Negative index metamaterials
Encyclopedia
Negative index metamaterials or negative index materials (NIM) 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 metamaterial
s. Metamaterial refers broadly to any synthetic material with unusual refractive properties, among other descriptions.
Metamaterials which exhibit a negative value for the refractive index (NIM) are often referred to by any of several names and terminologies: "left-handed media (LHM), backward wave media (BW media), media with negative refractive index, double negative (DNG) metamaterials, and other similar names.
in 1967. The proposed left-handed or negative index materials were theorized
to exhibit optical properties opposite to those of glass
, air, and the other transparent media
. Such materials were predicted to exhibit counter intuitive properties, like bending, or refracting, light in unusual and unnatural ways. The first metamaterial was constructed 33 years later.
Such negative index metamaterials are being developed in order to manipulate electromagnetic radiation
in new ways. For example, optical and electromagnetic
properties of natural materials are often altered through chemistry
. With metamaterials optical and electromagnetic properties can be engineered through the geometry of its unit cells. The unit cells are materials that are ordered in geometric arrangements with dimensions that are fractions of the wavelength of the radiated electromagnetic wave. Each artificial unit responds to the radiation from the source. The collective result is a material's response to the electromagnetic wave that is broader than normal.
By having the freedom to alter effects by adjusting the configurations and sizes of the unit cells, control over material parameters known as permittivity
and magnetic permeability can be achieved. These two parameters (or quantities) determine the propagation of electromagnetic waves in matter. In other words, the achievable electromagnetic and optical effects can be extended. For example by controlling the values of permittivity and permeability the refractive index
can be negative, or zero. Optical properties can be expanded beyond the capabilities of lens
es, mirrors, and other conventional materials. One of the effects most studied is the negative index of refraction.
When a negative index of refraction occurs propagation of the electromagnetic wave is reversed. Resolution below the diffraction limit becomes possible. This is known asSubwavelength imaging. Transmitting a beam of light via an electromagnetically flat surface is another capability. In contrast, conventional materials are usually curved, and cannot achieve resolution below the diffraction limit. Also, reversing the electromagnetic waves in a material, in conjunction with other ordinary materials (including air) could result in minimizing losses that would normally occur.
The reverse of the electromagnetic wave, characterized by an antiparallel phase velocity
is also an indicator of negative index of refraction.
Furthermore, negative index materials are customized composites. In other words, combinations of materials designed to achieve optical properties not seen in nature. The properties stem from the unique lattice structure of the composite material, with features smaller than the wavelength
of interest separated by distances that are also smaller than the wavelength of interest. By fabricating such metamaterials, researchers are trying to overcome fundamental limits tied to the wavelength
of light
.
The electromagnetic wave hitting a metamaterial is transformed into electromagnetic waves of a different variety, which are shorter in wavelength than the incident radiation. This transformation leads to unusual and counter intuitive properties that might be harnessed for practical use.
regime, or centimeter wavelengths, of the electromagnetic spectrum
(about 4.3 GHz). It was constructed of split-ring resonators and conducting straight wires (as unit cells). The unit cells were sized from 7 to 10 millimeters.
The unit cells were arranged in a two-dimensional (periodic
) repeating pattern; a crystal-like
geometry. Both, the unit cells and the lattice spacing were smaller than the radiated electromagnetic wave. This produced the first left-handed material when both the permittivity and permeability of the material were negative.
Research in the microwave range continued with split-ring resonators and conducting wires. Research also continued in the shorter wavelengths with this configuration of materials with scaled down unit cell sizes. However, at around 200 THz issues arise which make using the split ring resonator problematic. "Alternative materials become more suitable for the THz and
optical regimes".
At these wavelengths selection of materials and size limiations become important.
The challenge is to fabricate metamaterials so that they refract light at ever-smaller wavelengths.
are commercially available in the wireless domain, and these metamaterial apparatuses continue to be researched. Other potential applications are for microwave radar absorbers, electrically small resonator
s, waveguide
s that can go beyond the diffraction limit, phase compensators, advancements in focusing devices (e.g. microwave lens
), and improved electrically small antennas.
In the optic
al frequency regime developing the superlens
may allow for imaging below the diffraction limit. Other potential applications for negative index metamaterials are optical nanolithography
, nanotechnology
circuitry, A near field superlens (Pendry, 2000) could be useful for biomedical imaging and subwavelength photolithography.
, the Doppler effect
, the Cherenkov radiation
, Fresnel's equations, and Fermat's principle
.
The refractive index
is basic to the science of optics. Shifting the refractive index to a negative value may be a cause to revisit or reconsider the interpretation of some norms
, or basic laws
.
To describe any electromagnetic
properties of a given material such as an optical lens, two significant parameters should be noted. These are permittivity
, ε, and permeability, μ, which could allow for accurate prediction of light waves traveling
of within materials, and electromagnetic phenomena that occur at the surface between two materials (interface
).
For example, refractive index
is an electromagnetic phenomenon which occurs at the surface (or interface) between two materials. Snell's law
states that the relationship between the radiated
angle of incidence, and the resulting refracted angle of transmission
, rests on the refractive index, n, of the two media (materials). Mathematics provides a visualization with
. Hence, it can be seen that the behavior of the refractive index is dependent on the association of these two parameters, as well as their quantitative values
. Therefore, if designed or arbitrarily modified values can be inputs for ε, and, μ then the behavior of propagating electromagnetic waves inside the material can be manipulated at will. This ability then allows for intentional determination of the refractive index.
For example, in 1967, Victor Veselago
analytically determined that light will refract in the reverse direction (negatively) at the interface between a material with negative refractive index and a material exhibiting conventional refractive index
. This extraordinary material was realized, on paper, with simultaneous negative values for ε, and, μ, and could be termed a double negative material. However, in Veselago's day, a material which exhibits double negative parameters simultaneously seemed impossible, because no natural materials exist which can produce this effect. Therefore his work was ignored for three decades.
In general, the physical properties of natural materials cause limitations. Most dielectric
s only have positive permittivities, ε > 0 . Metals will exhibit negative permittivity, ε < 0 at optical frequencies, and plasmas exhibit negative permittivity values in certain frequency bands. Pendry et al. demonstrated that the plasma frequency can be made to occur in the lower microwave
frequencies for metals, with an effective medium of metal rods that replaces the bulk metal
. However, in each of these cases permeability remains always positive. At microwave frequencies, it is possible for negative μ to occur in some ferromagnetic materials. But, the inherent drawback is they are difficult to find above terahertz frequencies. In any case, a natural material that can achieve negative values for permittivity and permeability simultaneously has not been found, or discovered. Hence, all of this has led to constructing artificial composite materials known as metamaterials to achieve desired results.
and permeability.Negative permitivitty was explored in group of research papers which included: Pendry, J.B. et al. "Extremely Low Frequency Plasmons in Metallic Microstructures". Phys. Rev. Lett. 76, 4773 (1996). :Effective permeablitiy with large positive and negative values was explored in the following research: Pendry, J.B. et al. IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
These papers, along with Veselago's
1967 theoretical analysis of the properties of negative index materials, provided the background to fabricate a metamaterial
with negative effective permittivity and permeability. (See below)
A metamaterial
developed to exhibit negative index behavior is typically formed from individual components. Each component responds independently and differently to a radiated electromagnetic wave as it travels through the material. Since these components are smaller than the radiated wavelength
it is understood that a macroscopic
view includes an effective value for both permittivity and permeability.
s which exhibited unusual physical properties
that were never before produced in nature
. These materials obey the laws of physics, but behave differently from normal materials. In essence these negative index metamaterials were noted for having the ability to reverse many of the physical properties that govern the behavior of ordinary optical materials. One of those unusual properties is the ability to reverse, for the first time, Snell's law
of refraction. Until the demonstration by the UCSD team, the material was unavailable. Advances during the 1990s in fabrication and computation abilities allowed these first metamaterial
s to be constructed. Thus, the "new" metamaterial was tested for the effects described by Victor Veselago
30 years earlier, but only at first in the microwave frequency
domain. Reversal of phase velocity was established during this first test. Studies of this experiment, which followed shortly thereafter, announced that other effects had occurred.
To date (March 2010) these materials have only been commonly demonstrated at wavelengths longer than those in the visible spectrum
. In addition, NIMs are fabricated from opaque
materials, and usually made of non-magnetic constituents. However, as an illustration – if these materials could be demonstrated at visible frequencies, and a flashlight
is shone on a NIM slab, the material should focus the light
at a point on the other side. This is not possible with a sheet of ordinary opaque material.
When first demonstrated this composite material (NIM) was limited to transmitting microwave radiation
at frequencies of 4 to 7 gigahertz. This is approximated to be the range of operating frequencies between household microwave ovens(2.45 GHz
) and military radars (10 GHz). At demonstrated frequencies, pulses of electromagnetic radiation
moving through the material in one direction are composed of constituent waves moving in the opposite direction.
The metamaterial
was constructed as a periodic array
of copper
conducting elements. The design was such that the cells, and the lattice spacing between the cells, were much smaller than the radiated electromagnetic wavelength
. Hence, it behaves as an effective medium. The material has become notable because its range of (effective) permittivity
εeff and permeability μeff values have exceeded those found in any ordinary material
. Furthermore, the characteristic of negative (effective) permeability evinced by this medium is particularly notable, because it has not been found in ordinary materials. In addition, the negative values for the magnetic component is directly related to its left-handed nomenclature, and properties (discussed in a section below). The split-ring resonator (SRR), based on the prior 1999 theoretical article, is the tool employed to achieve negative permeability. This first composite metamaterial is then composed of split-ring resonators and electrical conducting posts.
With antiferromagnets and certain types of insulating ferromagnets, effective negative magnetic permeability is achievable when polariton
resonance exists. However, to achieve a negative index of refraction, permittivity with negative values must occur within the same frequency range. The artificially fabricated split-ring resonator is a design that accomplishes this, along with the promise of dampening high losses. With this first introduction of the metamaterial, it appears that the losses incurred were smaller than antiferromagnetic, or ferromagnetic materials.
. First, is to fabricate a material which can produce negative permeability μeff < 0. Second, negative values for both permittivity and permeability must occur simultaneously over a common range of frequencies.
Therefore, for the first metamaterial, the nuts and bolts are one split-ring resonator electromagnetically combined with one (electric) conducting post. These are designed to resonate at designated frequencies to achieve the desired values. Looking at the make-up of the split ring, the associated magnetic field
pattern from the SRR is dipolar. This dipolar behavior is notable because this means it mimics nature's atom
, but on a much larger scale, such as in this case at 2.5 millimeters. Atoms exist on the scale of picometers.
The splits in the rings create a dynamic where the SRR unit cell can be made resonant at radiated wavelengths much larger than the diameter
of the rings. If the rings were closed, a half wavelength boundary would be electromagnet
ically imposed as a requirement for resonance
. The first ever metamaterial with simultaneous effective permittivity and permeability was fabricated in the United States of America.
The split in the second ring is oriented opposite the split in the first ring. It is there to generate a large capacitance
, which occurs in the small gap. This capacitance substantially decreases the resonant frequency while concentrating the electric field
. The individual SRR depicted on the right had a resonant frequency of 4.845 GHz
, and the resonance curve, inset in the graph, is also shown. The radiative losses from absorption
and reflection
are noted to be small, because the unit dimensions are much smaller than the free space, radiated wavelength
.
When these units or cells, are combined into a periodic arrangement the magnetic coupling between the resonators is strengthened, and a strong magnetic coupling occurs. Properties unique in comparison to ordinary or conventional materials begin to emerge. For one thing, this periodic strong coupling creates a material which now has an effective magnetic permeability μeff in response to the radiated-incident
magnetic field.
, a region of propagation
occurs from zero up to a lower band edge, followed by a gap, and then an upper passband
. The presence of a 400 MHz gap between 4.2 GHz and 4.6 GHz
implies a band of frequencies where μeff < 0 occurs.
(Please see the image in the previous section)
Furthermore, when wires are added symmetrically between the split rings, a passband
occurs within the previously forbidden band of the split ring dispersion curves. That this passband occurs within a previously forbidden region indicates that the negative ´εeff for this region has combined with the negative μeff to allow propagation. This fit with theoretical predictions. Mathematically, the dispersion relation leads to a band with negative group velocity
everywhere, and a bandwidth that is independent of the plasma frequency, within the stated conditions.
Mathematical modeling and experiment have both shown that periodically arrayed conducting elements (non-magnetic by nature) respond predominately to the magnetic component
of incident electromagnetic fields
. The result is an effective medium and negative μeff over a band of frequencies. The permeability was verified to be the region of the forbidden band, where the gap in propagation occurred - from a finite section of material. This was combined with a negative permittivity material, εeff < 0, to form a “left-handed” medium, which formed a propagation band with negative group velocity where previously there was only attenuation. This validated predictions. In addition, a later work determined that this first metamaterial
had a range of frequencies over which the refractive index was predicted to be negative for one direction of propagation
(see ref #). Other predicted electrodynamic effects were to be investigated in other research.
, ε, and permeability, μ, in an overlapping frequency region. Since the values are derived from the effects of the composite medium system
as a whole, these are defined as effective permittivity, εeff, and effective permeability, μeff. Real values are then derived to denote the value of negative index of refraction, and wave vector
s. This means that in practice losses will occur for a given medium used to transmit
electromagnetic radiation such as microwave
, or infrared
frequencies, or visible light - for example. In this instance, real values describe either the amplitude
or the intensity
of a transmitted wave relative to an incident wave, while ignoring the negligible loss values.
was constructed with resonating elements, which exhibited one direction of incidence
and polarization. In other words, this structure exhibited left-handed propagation in one dimension. This was discussed in relation to Veselago's seminal work 33 years earlier (1967). He predicted that intrinsic to a material which manifests negative values of effective permittivity
and permeability, are several types of reversed physics phenomena
. Hence, there was then a critical need for a higher dimensional LHMs to confirm Veselago's theory, as expected. The confirmation would include reversal of Snell's law
(index of refraction), along with other reversed phenomena.
In the beginning of 2001 the existence of a higher dimensional structure was reported. It was two dimensional and demonstrated by both experiment and numerical confirmation. It was an LHM, a composite constructed of wire strips mounted behind the split-ring resonators (SRRs) in a periodic configuration. It was created for the express purpose of being suitable for further experiments to produce the Veselago predicted effects.
, when refraction of light
is measured or observed for ordinary materials
surrounded by air, the value is always greater than one, n > 1. A refracted ray entering a material from air will be bent towards, but never end up on the same side as the normal. In addition, the science and practice of optical lensing and imaging is based on the knowledge that any material with a refractive index different from its environment will alter the direction of incoming rays which do not arrive in a straight line in relation to the interface (of the material surface and air). Also, lenses have been designed to focus and steer the various spectra of light (EM radiation) in frequency
ranges from radio
to the visible spectra. Furthermore, all known natural occurring materials demonstrate refractive indices that are positive. However, a theoretical work in 1967 showed that a refractive index with negative values is possible and that this does not violate the laws of physics. As discussed previously (above), the first metamaterial
had a range of frequencies over which the refractive index was predicted to be negative for one direction of propagation
were reported in May of the year 2000.
In 2001, a team of researcher
s constructed a prism composed of metamaterials (negative index metamaterials) to experimentally test for negative refractive index. The experiment used a waveguide to help transmit the proper frequency and isolate the material.
The experimental demonstration of negative refractive index was followed by another demonstration, in 2003, of a reversal of Snell's law, or reversed refraction. However, in this experiment negative index of refraction material is in free space from 12.6 to 13.2 GHz. Although the radiated frequency range is about the same, a notable distinction is this experiment is conducted in free space rather employing waveguide.
Furthering the authenticity of negative refraction, the power flow of a wave transmitted through a dispersive left-handed material was calculated and compared to a dispersive right-handed material. The transmission of an incident field, composed of many frequencies, from an isotropic nondispersive material into an isotropic dispersive media is employed. The direction of power flow for both nondispersive and dispersive media is determined by the time-averaged
Poynting vector. Negative refraction was shown to be possible for multifrequency signals by explicit calculation of the Poynting vector in the LHM.
– a right-handed material (RHM) – the wave front is transmitted away from the source. In a NIM the wavefront travels toward the source. However, the magnitude and direction of the flow of energy essentially remains the same in both the ordinary material and the NIM. Since, the flow of energy remains the same in both materials (media) the impedance of the NIM matches the RHM. Hence, the sign of the intrinsic impedance is still positive in a NIM.
Light incident on a left-handed material, or NIM, will bend to the same side as the incident beam, and for Snell’s law to hold, the refraction angle should be negative. In a passive metamaterial medium this determines a negative real and imaginary part of the refractive index.
In 1968 Victor Veselago
's paper showed that the opposite directions of EM plane waves and the flow of energy was derived from the individual Maxwell curl equations
. In ordinary optical materials, the curl equation for the electric field
show a "right hand rule" for the directions of the electric field E, the magnetic induction B, and wave propagation, which goes in the direction of wave vector k
. However, the direction of energy flow formed by E × H is right-handed only when permeability is greater than zero. This means that when permeability is less than zero, e.g. negative, wave propagation
is reversed (determined by k), and contrary to the direction of energy flow. Furthermore, the relations of vectors E, H, and k form a "left-handed" system – and it was Veselago who coined the term "left-handed" (LH) material, which is in wide use today (2011). He contended that an LH material has a negative refractive index and relied on the steady-state solutions
of Maxwell's equations
as a center for his argument.
After a 30 year void, when LH materials were finally demonstrated, it could be said that the designation of negative refractive index is unique to LH systems; even when compared to photonic crystal
s. Photonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase and group velocities. But, negative refraction does not occur in these systems, and not yet realistically in Photonic crystals.
. But the results of two such demonstrations are considered ambiguous by later studies. Another most recent, published, demonstration at one single visible frequency is still not the norm, or common, for the large body of work that has been produced in the field of metamaterials. To date, hundreds of scientific, peer review
ed, articles have been published regading some aspect of metamaterial
s. This is compared to some minscule number, the studies that have apparent results in the visible spectrum. In an encyclopedia article such as this it is problematic to give undue weight to such studies, until these become common, or part of the norm, for metamaterials.
Moreover, although previous research efforts have announced negative refraction of one single frequency in the visible light spectrum, this most recent (April, 2010) is being reported as "the first one that operates on visible light." Also as before, the stated achievement is for one single frequency in the visible spectrum. In other words there is no broad band ability.
CR and the 1937 theory
has led to a large array of applications in high energy physics. A notable application are the Cherenkov counters. These are used to determine various properties of a charged particle such as its velocity, charge, direction of motion, and energy. These properties are important in the identification of different particles. For example, the counters were applied in the discovery of the anti-proton and the J particle. Six large Cherenkov counters
were used in the discovery of the J particle.
It has been difficult to experimentally prove the reversed Cherenkov radiation.
. The research began with Pendry's proposed "Perfect lens". Several research investigations that followed Pendry's concluded that the "Perfect lens" was possible in theory but impractical. One direction in subwavelength focusing proceeded with the use of negative index metamaterials, but based on the enhancements for imaging with surface plasmons. In another direction researchers explored paraxial approximation
s of DNG slabs.
, Sheldon Schultz, Norman Kroll, Richard A. Shelby.
The invention achieves simultaneous negative permittivity and permeability over a common band of frequencies. The material can integrate media which is already composite or continuous, but which will produce negative permittivity and permeability within the same spectrum of frequencies. Different types of continuous or composite may be deemed appropriate when combined for the desired effect. However, the inclusion of a periodic array of conducting elements is preferred. The array scatters electromagnetic radiation
at wavelengths longer than the size of the element and lattice spacing. The array is then viewed as an effective medium.
Also see the Preprint copy.
Metamaterials scientists
, US Air Force, and US Army. Many scientific institutions are involved including:
Refractive index
In 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....
has a negative value over some frequency
Frequency
Frequency 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. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s. Metamaterial refers broadly to any synthetic material with unusual refractive properties, among other descriptions.
Metamaterials which exhibit a negative value for the refractive index (NIM) are often referred to by any of several names and terminologies: "left-handed media (LHM), backward wave media (BW media), media with negative refractive index, double negative (DNG) metamaterials, and other similar names.
Properties and characteristics
Metamaterials are incarnations of materials first proposed by a Russian theorist Victor VeselagoVictor Veselago
Victor 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. The proposed left-handed or negative index materials were theorized
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
to exhibit optical properties opposite to those of glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
, air, and the other transparent media
Optical Materials
Optical Materials is a peer-reviewed scientific journal that publishes original papers and review articles on the design, synthesis, characterisation and applications of materials, suitable for various optical devices...
. Such materials were predicted to exhibit counter intuitive properties, like bending, or refracting, light in unusual and unnatural ways. The first metamaterial was constructed 33 years later.
Such negative index metamaterials are being developed in order to manipulate electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
in new ways. For example, optical and electromagnetic
Electromagnetic
Electromagnetic may refer to:* Electromagnetism* Electromagnetic field* Electromagnetic force* Electromagnetic radiation* Electromagnetic induction* Electromagnetic spectrum...
properties of natural materials are often altered through chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
. With metamaterials optical and electromagnetic properties can be engineered through the geometry of its unit cells. The unit cells are materials that are ordered in geometric arrangements with dimensions that are fractions of the wavelength of the radiated electromagnetic wave. Each artificial unit responds to the radiation from the source. The collective result is a material's response to the electromagnetic wave that is broader than normal.
By having the freedom to alter effects by adjusting the configurations and sizes of the unit cells, control over material parameters known as permittivity
Permittivity
In 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 can be achieved. These two parameters (or quantities) determine the propagation of electromagnetic waves in matter. In other words, the achievable electromagnetic and optical effects can be extended. For example by controlling the values of permittivity and permeability the refractive index
Refractive index
In 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....
can be negative, or zero. Optical properties can be expanded beyond the capabilities of lens
Lens
-Optics:*Lens , an optical element which converges or diverges light**Lens , a part of the eye**Corrective lens for correction of human vision***Contact lens, placed on the cornea of the eye**Photographic lens, a lens designed for use on a camera...
es, mirrors, and other conventional materials. One of the effects most studied is the negative index of refraction.
When a negative index of refraction occurs propagation of the electromagnetic wave is reversed. Resolution below the diffraction limit becomes possible. This is known asSubwavelength imaging. Transmitting a beam of light via an electromagnetically flat surface is another capability. In contrast, conventional materials are usually curved, and cannot achieve resolution below the diffraction limit. Also, reversing the electromagnetic waves in a material, in conjunction with other ordinary materials (including air) could result in minimizing losses that would normally occur.
The reverse of the electromagnetic wave, characterized by an antiparallel phase velocity
Phase velocity
The 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...
is also an indicator of negative index of refraction.
Furthermore, negative index materials are customized composites. In other words, combinations of materials designed to achieve optical properties not seen in nature. The properties stem from the unique lattice structure of the composite material, with features smaller than the wavelength
Wavelength
In 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...
of interest separated by distances that are also smaller than the wavelength of interest. By fabricating such metamaterials, researchers are trying to overcome fundamental limits tied to the wavelength
Wavelength
In 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...
of light
Light
Light 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...
.
The electromagnetic wave hitting a metamaterial is transformed into electromagnetic waves of a different variety, which are shorter in wavelength than the incident radiation. This transformation leads to unusual and counter intuitive properties that might be harnessed for practical use.
Materials
The first actual metamaterials worked in the microwaveMicrowave
Microwaves, 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...
regime, or centimeter wavelengths, of the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
(about 4.3 GHz). It was constructed of split-ring resonators and conducting straight wires (as unit cells). The unit cells were sized from 7 to 10 millimeters.
The unit cells were arranged in a two-dimensional (periodic
Periodic function
In 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,...
) repeating pattern; a crystal-like
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
geometry. Both, the unit cells and the lattice spacing were smaller than the radiated electromagnetic wave. This produced the first left-handed material when both the permittivity and permeability of the material were negative.
Research in the microwave range continued with split-ring resonators and conducting wires. Research also continued in the shorter wavelengths with this configuration of materials with scaled down unit cell sizes. However, at around 200 THz issues arise which make using the split ring resonator problematic. "Alternative materials become more suitable for the THz and
optical regimes".
At these wavelengths selection of materials and size limiations become important.
The challenge is to fabricate metamaterials so that they refract light at ever-smaller wavelengths.
Applications
Negative index metamaterials show potential to be employed in various electromagnetic components and devices. Metamaterial antennasMetamaterial antennas
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...
are commercially available in the wireless domain, and these metamaterial apparatuses continue to be researched. Other potential applications are for microwave radar absorbers, electrically small resonator
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...
s, waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...
s that can go beyond the diffraction limit, phase compensators, advancements in focusing devices (e.g. microwave lens
Microwave Engineering
Microwave 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...
), and improved electrically small antennas.
In the optic
Optic
Optic may mean:* optic, a British term for a device for dispensing fixed amounts of alcoholic spirits* Optics, the study of the behavior and properties of light* An optical element or component, such as a lens, prism, or mirror...
al frequency regime developing the superlens
Superlens
A 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...
may allow for imaging below the diffraction limit. Other potential applications for negative index metamaterials are optical nanolithography
Nanolithography
Nanolithography is the branch of nanotechnology concerned with the study and application of fabricating nanometer-scale structures, meaning patterns with at least one lateral dimension between the size of an individual atom and approximately 100 nm...
, nanotechnology
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
circuitry, A near field superlens (Pendry, 2000) could be useful for biomedical imaging and subwavelength photolithography.
Implications of negative refractive materials
The existence of negative refractive materials can result in a change in electrodynamic calucalations for the case of permeability μ = 1 . A change from a conventional refractive index to a negative value gives incorrect results for conventional calculations, because some properties and effects have been altered. When permeability μ has values other than 1 this affects Snell's lawSnell'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...
, the Doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
, the Cherenkov radiation
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...
, Fresnel's equations, and Fermat's principle
Fermat's principle
In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light...
.
The refractive index
Refractive index
In 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 basic to the science of optics. Shifting the refractive index to a negative value may be a cause to revisit or reconsider the interpretation of some norms
Convention (norm)
A convention is a set of agreed, stipulated or generally accepted standards, norms, social norms or criteria, often taking the form of a custom....
, or basic laws
Optics
Optics 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...
.
Manipulating permittivity and permeability
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
properties of a given material such as an optical lens, two significant parameters should be noted. These are permittivity
Permittivity
In 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 permeability, μ, which could allow for accurate prediction of light waves traveling
Wave propagation
Wave 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....
of within materials, and electromagnetic phenomena that occur at the surface between two materials (interface
Interface (chemistry)
An 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,...
).
For example, refractive index
Refractive index
In 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 electromagnetic phenomenon which occurs at the surface (or interface) between two materials. Snell's law
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...
states that the relationship between the radiated
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
angle of incidence, and the resulting refracted angle of transmission
Transmission coefficient
The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered...
, rests on the refractive index, n, of the two media (materials). Mathematics provides a visualization with
. Hence, it can be seen that the behavior of the refractive index is dependent on the association of these two parameters, as well as their quantitative valuesQuantitative property
A quantitative property is one that exists in a range of magnitudes, and can therefore be measured with a number. Measurements of any particular quantitative property are expressed as a specific quantity, referred to as a unit, multiplied by a number. Examples of physical quantities are distance,...
. Therefore, if designed or arbitrarily modified values can be inputs for ε, and, μ then the behavior of propagating electromagnetic waves inside the material can be manipulated at will. This ability then allows for intentional determination of the refractive index.
For example, in 1967, Victor Veselago
Victor Veselago
Victor 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....
analytically determined that light will refract in the reverse direction (negatively) at the interface between a material with negative refractive index and a material exhibiting conventional refractive index
Refractive index
In 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....
. This extraordinary material was realized, on paper, with simultaneous negative values for ε, and, μ, and could be termed a double negative material. However, in Veselago's day, a material which exhibits double negative parameters simultaneously seemed impossible, because no natural materials exist which can produce this effect. Therefore his work was ignored for three decades.
In general, the physical properties of natural materials cause limitations. Most dielectric
Dielectric
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 in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
s only have positive permittivities, ε > 0 . Metals will exhibit negative permittivity, ε < 0 at optical frequencies, and plasmas exhibit negative permittivity values in certain frequency bands. Pendry et al. demonstrated that the plasma frequency can be made to occur in the lower microwave
Microwave
Microwaves, 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...
frequencies for metals, with an effective medium of metal rods that replaces the bulk metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
. However, in each of these cases permeability remains always positive. At microwave frequencies, it is possible for negative μ to occur in some ferromagnetic materials. But, the inherent drawback is they are difficult to find above terahertz frequencies. In any case, a natural material that can achieve negative values for permittivity and permeability simultaneously has not been found, or discovered. Hence, all of this has led to constructing artificial composite materials known as metamaterials to achieve desired results.
Physical properties never before produced in nature
Theoretical articles were published in 1996 and 1999 which showed that synthetic materials could be constructed to purposely exhibit an negative permittivityPermittivity
In 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.Negative permitivitty was explored in group of research papers which included: Pendry, J.B. et al. "Extremely Low Frequency Plasmons in Metallic Microstructures". Phys. Rev. Lett. 76, 4773 (1996). :Effective permeablitiy with large positive and negative values was explored in the following research: Pendry, J.B. et al. IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
These papers, along with Veselago's
Victor Veselago
Victor 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....
1967 theoretical analysis of the properties of negative index materials, provided the background to fabricate a metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
with negative effective permittivity and permeability. (See below)
A metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
developed to exhibit negative index behavior is typically formed from individual components. Each component responds independently and differently to a radiated electromagnetic wave as it travels through the material. Since these components are smaller than the radiated wavelength
Wavelength
In 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...
it is understood that a macroscopic
Macroscopic
The 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...
view includes an effective value for both permittivity and permeability.
Composite material
In the year 2000 a team of UCSD researchers produced a new class of composite materialComposite material
Composite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...
s which exhibited unusual physical properties
Physics
Physics 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...
that were never before produced in nature
Nature
Nature, 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...
. These materials obey the laws of physics, but behave differently from normal materials. In essence these negative index metamaterials were noted for having the ability to reverse many of the physical properties that govern the behavior of ordinary optical materials. One of those unusual properties is the ability to reverse, for the first time, Snell's law
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...
of refraction. Until the demonstration by the UCSD team, the material was unavailable. Advances during the 1990s in fabrication and computation abilities allowed these first metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s to be constructed. Thus, the "new" metamaterial was tested for the effects described by Victor Veselago
Victor Veselago
Victor 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....
30 years earlier, but only at first in the microwave frequency
Microwave
Microwaves, 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...
domain. Reversal of phase velocity was established during this first test. Studies of this experiment, which followed shortly thereafter, announced that other effects had occurred.
To date (March 2010) these materials have only been commonly demonstrated at wavelengths longer than those in the visible spectrum
Visible spectrum
The 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...
. In addition, NIMs are fabricated from opaque
Opacity (optics)
Opacity 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...
materials, and usually made of non-magnetic constituents. However, as an illustration – if these materials could be demonstrated at visible frequencies, and a flashlight
Flashlight
A flashlight is a hand-held electric-powered light source. Usually the light source is a small incandescent lightbulb or light-emitting diode...
is shone on a NIM slab, the material should focus the light
Light
Light 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...
at a point on the other side. This is not possible with a sheet of ordinary opaque material.
When first demonstrated this composite material (NIM) was limited to transmitting microwave radiation
Microwave
Microwaves, 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...
at frequencies of 4 to 7 gigahertz. This is approximated to be the range of operating frequencies between household microwave ovens(2.45 GHz
GHZ
GHZ or GHz may refer to:# Gigahertz .# Greenberger-Horne-Zeilinger state — a quantum entanglement of three particles.# Galactic Habitable Zone — the region of a galaxy that is favorable to the formation of life....
) and military radars (10 GHz). At demonstrated frequencies, pulses of electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
moving through the material in one direction are composed of constituent waves moving in the opposite direction.
The metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
was constructed as a periodic array
Periodic function
In 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,...
of copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
conducting elements. The design was such that the cells, and the lattice spacing between the cells, were much smaller than the radiated electromagnetic wavelength
Wavelength
In 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...
. Hence, it behaves as an effective medium. The material has become notable because its range of (effective) permittivity
Permittivity
In 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...
εeff and permeability μeff values have exceeded those found in any ordinary material
Optics
Optics 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...
. Furthermore, the characteristic of negative (effective) permeability evinced by this medium is particularly notable, because it has not been found in ordinary materials. In addition, the negative values for the magnetic component is directly related to its left-handed nomenclature, and properties (discussed in a section below). The split-ring resonator (SRR), based on the prior 1999 theoretical article, is the tool employed to achieve negative permeability. This first composite metamaterial is then composed of split-ring resonators and electrical conducting posts.
With antiferromagnets and certain types of insulating ferromagnets, effective negative magnetic permeability is achievable when polariton
Polariton
In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also known as the anti-crossing principle...
resonance exists. However, to achieve a negative index of refraction, permittivity with negative values must occur within the same frequency range. The artificially fabricated split-ring resonator is a design that accomplishes this, along with the promise of dampening high losses. With this first introduction of the metamaterial, it appears that the losses incurred were smaller than antiferromagnetic, or ferromagnetic materials.
Simultaneous negative permittivity and permeability
Negative permittivity εeff < 0 had already been discovered and realized in metals for frequencies all the way up to the plasma frequency, before the first metamaterial. There are two requirements to achieve a negative value for refractionRefraction
Refraction 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...
. First, is to fabricate a material which can produce negative permeability μeff < 0. Second, negative values for both permittivity and permeability must occur simultaneously over a common range of frequencies.
Therefore, for the first metamaterial, the nuts and bolts are one split-ring resonator electromagnetically combined with one (electric) conducting post. These are designed to resonate at designated frequencies to achieve the desired values. Looking at the make-up of the split ring, the associated magnetic field
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;...
pattern from the SRR is dipolar. This dipolar behavior is notable because this means it mimics nature's atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
, but on a much larger scale, such as in this case at 2.5 millimeters. Atoms exist on the scale of picometers.
The splits in the rings create a dynamic where the SRR unit cell can be made resonant at radiated wavelengths much larger than the diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of the rings. If the rings were closed, a half wavelength boundary would be electromagnet
Electromagnet
An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. The magnetic field disappears when the current is turned off...
ically imposed as a requirement for resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
. The first ever metamaterial with simultaneous effective permittivity and permeability was fabricated in the United States of America.
The split in the second ring is oriented opposite the split in the first ring. It is there to generate a large capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
, which occurs in the small gap. This capacitance substantially decreases the resonant frequency while concentrating the electric field
Electric field
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...
. The individual SRR depicted on the right had a resonant frequency of 4.845 GHz
Microwave
Microwaves, 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 the resonance curve, inset in the graph, is also shown. The radiative losses from absorption
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
and reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
are noted to be small, because the unit dimensions are much smaller than the free space, radiated wavelength
Wavelength
In 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...
.
When these units or cells, are combined into a periodic arrangement the magnetic coupling between the resonators is strengthened, and a strong magnetic coupling occurs. Properties unique in comparison to ordinary or conventional materials begin to emerge. For one thing, this periodic strong coupling creates a material which now has an effective magnetic permeability μeff in response to the radiated-incident
Physical optics
In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...
magnetic field.
Composite material passband
Graphing the general dispersion curveDispersion (optics)
In 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...
, a region of propagation
Wave propagation
Wave 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....
occurs from zero up to a lower band edge, followed by a gap, and then an upper passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
. The presence of a 400 MHz gap between 4.2 GHz and 4.6 GHz
Microwave
Microwaves, 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...
implies a band of frequencies where μeff < 0 occurs.
(Please see the image in the previous section)
Furthermore, when wires are added symmetrically between the split rings, a passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
occurs within the previously forbidden band of the split ring dispersion curves. That this passband occurs within a previously forbidden region indicates that the negative ´εeff for this region has combined with the negative μeff to allow propagation. This fit with theoretical predictions. Mathematically, the dispersion relation leads to a band with negative group velocity
Group velocity
The 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....
everywhere, and a bandwidth that is independent of the plasma frequency, within the stated conditions.
Mathematical modeling and experiment have both shown that periodically arrayed conducting elements (non-magnetic by nature) respond predominately to the magnetic component
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;...
of incident electromagnetic fields
Physical optics
In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...
. The result is an effective medium and negative μeff over a band of frequencies. The permeability was verified to be the region of the forbidden band, where the gap in propagation occurred - from a finite section of material. This was combined with a negative permittivity material, εeff < 0, to form a “left-handed” medium, which formed a propagation band with negative group velocity where previously there was only attenuation. This validated predictions. In addition, a later work determined that this first metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
had a range of frequencies over which the refractive index was predicted to be negative for one direction of propagation
Wave propagation
Wave 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....
(see ref #). Other predicted electrodynamic effects were to be investigated in other research.
Describing a left-handed material
From the conclusions in the above section a left-handed material (LHM) can be defined. It is a material which exhibits simultaneous negative values for permittivityPermittivity
In 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 permeability, μ, in an overlapping frequency region. Since the values are derived from the effects of the composite medium system
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
as a whole, these are defined as effective permittivity, εeff, and effective permeability, μeff. Real values are then derived to denote the value of negative index of refraction, and wave vector
Wave vector
In 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...
s. This means that in practice losses will occur for a given medium used to transmit
Transmission coefficient
The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered...
electromagnetic radiation such as microwave
Microwave
Microwaves, 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...
, or infrared
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...
frequencies, or visible light - for example. In this instance, real values describe either the amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
or the intensity
Intensity (physics)
In 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 a transmitted wave relative to an incident wave, while ignoring the negligible loss values.
Isotropic, negative index in two dimensions
In sections above, the first fabricated metamaterialMetamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
was constructed with resonating elements, which exhibited one direction of incidence
Angle of incidence
Angle of incidence is a measure of deviation of something from "straight on", for example:* in the approach of a ray to a surface, or* the angle at which the wing or horizontal tail of an airplane is installed on the fuselage, measured relative to the axis of the fuselage.-Optics:In geometric...
and polarization. In other words, this structure exhibited left-handed propagation in one dimension. This was discussed in relation to Veselago's seminal work 33 years earlier (1967). He predicted that intrinsic to a material which manifests negative values of effective permittivity
Permittivity
In 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 several types of reversed physics phenomena
Physical property
A physical property is any property that is measurable whose value describes a physical system's state. The changes in the physical properties of a system can be used to describe its transformations ....
. Hence, there was then a critical need for a higher dimensional LHMs to confirm Veselago's theory, as expected. The confirmation would include reversal of Snell's law
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...
(index of refraction), along with other reversed phenomena.
In the beginning of 2001 the existence of a higher dimensional structure was reported. It was two dimensional and demonstrated by both experiment and numerical confirmation. It was an LHM, a composite constructed of wire strips mounted behind the split-ring resonators (SRRs) in a periodic configuration. It was created for the express purpose of being suitable for further experiments to produce the Veselago predicted effects.
Experimental verification of a negative index of refraction
According to Snell's lawSnell'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...
, when refraction of light
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...
is measured or observed for ordinary materials
Natural material
A natural material is any product or physical matter that comes from plants, animals, or the ground. Minerals and the metals that can be extracted from them are also considered to belong into this category.* Biotic materials...
surrounded by air, the value is always greater than one, n > 1. A refracted ray entering a material from air will be bent towards, but never end up on the same side as the normal. In addition, the science and practice of optical lensing and imaging is based on the knowledge that any material with a refractive index different from its environment will alter the direction of incoming rays which do not arrive in a straight line in relation to the interface (of the material surface and air). Also, lenses have been designed to focus and steer the various spectra of light (EM radiation) in frequency
Frequency
Frequency 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...
ranges from radio
Radio frequency
Radio 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...
to the visible spectra. Furthermore, all known natural occurring materials demonstrate refractive indices that are positive. However, a theoretical work in 1967 showed that a refractive index with negative values is possible and that this does not violate the laws of physics. As discussed previously (above), the first metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
had a range of frequencies over which the refractive index was predicted to be negative for one direction of propagation
Wave propagation
Wave 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....
were reported in May of the year 2000.
In 2001, a team of researcher
Researcher
A researcher is somebody who performs research, the search for knowledge or in general any systematic investigation to establish facts. Researchers can work in academic, industrial, government, or private institutions.-Examples of research institutions:...
s constructed a prism composed of metamaterials (negative index metamaterials) to experimentally test for negative refractive index. The experiment used a waveguide to help transmit the proper frequency and isolate the material.
The experimental demonstration of negative refractive index was followed by another demonstration, in 2003, of a reversal of Snell's law, or reversed refraction. However, in this experiment negative index of refraction material is in free space from 12.6 to 13.2 GHz. Although the radiated frequency range is about the same, a notable distinction is this experiment is conducted in free space rather employing waveguide.
Furthering the authenticity of negative refraction, the power flow of a wave transmitted through a dispersive left-handed material was calculated and compared to a dispersive right-handed material. The transmission of an incident field, composed of many frequencies, from an isotropic nondispersive material into an isotropic dispersive media is employed. The direction of power flow for both nondispersive and dispersive media is determined by the time-averaged
Poynting vector. Negative refraction was shown to be possible for multifrequency signals by explicit calculation of the Poynting vector in the LHM.
Fundamental electromagnetic properties of the NIM
In a slab of conventional material, with an ordinary refractive indexRefractive index
In 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....
– a right-handed material (RHM) – the wave front is transmitted away from the source. In a NIM the wavefront travels toward the source. However, the magnitude and direction of the flow of energy essentially remains the same in both the ordinary material and the NIM. Since, the flow of energy remains the same in both materials (media) the impedance of the NIM matches the RHM. Hence, the sign of the intrinsic impedance is still positive in a NIM.
Light incident on a left-handed material, or NIM, will bend to the same side as the incident beam, and for Snell’s law to hold, the refraction angle should be negative. In a passive metamaterial medium this determines a negative real and imaginary part of the refractive index.
Negative refractive index in left-handed materials
Victor Veselago
Victor 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....
's paper showed that the opposite directions of EM plane waves and the flow of energy was derived from the individual Maxwell curl equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
. In ordinary optical materials, the curl equation for the electric field
Electric field
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...
show a "right hand rule" for the directions of the electric field E, the magnetic induction B, and wave propagation, which goes in the direction of wave vector k
Wave vector
In 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...
. However, the direction of energy flow formed by E × H is right-handed only when permeability is greater than zero. This means that when permeability is less than zero, e.g. negative, wave propagation
Wave propagation
Wave 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 reversed (determined by k), and contrary to the direction of energy flow. Furthermore, the relations of vectors E, H, and k form a "left-handed" system – and it was Veselago who coined the term "left-handed" (LH) material, which is in wide use today (2011). He contended that an LH material has a negative refractive index and relied on the steady-state solutions
Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...
of Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
as a center for his argument.
After a 30 year void, when LH materials were finally demonstrated, it could be said that the designation of negative refractive index is unique to LH systems; even when compared to photonic crystal
Photonic crystal
Photonic 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. Photonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase and group velocities. But, negative refraction does not occur in these systems, and not yet realistically in Photonic crystals.
Negative refraction at visible frequencies
As of May 2010 - In previous years, several anomalous studies have announced negative refraction at one single frequency, or other, in the visible spectrumVisible spectrum
The 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...
. But the results of two such demonstrations are considered ambiguous by later studies. Another most recent, published, demonstration at one single visible frequency is still not the norm, or common, for the large body of work that has been produced in the field of metamaterials. To date, hundreds of scientific, peer review
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...
ed, articles have been published regading some aspect of metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s. This is compared to some minscule number, the studies that have apparent results in the visible spectrum. In an encyclopedia article such as this it is problematic to give undue weight to such studies, until these become common, or part of the norm, for metamaterials.
Moreover, although previous research efforts have announced negative refraction of one single frequency in the visible light spectrum, this most recent (April, 2010) is being reported as "the first one that operates on visible light." Also as before, the stated achievement is for one single frequency in the visible spectrum. In other words there is no broad band ability.
Experimental verification of reversed Cherenkov radiation
Besides reversed values for index of refraction, Veselago predicted the occurrence of reversed Cherenkov radiation (also known simply as CR) in a left-handed medium. In 1934 Pavel Cherenkov discovered a coherent radiation (laser) that occurs when certain types of media are bombarded by fast moving electron beams. In 1937 a theory built around CR stated that when charged particles, such as electrons, travel through a medium at speeds faster than the speed of light in the medium only then will CR radiate. As the CR occurs, electromagnetic radiation is emitted in a cone shape, fanning out in the forward direction.CR and the 1937 theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
has led to a large array of applications in high energy physics. A notable application are the Cherenkov counters. These are used to determine various properties of a charged particle such as its velocity, charge, direction of motion, and energy. These properties are important in the identification of different particles. For example, the counters were applied in the discovery of the anti-proton and the J particle. Six large Cherenkov counters
Cherenkov detector
A Cherenkov detector is a particle detector using the mass-dependent threshold energy of Cherenkov radiation. This allows a discrimination between a lighter particle and a heavier particle ....
were used in the discovery of the J particle.
It has been difficult to experimentally prove the reversed Cherenkov radiation.
Paraxial approximation of DNG slabs
Theoretical work, along with numerical simulations, began early in the decade of the new millennium on the abilities of the DNG slab for subwavelength focusingSuperlens
A 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...
. The research began with Pendry's proposed "Perfect lens". Several research investigations that followed Pendry's concluded that the "Perfect lens" was possible in theory but impractical. One direction in subwavelength focusing proceeded with the use of negative index metamaterials, but based on the enhancements for imaging with surface plasmons. In another direction researchers explored paraxial approximation
Paraxial approximation
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system ....
s of DNG slabs.
US patent on left-handed composite media
The first US patent granted for a fabricated metamaterial is , titled "Left handed composite media." The listed inventors are David R. SmithDavid 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...
, Sheldon Schultz, Norman Kroll, Richard A. Shelby.
The invention achieves simultaneous negative permittivity and permeability over a common band of frequencies. The material can integrate media which is already composite or continuous, but which will produce negative permittivity and permeability within the same spectrum of frequencies. Different types of continuous or composite may be deemed appropriate when combined for the desired effect. However, the inclusion of a periodic array of conducting elements is preferred. The array scatters electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
at wavelengths longer than the size of the element and lattice spacing. The array is then viewed as an effective medium.
Anomalous dispersion
Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium. However the speed of transmitting information is always limited to c.Further reading
- J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett., vol. 76, pp. 4773–4776, June 1996. (Free PDF downloads)
Also see the Preprint copy.
- Slyusar V.I. Metamaterials on antenna solutions. (Free PDF download). International Conference on Antenna Theory and Techniques, 6–9 October 2009, Lviv, Ukraine.
See also
- History of metamaterialsHistory of metamaterialsHistory of metamaterials shares a common history with artificial dielectrics in microwave engineering, as it developed just after World War II. However, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 19th century...
- SuperlensSuperlensA 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...
- Metamaterial cloakingMetamaterial 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....
- Photonic metamaterialsPhotonic 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...
- Metamaterial antennasMetamaterial antennasMetamaterial 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...
- Nonlinear metamaterialsNonlinear metamaterialsA 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...
- Photonic crystalPhotonic 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...
- Seismic metamaterialsSeismic 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...
- Split-ring resonator
- Acoustic metamaterialsAcoustic metamaterialsAcoustic 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...
- Metamaterial absorberMetamaterial absorberA metamaterial absorber manipulates the loss components of the complex effective parameters, permittivity and magnetic permeability of metamaterials, to create a material with particularly high absorption...
- MetamaterialMetamaterialMetamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
- Plasmonic metamaterialsPlasmonic metamaterialsPlasmonic metamaterials are negative index metamaterials that exploit surface plasmons, which are produced from the interaction of light with metal-dielectric materials. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating...
- Terahertz metamaterialsTerahertz metamaterialsTerahertz metamaterials are a new class of composite, artificial materials which interact at terahertz frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz...
- Tunable metamaterialsTunable 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...
- Transformation opticsTransformation opticsTransformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
- Theories of cloaking
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- Academic journals
- Metamaterials (journal)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 (journal)
- Metamaterials books
- Metamaterials HandbookMetamaterials HandbookMetamaterials 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 ExplorationsMetamaterials: Physics and Engineering ExplorationsMetamaterials: 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 Handbook
- Academic journals
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Metamaterials scientists
- John PendryJohn PendrySir 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"...
- David R. SmithDavid R. SmithDavid 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. ZiolkowskiRichard W. ZiolkowskiRichard 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....
- Nader EnghetaNader EnghetaNader Engheta is an Iranian scientist and engineer. He has significantly contributed to novel artificial materials, photonics, nano-structured materials, novel graphene materials, and plasmonics....
Institutional research
The research in the field of Metamaterials has diffused out into the American government science research departments, including the US Naval Air Systems CommandNaval Air Systems Command
The Naval Air Systems Command provides material support for aircraft and airborne weapon systems for the United States Navy. NAVAIR was established in 1966 as the successor to the Navy's Bureau of Naval Weapons . Current Commander, Naval Air Systems Command, is Vice Adm. David Architzel since May...
, US Air Force, and US Army. Many scientific institutions are involved including:
- California Institute of TechnologyCalifornia 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...
- University of Colorado at Colorado SpringsUniversity of Colorado at Colorado SpringsThe University of Colorado Colorado Springs is a campus of the University of Colorado system, the state university system of Colorado....
- Duke UniversityDuke 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...
- Harvard UniversityHarvard 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...
- Helsinki University of TechnologyHelsinki University of TechnologyAalto University School of Science and Technology , was the temporary name for Helsinki University of Technology during the process of forming the Aalto University...
- Iowa State UniversityIowa State UniversityIowa State University of Science and Technology, more commonly known as Iowa State University , is a public land-grant and space-grant research university located in Ames, Iowa, United States. Iowa State has produced astronauts, scientists, and Nobel and Pulitzer Prize winners, along with a host of...
- Imperial College LondonImperial College LondonImperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
- Max Planck SocietyMax Planck SocietyThe 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....
- National Institute of Standards and TechnologyNational Institute of Standards and TechnologyThe National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...
- Nederlandse Organisatie voor Wetenschappelijk OnderzoekNederlandse Organisatie voor Wetenschappelijk OnderzoekThe Nederlandse Organisatie voor Wetenschappelijk Onderzoek is a scientific research organization in the Netherlands....
- University College LondonUniversity College LondonUniversity College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
- University of California, BerkeleyUniversity of California, BerkeleyThe University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
- University of California, IrvineUniversity of California, IrvineThe University of California, Irvine , founded in 1965, is one of the ten campuses of the University of California, located in Irvine, California, USA...
- University of California, Los AngelesUniversity of California, Los AngelesThe 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...
- University of California, San DiegoUniversity of California, San DiegoThe University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
- University of ColoradoUniversity of Colorado SystemThe University of Colorado system is a system of public universities in Colorado consisting of three universities in four campuses: University of Colorado Boulder, University of Colorado Colorado Springs, and University of Colorado Denver in downtown Denver and at the Anschutz Medical Campus in...
- University of RochesterUniversity of RochesterThe University of Rochester is a private, nonsectarian, research university in Rochester, New York, United States. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The university has six schools and various interdisciplinary programs.The...
- Clemson UniversityClemson UniversityClemson University is an American public, coeducational, land-grant, sea-grant, research university located in Clemson, South Carolina, United States....
External links
- Manipulating the Near Field with Metamaterials Slide show, with audio available, by Dr. John Pendry, Imperial College, London
- List of science website news stories on Left Handed Materials