISSN   2195-1071.
  63. Pendry, J. B. (2000). "Negative Refraction Makes a Perfect Lens". Physical Review Letters. 85 (18): 3966–69. Bibcode:2000PhRvL..85.3966P. doi:10.1103/PhysRevLett.85.3966. PMID   11041972.
  64. Fang, N.; Lee, H; Sun, C; Zhang, X (2005). "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens". Science. 308 (5721): 534–37. Bibcode:2005Sci...308..534F. doi:10.1126/science.1108759. PMID   15845849.
  65. "First Demonstration of a Working Invisibility Cloak". Office of News & Communications Duke University. Archived from the original on July 19, 2009. Retrieved 2009-05-05.
  66. 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.
  67. "Experts test cloaking technology". BBC News . 2006-10-19. Retrieved 2008-08-05.
  68. "Engineers see progress in creating 'invisibility cloak'".
  69. Alù, Andrea; Engheta, Nader (2005). "Achieving transparency with plasmonic and metamaterial coatings". Phys. Rev. E. 72 (1): 016623. arXiv: cond-mat/0502336 . Bibcode:2005PhRvE..72a6623A. doi:10.1103/PhysRevE.72.016623. PMID   16090123.
  70. Merritt, Richard (January 2009) "Next Generation Cloaking Device Demonstrated: Metamaterial renders object 'invisible'" Archived February 20, 2009, at the Wayback Machine
  71. A. Y. Modi; C. A. Balanis; C. R. Birtcher; H. Shaman, "New Class of RCS-Reduction Metasurfaces Based on Scattering Cancellation Using Array Theory," in IEEE Transactions on Antennas and Propagation, vol.67, no.1, pp. 298-308, Jan. 2019. doi : 10.1109/TAP.2018.2878641
  72. A. Y. Modi; C. A. Balanis; C. R. Birtcher; H. Shaman, "Novel Design of Ultra-Broadband Radar Cross Section Reduction Surfaces using Artificial Magnetic Conductors," in IEEE Transactions on Antennas and Propagation, vol.65, no.10, pp.5406-5417, Oct. 2017. doi : 10.1109/TAP.2017.2734069
  73. M. E. de Cos, Y. Alvarez-Lopez, and F. Las Heras Andres, "A novel approach for RCS reduction using a combination of artificial magnetic conductors," Progress In Electromagnetics Research, Vol. 107, 147–59, 2010. doi : 10.2528/PIER10060402
  74. Appl. Phys. Lett. 104, 221110 (2014). doi : 10.1063/1.4881935
  75. Yu, Nanfang; Genevet, Patrice; Kats, Mikhail A.; Aieta, Francesco; Tetienne, Jean-Philippe; Capasso, Federico; Gaburro, Zeno (October 2011). "Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction". Science. 334 (6054): 333–7. Bibcode:2011Sci...334..333Y. doi:10.1126/science.1210713. PMID   21885733.
  76. Johnson, R. Colin (2009-07-23). "Metamaterial cloak could render buildings 'invisible' to earthquakes". Retrieved 2009-09-09.
  77. Barras, Colin (2009-06-26). "Invisibility cloak could hide buildings from quakes". New Scientist. p. 1. Retrieved 2009-10-20.
  78. "Wrinkled metamaterials for controlling light and sound propagation". KurzweilAI. 2014-01-28. Retrieved 2014-04-15.
  79. Rudykh, S.; Boyce, M. C. (2014). "Transforming Wave Propagation in Layered Media via Instability-Induced Interfacial Wrinkling". Physical Review Letters. 112 (3): 034301. Bibcode:2014PhRvL.112c4301R. doi:10.1103/PhysRevLett.112.034301. PMID   24484141.
  80. Shore, R. A.; Yaghjian, A. D. (2007). "Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers". Radio Science. 42 (6): RS6S21. Bibcode:2007RaSc...42.6S21S. doi:10.1029/2007RS003647.
  81. Li, Y.; Bowler, N. (2012). "Traveling waves on three-dimensional periodic arrays of two different magnetodielectric spheres arbitrarily arranged on a simple tetragonal lattice". IEEE Transactions on Antennas and Propagation. 60 (6): 2727–39. Bibcode:2012ITAP...60.2727L. doi:10.1109/tap.2012.2194637.
  82. MURI metamaterials, UC Berkely (2009). "Scalable and Reconfigurable Electromagnetic Metamaterials and Devices" . Retrieved 2009-12-08.
  83. 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. Archived from the original on March 2, 2010. Retrieved 2009-12-08.
  84. 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. Metamorphose VI. Retrieved 2009-12-13.
  85. de Baas, A. F.; J. L. Vallés (2007-02-11). "Success stories in the Materials domain" (PDF). Metamorphose. Networks of Excellence Key for the future of EU research: 19. Retrieved 2009-12-13.