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
inhomogeneitiesIn general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
to create effective macroscopic behavior.
The primary research in metamaterials investigates materials with negative
refractive indexIn optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
. Negative refractive index materials appear to permit the creation of
superlensA superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
es which can have a
spatial resolutionOptical resolution describes the ability of an imaging system to resolve detail in the object that is being imaged.An imaging system may have many individual components including a lens and recording and display components...
below that of the
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. In other work, a form of 'invisibility' has been demonstrated at least over a narrow
wave bandFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
with
gradient-index materialsMetamaterial cloaking is the scientific application of metamaterials in order to achieve invisibility-cloaking. This is accomplished by manipulating the paths traversed by light through a novel optical material....
. Although the first metamaterials were electromagnetic,
acousticAcoustic 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...
and
seismic metamaterialsSeismic metamaterials, are metamaterials which are designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth...
are also areas of active research.
Potential applications of metamaterials are diverse and include
remote aerospaceAerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...
applications,
sensorA sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument. For example, a mercury-in-glass thermometer converts the measured temperature into expansion and contraction of a liquid which can be read on a calibrated...
detection and
infrastructure monitoringInfrastructure security is the security provided to protect infrastructure, especially critical infrastructure, such as airports, highways rail transport, hospitals, bridges, transport hubs, network communications, media, the electricity grid, dams, power plants, seaports, oil refineries, and...
, smart
solar powerSolar energy, radiant light and heat from the sun, has been harnessed by humans since ancient times using a range of ever-evolving technologies. Solar radiation, along with secondary solar-powered resources such as wind and wave power, hydroelectricity and biomass, account for most of the available...
management,
public safetyPublic safety involves the prevention of and protection from events that could endanger the safety of the general public from significant danger, injury/harm, or damage, such as crimes or disasters .-See also:* By nation...
,
radomeA radome is a structural, weatherproof enclosure that protects a microwave or radar antenna. The radome is constructed of material that minimally attenuates the electromagnetic signal transmitted or received by the antenna. In other words, the radome is transparent to radar or radio waves...
s,
high-frequency battlefield communicationBattlespace is a term used to signify a unified military strategy to integrate and combine armed forces for the military theatre of operations, including air, information, land, sea, and space to achieve military goals. It includes the environment, factors, and conditions that must be understood...
and lenses for high-gain antennas, improving
ultrasonic sensorsLevel sensors detect the level of substances that flow, including liquids, slurries, granular materials, and powders. Fluids and fluidized solids flow to become essentially level in their containers because of gravity whereas most bulk solids pile at an angle of repose to a peak...
, and even
shielding structures from earthquakesEarthquake engineering is the scientific field concerned with protecting society, the natural and the man-made environment from earthquakes by limiting the seismic risk to socio-economically acceptable levels...
.
The research in metamaterials is interdisciplinary and involves such fields as
electrical engineeringElectrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
, electromagnetics, solid state physics, microwave and antennae engineering,
optoelectronicsOptoelectronics is the study and application of electronic devices that source, detect and control light, usually considered a sub-field of photonics. In this context, light often includes invisible forms of radiation such as gamma rays, X-rays, ultraviolet and infrared, in addition to visible light...
, classic
opticsOptics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, material sciences, semiconductor engineering, nanoscience and others.
Electromagnetic metamaterials
Metamaterials have become a new subdiscipline within
physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and
electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
(especially
opticsOptics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
and
photonicsThe science of photonics includes the generation, emission, transmission, modulation, signal processing, switching, amplification, detection and sensing of light. The term photonics thereby emphasizes that photons are neither particles nor waves — they are different in that they have both particle...
).
They show promise for optical and
microwaveMicrowaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
applications such as new types of beam steerers, modulators,
band-pass filterA band-pass filter is a device that passes frequencies within a certain range and rejects frequencies outside that range.Optical band-pass filters are of common usage....
s,
lensesA superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
, microwave couplers, and
antenna systemsMetamaterial 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...
. Furthermore, the lower density of materials means that components,
devicesAn electronic component is a basic electronic element and may be available in a discrete form having two or more electrical terminals . These are intended to be connected together, usually by soldering to a printed circuit board, in order to create an electronic circuit with a particular function...
, and
systemsSystems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...
can be lightweight and small, while at the same time enhancing system and component performance.
Metamaterials consist of
periodic structureIn mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
s. An electromagnetic metamaterial affects electromagnetic waves by having structural features smaller than the wavelength of light. In addition, if a metamaterial is to behave as a
homogeneous materialIn general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
accurately described by an effective
refractive indexIn optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
, its features must be much smaller than the wavelength. To date, subwavelength structures have shown only a few questionable results at visible wavelengths.
For
microwave radiationMicrowaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
, the structures need only be on the order of few centimeters. Microwave frequency metamaterials are usually synthetic, constructed as arrays of electrically conductive elements (such as loops of wire) which have suitable
inductiveAn inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
and
capacitiveA capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
characteristics. These are known as split-ring resonators.
Another structure which can exhibit subwavelength characteristics are frequency selective surfaces (FSS) known as Artificial Magnetic Conductors (AMC) or alternately called High Impedance Surfaces (HIS). These also have inductive and capacitive characteristics, which are directly related to its subwavelength structure.
Photonic crystals and frequency-selective surfaces such as
diffraction gratingIn optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as...
s,
dielectric mirrorA dielectric mirror is a type of a mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified...
s, and
optical coatingAn optical coating is one or more thin layers of material deposited on an optical component such as a lens or mirror, which alters the way in which the optic reflects and transmits light. One type of optical coating is an antireflection coating, which reduces unwanted reflections from surfaces, and...
s do have apparent similarities to subwavelength structured metamaterials. However, these are usually considered distinct from subwavelength structures, as their features are structured for the
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
at which they function, and thus cannot be approximated as a homogeneous material.
However, novel-material structures such as photonic crystals are effective with the visible light spectrum. The middle of the visible spectrum has a wavelength of approximately 560 nm (for sunlight), the photonic crystal structures are generally half this size or smaller, that is <280 nm.
Winston E. KockWinston Kock was the first Director of NASA Electronics Research Center in Cambridge, Massachusetts from September 1, 1964 to October 1, 1966...
developed materials that had similar characteristics to metamaterials in the late 1940s. Materials, which exhibited reversed physical characteristics were first described theoretically by
Victor VeselagoVictor Georgievich Veselago is a Russian physicist. In 1967, he was the first to publish a theoretical analysis of materials with negative permittivity, ε, and permeability μ....
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,
periodicallyIn mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
, 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
microstripMicrostrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
technology. At microwave frequencies, the first real invisibility cloak was realized in 2006. However, only a very small object was imperfectly hidden.
In 2007, one researcher stated that for metamaterial applications to be realized, several goals must be achieved. Reducing energy loss, which is a major limiting factor, keep developing three-dimensional isotropic materials instead of planar structures, then finding ways to mass produce.
Negative refractive index
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
permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
ε and
permeabilityIn electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
µ. However, many metals (such as
silverSilver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...
and
goldGold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...
) have negative ε at visible wavelengths. A material having either (but not both) ε or µ negative is
opaqueOpacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...
to electromagnetic radiation (see
surface plasmonSurface plasmons , are coherent electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface...
for more details).
Although the optical properties of a transparent material are fully specified by the parameters ε and µ, refractive index
n is often used in practice, which can be determined from
. All known non-metamaterial transparent materials possess positive ε and µ. By convention the positive square root is used for
n.
However, some engineered metamaterials have ε < 0 and µ < 0. Because the product εµ is positive,
n is
realIn mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
. Under such circumstances, it is necessary to take the negative square root for
n. Physicist
Victor VeselagoVictor Georgievich Veselago is a Russian physicist. In 1967, he was the first to publish a theoretical analysis of materials with negative permittivity, ε, and permeability μ....
proved that such substances can transmit light.
The foregoing considerations are simplistic for actual materials, which must have complex-valued
ε and µ. The real parts of both ε and µ do not have to be negative for a passive material to display negative refraction. Metamaterials with negative
n have numerous interesting properties:
- Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...
(n1sinθ1 = n2sinθ2), but as n2 is negative, the rays will be refracted on the same side of the normal on entering the material.
- The Doppler shift is reversed: that is, a light source moving toward an observer appears to reduce its frequency.
- Cherenkov radiation
Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...
points the other way.
- The time-averaged Poynting vector
In physics, the Poynting vector can be thought of as representing the directional energy flux density of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector...
is antiparallel-Definitions:Given two lines m_1 \, and m_2 \,, lines l_1 \, and l_2 \, are anti-parallel with respect to m_1 \, and m_2 \, if \angle 1 = \angle 2 \,....
to phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
. This means that unlike a normal right-handed material, the wave fronts are moving in the opposite direction to the flow of energy.
For
plane waveIn the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....
s propagating in electromagnetic metamaterials, the electric field, magnetic field and
wave vectorIn physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...
follow a left-hand rule. This is a reversal of direction when compared to the behavior of conventional optical materials.
Negative
refractive indexIn optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
is an important characteristic in metamaterial design and fabrication. As reverse-refraction media, these occur when both
permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
ε and
permeabilityIn electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
µ are negative. Furthermore, this condition occurs mathematically from the vector triplet
E,
H and
k.
In ordinary, everyday materials – solid, liquid, or gas; transparent or opaque; conductor or insulator – the
conventional refractive indexIn optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...
dominates. This means that
permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and
permeabilityIn electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
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.
Classification of electromagnetic metamaterials
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:
Negative index materials
In
negative index metamaterials (NIM), both
permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and permeability are negative resulting in a negative index of refraction. Hence, because of the double negative parameters these are also known as Double Negative Metamaterials or double negative materials (DNG). Other terminologies for NIMs are "left-handed media", "media with a negative refractive index", and "backward-wave media", along with other nomenclatures.
In optical materials, if both permittivity
ε and permeability
µ are positive this results in propagation in the
forward direction. If both ε and µ are negative, a
backward wave is produced. If ε and µ have different polarities, then this does not result in wave propagation. Mathematically, quadrant II and quadrant IV have coordinates (0,0) in a coordinate plane where ε is the horizontal axis, and µ is the vertical axis.
In 1968
Victor VeselagoVictor Georgievich Veselago is a Russian physicist. In 1967, he was the first to publish a theoretical analysis of materials with negative permittivity, ε, and permeability μ....
published a paper theorizing plane
wave propagationWave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
in a material whose permittivity and permeability were assumed to be simultaneously negative. In such a material, he showed that the
phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
would be anti-parallel to the direction of
Poynting vectorIn physics, the Poynting vector can be thought of as representing the directional energy flux density of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector...
. This is contrary to
wave propagationWave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
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.
To date, materials exhibiting a negative index of refraction have only been demonstrated as artificially constructed materials.
Single negative metamaterials
In single negative (SNG) metamaterials either permittivity or permeability 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 permittivity ε, permeability µ, and refraction index n, will alter with changes in frequency.
- Epsilon negative media (ENG) – permittivity ε is negative while permeability µ is positive. Many plasmas exhibit this characteristic. For example noble metals such as gold or silver will exhibit this characteristic in the infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
and visible spectrumThe visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
s.
- Mu-negative media (MNG) – permittivity ε is positive while permeability µ is negative. 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
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. This results in the magneto-optic effect. A magneto-optic effectA 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...
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 effectIn physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon, that is, an interaction between light and a magnetic field in a medium...
: the plane of polarization can be rotated, forming a Faraday rotatorA Faraday rotator is an optical device that rotates the polarization of light due to the Faraday effect, which in turn is based on a magneto-optic effect....
. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effectMagneto-optic Kerr effect is one of the magneto-optic effects. It describes the changes of light reflected from magnetized media.-Definition:The light that is reflected from a magnetized surface can change in both polarization and reflected intensity...
(not to be confused with the nonlinearNonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
Kerr effectThe Kerr effect, also called the quadratic electro-optic effect , is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric...
). Two gyrotropic materials with reversed rotation directions of the two principal polarizations are called optical isomers.
Electromagnetic bandgap metamaterials
Electromagnetic bandgap metamaterials control the propagation of light. This is accomplished with either a class of metamaterial known as photonic crystals (PC), or another class known as left-handed materials (LHM) Both are a novel class of artificially engineered structure, and both control and manipulate the propagation of electromagnetic waves (light). PCs can prohibit light propagation altogether. However, both the PC and LHM are capable of allowing it to propagate in certain, designed directions, and both can be designed to have electromagnetic bandgaps at desired frequencies.
In addition, metamaterials such as
Photonic crystalPhotonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons...
s (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 metamaterialsA 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 capablitity to determine whether the EM wave is transmitted, reflected, or...
, because the PC derives its properties from its band gap characteristics. In addition the PC operates at the wavelength of light, compared to other metamaterials which operate as a sub-wavelength structure. Furthermore, the complex response of photonic crystals functions by diffracting light. In contrast, a permittivity and permeability defines metamaterials (also a complex response), which is derived from their sub-wavelength structure and diffraction must be eliminated.
The PC is also a material in which periodic inclusions inhibit wave propagation due to destructive interference from scattering from the periodic repetition. The photonic bandgap property of PCs makes them the EM analog of the electronic semi-conductor crystals.
Intended material fabrication of EBGs has the goal of creating periodic, dielectric structures, with low loss, and that are of high quality. An EBG affects the properties of the photon in the same way semiconductor materials affect the properties of the electron. So, it happens that the PC is the perfect bandgap material, because it allows no propagation of light. Each unit of the prescribed periodic structure acts like large scale atoms.
Electromagnetic bandgap structured (EBG) metamaterials are designed to prevent the propagation of an allocated bandwidth of frequencies, for certain arrival angles and polarizations. With
EBG materials new methods utilize the properties of various
dielectricA 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 in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
s 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,
researchResearch can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
, testing and development, along with the prospects of significant
technological solutionsInnovation is the creation of better or more effective products, processes, technologies, or ideas that are accepted by markets, governments, and society...
, have driven the development of EBG
applied scienceApplied science is the application of scientific knowledge transferred into a physical environment. Examples include testing a theoretical model through the use of formal science or solving a practical problem through the use of natural science....
.
Commercial production of dielectric EBG devices has lagged, because commercial rewards are not readily apparent. However, start-up companies are cropping up solely focused on exploiting EBG metamaterials. These metamaterials have been manufactured for frequencies ranging from a few gigahertz (GHz) up to several terahertz (THz). In other words, applications have achieved fabricated media for radio frequency, microwave and mid-infrared regions. "It now appears that EBG concepts can, in many cases act as improved replacements for conventional solutions to electromagnetic problems." Applicable developments include an EBG
transmission lineIn communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
, fabricated utilizing the special properties of metamaterials, EBG woodpiles made of square dielectric bars, and several different types of low gain
antennaAn antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
s.
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 medium
Double positive mediums (DPS) do occur in
natureNature, in the broadest sense, is equivalent to the natural world, physical world, or material world. "Nature" refers to the phenomena of the physical world, and also to life in general...
such as naturally occurring
dielectricA 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 in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
s.
PermittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and magnetic permeability are both positive and
wave propagationWave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
is in the forward direction. Artificial materials have been fabricated which have DPS, ENG, and MNG properties combined.
Bi-isotropic and bianisotropic metamaterials
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 fieldIn physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
causes magnetic polarization, and the magnetic field induces an electrical polarization, i.e., magnetoelectric coupling. Such media are denoted as being
bi-isotropicIn physics, engineering and materials science, bi-isotropic materials have the special optical property that they can twist the polarization of light in either refraction or transmission. This does not mean all materials with twist effect fall in the bi-isotropic class...
. Media which exhibit magneto-electric coupling, and which are also anisotropic (which is the case for many commonly used metamaterial structures), are referred to as bi-anisotropic. are denoted as bi-anisotropic.
Intrinsic to magnetoelectric coupling of
bi-isotropic media, are four material parameters interacting with the
electric (E)In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and
magnetic (H)A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
field strengths, and
electric (D) and
magnetic (B)Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
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 systemIn geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...
of measurements. In this way they are also defined as invariant or
scalarIn physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
.
The intrinsic magnetoelectric parameters,
κ and
χ, affect the
phasePhase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
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.
Chiral metamaterials
When a metamaterial is constructed from
chiralThe term chiral describes an object, especially a molecule, which has or produces a non-superimposeable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism...
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 interactionIn optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
with metallic helices as artificial
chiral mediaA chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....
in the early twentieth century. In the 1950s and 1960s, artificial
dielectricA 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 in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
s were studied for lightweight microwave antennas. Microwave radar absorbers moved into the research arena in the 1980s and 1990s as applications for artificial chiral media.
Wave propagation properties in chiral metamaterials demonstrate that negative refraction can be realized in chiral metamaterials with a strong chirality, with neither negative ε nor μ as a requirement.
This is because the refractive index of the medium has distinct values for the left and right, given by
It can be seen that a negative index will occur
for one polarization if
κ > . In this case, it is not necessary that either or both ε and µ be negative for
backward wave propagation.
History of metamaterials
History of metamaterials shares a common history with
artificial dielectricsArtificial dielectrics are artificial electromagnetic materials consisting of arrayed, synthetic substances. The arrays themselves, and the distances between synthetic substances are usually evenly spaced on, or within, a substrate. Hence, the arrays of inclusions are in a periodic or lattice...
in
microwave engineeringMicrowave engineering pertains to the study and design of microwave circuits, components, and systems. Fundamental principles are applied to analysis, design and measurement techniques in this field. The short wavelengths involved distinguish this discipline from Electronic engineering...
, as it developed just after
World War IIThe history of radar starts with experiments by Heinrich Hertz in the late 19th century that showed that radio waves were reflected by metallic objects. This possibility was suggested in James Clerk Maxwell's seminal work on electromagnetism...
. However, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 19
th century. The history of metamaterials is essentially a history of developing certain types of manufactured materials, which interact at
radio frequencyRadio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
,
microwaveMicrowaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
and later,
optical frequenciesFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
.
Application of metamaterials
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 metamaterials
Terahertz radiationIn physics, terahertz radiation refers to electromagnetic waves propagating at frequencies in the terahertz range. It is synonymously termed submillimeter radiation, terahertz waves, terahertz light, T-rays, T-waves, T-light, T-lux, THz...
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
researchResearch can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
or applications of the terahertz range for metamaterials and other materials, the
frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
range is usually defined as 0.1 to 10 THz. This corresponds to the millimeter and submillimeter wavelengths between 3
mmThe millimetre is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length....
(
EHFExtremely high frequency is the highest radio frequency band. EHF runs the range of frequencies from 30 to 300 gigahertz, above which electromagnetic radiation is considered to be low infrared light, also referred to as terahertz radiation...
band) and 0.03 mm (long-wavelength edge of far-infrared light).
Photonic metamaterials
A
Photonic metamaterial is an artificially fabricated, sub-wavelength,
periodicIn mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
structure, designed to interact with optical frequencies (mid-infrared). The sub-wavelength period distinguishes the photonic metamaterial from photonic band gap structures.
Tunable metamaterials
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
Plasmonic metamaterials are
negative index metamaterialsNegative index metamaterials or negative index materials are artificial structures where the refractive index has a negative value over some frequency range. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as 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 polaritonsSurface plasmon polaritons , are infrared or visible frequency electromagnetic waves trapped at or guided along metal-dielectric interfaces. These are shorter in wavelength than the incident light...
Metamaterial antennas
Metamaterial antennas are a class of
antennasAn antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
which use metamaterials to improve the performance of the antenna systems. Applying metamaterials to increase performance of antennas has garnered much interest. Demonstrations have shown that metamaterials could enhance the
radiated powerIn physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...
of an antenna. Materials which can attain negative permeability could possibly allow for properties such as an electrically small antenna size, high directivity, and tunable operational frequency.
FSS based metamaterials
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
mediumA transmission medium is a material substance that can propagate energy waves...
(metamaterial), rather than the restrictive limitations of a fixed
frequency responseFrequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
. Other applications are also being explored.
Nonlinear metamaterials
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 opticsNonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
. 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 fieldAn electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
.
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.
Metamaterial absorber
A
metamaterial absorber manipulates the loss components of the complex effective parameters,
permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and magnetic permeability of metamaterials, to create a high
electromagneticElectromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
absorber. Loss components are often noted in applications of negative refractive index (
photonic metamaterialsPhotonic metamaterials, also known as Optical metamaterials, are a type of electromagnetic metamaterial, which are designed to interact with optical frequencies which are terahertz , infrared , and eventually, visible wavelengths. As a type of metamaterial, the periodic structures are made up of...
,
antenna systems metamaterialsMetamaterial 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...
) or transformation optics (
metamaterial cloakingMetamaterial cloaking is the scientific application of metamaterials in order to achieve invisibility-cloaking. This is accomplished by manipulating the paths traversed by light through a novel optical material....
, celestial mechanics), but often not utilized in these applications.
Superlens
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.
Cloaking devices
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.
Elastic metamaterials
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
acousticIn physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
, elastic and seismic waves."
Acoustic metamaterials
Acoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate
soundSound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
in the form of sonic, infrasonic, or
ultrasonicUltrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Ultrasound is thus not separated from "normal" sound based on differences in physical properties, only the fact that humans cannot hear it. Although this limit varies from person to person, it is...
waves, as these might occur in
gasGas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
es,
liquidLiquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
s, and
solidSolid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
s. 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 refractionNegative refraction is the name for an electromagnetic phenomenon where light rays are refracted at an interface in the reverse sense to that normally expected...
domain.
Control of the various forms of sound
waveIn physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
s is mostly accomplished through the
bulk modulusThe bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e...
β, mass density
ρ, and
ChiralityThe term chiral describes an object, especially a molecule, which has or produces a non-superimposeable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism...
. The
bulk modulusThe bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e...
and density are analogies of the electromagnetic parameters,
permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and
permeabilityIn electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
, in electromagnetic metamaterials. Related to this is the mechanics of sound wave propagation in a
latticeIn physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are...
structure. Also materials have
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, and intrinsic degrees of
stiffnessStiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...
. Together, these form a resonant system, and the mechanical (sonic) resonance may be excited by appropriate sonic frequencies (for example
pulseIn medicine, one's pulse represents the tactile arterial palpation of the heartbeat by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed against a bone, such as at the neck , at the wrist , behind the knee , on the inside of the elbow , and near the...
s at audio frequencies).
Seismic metamaterials
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.
Artificial dielectrics
Artificial dielectrics came into use with the radar
microwave technologiesMicrowave engineering pertains to the study and design of microwave circuits, components, and systems. Fundamental principles are applied to analysis, design and measurement techniques in this field. The short wavelengths involved distinguish this discipline from Electronic engineering...
developed between the 1940s and 1970s. The term "artificial dielectrics" came into use because these are
macroscopicThe macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...
analogues of naturally occurring dielectrics.
Split-ring resonators
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
Negative refraction is the name for an
electromagneticElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
phenomenon where
lightLight or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
rays are
refractedRefraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
at an
interfaceAn interface is a surface forming a common boundary among two different phases, such as an insoluble solid and a liquid, two immiscible liquids or a liquid and an insoluble gas. The importance of the interface depends on which type of system is being treated: the bigger the quotient area/volume,...
in the reverse sense to that normally expected.
Theoretical models
Left-handed materials were first described theoretically by
Victor VeselagoVictor Georgievich Veselago is a Russian physicist. In 1967, he was the first to publish a theoretical analysis of materials with negative permittivity, ε, and permeability μ....
in 1967.
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 ruleIn mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century....
is not followed, allowing an electromagnetic wave to convey energy (have a
group velocityThe group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
) in the lode against its
phase velocityThe phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the 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
ferroelectricsFerroelectricity is a property of certain materials which possess a spontaneous electric polarization that can be reversed by the application of an external electric field. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was...
) 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
dipoleIn physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
s. 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 circuitAn LC circuit, also called a resonant circuit or tuned circuit, consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C...
. 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 articlesAn academic journal is a peer-reviewed periodical in which scholarship relating to a particular academic discipline is published. Academic journals serve as forums for the introduction and presentation for scrutiny of new research, and the critique of existing research...
(see References), there are several (mathematical) material models which describe
frequency responseFrequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
in DNGs. One of these is the Lorentz model. This describes electron motion in terms of a driven-damped,
harmonic oscillatorIn classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
. When the
accelerationIn physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
component of the Lorentz mathematical model is small compared to the other components of the equation, then the
Debye modelIn thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat in a solid. It treats the vibrations of the atomic lattice as phonons in a box, in contrast to the Einstein model, which treats the...
is applied. When the
restoring forceRestoring force, in a physics context, is a variable force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium....
component is negligible, and the coupling coefficient is generally the plasma frequency, then the
Drude modelThe Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials...
is applied. There are other component distinctions that call for the use of one of these models, depending on its polarity, or purpose.
Novel electromagnetic materials
The number of groups studying metamaterials is continuously increasing. For example,
Duke UniversityDuke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...
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 TechnologyThe California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
,
Harvard UniversityHarvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
,
UCLAThe University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
,
Max Planck InstituteThe Max Planck Society for the Advancement of Science is a formally independent non-governmental and non-profit association of German research institutes publicly funded by the federal and the 16 state governments of Germany....
of
GermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, and the FOM Institute of the
NetherlandsThe Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
. In addition, there are currently six groups connected to this umbrella organization, which are conducting intense metamaterial research:
MURI
MURI stands for Multidisciplinary University Research Initiative. Tens of Universities and a few government organizations participate in the
MURI program. A
MURI Metamaterials web page can be found at UC Berkeley. A few other Universities which participate in MURI are UC Los Angeles, UC San Diego, Massachusetts Institute of Technology, and Imperial College in London, UK. The sponsors are Office of Naval Research (ONR) and the Defense Advanced Research Project Agency (DARPA).
The
MURI program supports research by teams of research investigators that intersect more than one traditional science and engineering discipline in order to accelerate both research progress and transition of research results to application. Most MURI efforts involve researchers from multiple academic institutions and academic departments. Based on the proposals selected in the fiscal 2009, a total of 69 academic institutions are expected to participate in 41 research efforts.
Metamorphose
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.
See also
-
-
-
- Academic journals
- Metamaterials (journal)
Metamaterials is a peer-reviewed scientific journal that was established in March 2007. It is published by Elsevier in association with the Metamorphose Network of Excellence. The Coordinating Editor is Mikhail Lapine. The journal is published quarterly, with occasional special issues...
- Metamaterials books
- Metamaterials Handbook
Metamaterials Handbook is a two-volume handbook on metamaterials edited by Filippo Capolino .The series is designed to cover all theory and application topics related to electromagnetic metamaterials. Disciplines have combined to study, and develop electromagnetic metamaterials...
- Metamaterials: Physics and Engineering Explorations
Metamaterials: Physics and Engineering Explorations is a book length introduction to the fundamental research and advancements in electromagnetic composite substances known as electromagnetic metamaterials. The discussion encompasses examination of the physics of metamaterial interactions, the...
Metamaterials scientists
- Nader Engheta
Nader Engheta is an Iranian scientist and engineer. He has significantly contributed to novel artificial materials, photonics, nano-structured materials, novel graphene materials, and plasmonics....
- Ulf Leonhardt
Ulf Leonhardt is a German scientist, born in Schlema, Germany . In 2006, he published the first scientific paper on invisibility cloaking with metamaterials at the same time Pendry's group published their paper in the journal Science...
- John Pendry
Sir John Brian Pendry, FRS FInstP is an English theoretical physicist known for his research into refractive indexes and creation of the first practical "Invisibility Cloak"...
- Vladimir Shalaev
Vladimir M. Shalaev , the Robert and Anne Burnett Professor of Electrical and Computer Engineering and Professor of Biomedical Engineering at Purdue University, specializes in metamaterials, transformation optics, nanophotonics and plasmonics...
- David R. Smith
David R. Smith is a renowned American physicist and professor of electrical and computer engineering at Duke University in North Carolina. Smith's research focuses on electromagnetic metamaterials, or materials with a negative index of refraction...
- Richard W. Ziolkowski
Richard W. Ziolkowski is a past president of the IEEE Antennas and Propagation Society , and a former vice president of this same society . In 2006 he was awarded OSA Fellow. He is also an IEEE Fellow....
External links
-
-
- Educational pages on metamaterials:
- Nanophotonics group. Prof. Min Qiu. Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
(KTH). Sweden.
- ETA research group. Prof. Christophe Caloz. Polytechnique Montréal.
- Metamaterials. Electromagnetics Group. George Eleftheriades. University of Toronto.
- The Engheta Group. Nader Engheta
Nader Engheta is an Iranian scientist and engineer. He has significantly contributed to novel artificial materials, photonics, nano-structured materials, novel graphene materials, and plasmonics....
. University of PennsylvaniaThe University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
.
- Electromagnetic Metamaterials. Fraunhofer FHR
The Fraunhofer Society is a German research organization with 60 institutes spread throughout Germany, each focusing on different fields of applied science . It employs around 18,000, mainly scientists and engineers, with an annual research budget of about €1.65 billion...
. Germany.
- Antennas Research Group. Prof. Yang Hao. University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
.
- Inano Group. Prof. M. Saif Islam. UC Davis.
- Mediums with Negative Phase Velocity. Prof. Akhlesh Lakhtakia
Akhlesh Lakhtakia is a professor of Engineering Science and Mechanics at the Pennsylvania State University. His research focuses on electromagnetic fields in complex materials, such as sculptured thin films, chiral materials, and bianisotropy...
. Penn State University.
- Condensed Matter Theory Group. Sir John Pendry
Sir John Brian Pendry, FRS FInstP is an English theoretical physicist known for his research into refractive indexes and creation of the first practical "Invisibility Cloak"...
. Imperial College. London.
- Computational Nano Materials Group Viktor Podolskiy (Assoc. Prof.). UMass Lowell.
- Shvets Research Group, University of Texas at Austin – US
- David Smith's research group — Duke University — US
- Costas Soukoulis at IESL, Greece — Photonic, Phononic & MetaMaterials Group
- Srinivas Sridhar's Group Northeastern University
- Irina Veretennicoff's research group, Vrije Universiteit Brussel — Belgium
- Christophe Craeye's research group – Belgium
- Martin Wegener's Metamaterials group Universität Karlsruhe (TH) — Germany
- Georgios Zouganelis's Metamaterials Group – NIT — Japan]
- Xiang Zhang's group – UC Berkeley – US
- Sergei Tretyakov's group – Helsinki University of Technology, Finland
- Gengkai Hu's group – Beijing Institute of Technology, (PRC)
- Institute of Applied Phyisical Problems – BSU – Belarus]
- Centre for Photonic Metamaterials, University of Southhampton
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