{"history":[],"article":{"id":"157712b5-2355-45ef-ae56-56e801c215df","title":"Negative-index metamaterial","slug":"negative-index-metamaterial","content":":::summary\n:::\n\n# \n**Negative-index [metamaterial](https://bliptext.com/articles/metamaterial)** or **negative-index material** (**NIM**) is a [metamaterial](https://bliptext.com/articles/metamaterial) whose [refractive index](https://bliptext.com/articles/refractive-index) for an [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave) has a negative value over some [frequency](https://bliptext.com/articles/frequency) range.\nNIMs are constructed of periodic basic parts called [unit cells](https://bliptext.com/articles/unit-cell), which are usually significantly smaller than the [wavelength](https://bliptext.com/articles/wavelength) of the externally applied [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation).\nThe unit cells of the first experimentally investigated NIMs were constructed from [circuit board](https://bliptext.com/articles/circuit-board) material, or in other words, wires and [dielectrics](https://bliptext.com/articles/dielectric).\nIn general, these artificially constructed cells are stacked or [planar](https://bliptext.com/articles/plane-geometry) and configured in a particular repeated pattern to compose the individual NIM.\nFor instance, the unit cells of the first NIMs were stacked horizontally and vertically, resulting in a pattern that was repeated and intended (see below images).\nSpecifications for the response of each unit cell are predetermined prior to construction and are based on the intended response of the entire, newly constructed, material.\nIn other words, each cell is individually tuned to respond in a certain way, based on the desired output of the NIM.\nThe aggregate response is mainly determined by each unit cell's geometry and substantially differs from the response of its constituent materials.\nIn other words, the way the NIM responds is that of a new material, unlike the wires or metals and dielectrics it is made from.\nHence, the NIM has become an [effective medium](https://bliptext.com/articles/effective-medium).\nAlso, in effect, this metamaterial has become an “ordered [macroscopic](https://bliptext.com/articles/macroscopic) material, synthesized from the bottom up”, and has emergent properties beyond its components.\nMetamaterials that exhibit a negative value for the [refractive index](https://bliptext.com/articles/refractive-index) are often referred to by any of several terminologies: left-handed media or left-handed material (LHM), backward-wave media (BW media), media with negative [refractive index](https://bliptext.com/articles/refractive-index), double negative (DNG) metamaterials, and other similar names.\n# [A negative-index metamaterial causes light to refract, or bend, differently than in more common positive-index materials such as glass lenses | upload.wikimedia.org/wikipedia/commons/c/c3/Artist%27s///rendition///of///the///new///light-bending///metamaterial.jpg]\n\n# Properties and characteristics\n[Electrodynamics](https://bliptext.com/articles/electrodynamics) of media with negative indices of refraction were first studied by Russian theoretical physicist [Victor Veselago](https://bliptext.com/articles/victor-veselago) from [Moscow Institute of Physics and Technology](https://bliptext.com/articles/moscow-institute-of-physics-and-technology) in 1967.\nThe proposed left-handed or negative-index materials were [theorized](https://bliptext.com/articles/theory) to exhibit [optical properties](https://bliptext.com/articles/classical-optics) opposite to those of [glass](https://bliptext.com/articles/glass), [air](https://bliptext.com/articles/air), and other [transparent media](https://bliptext.com/articles/optical-materials).\nSuch materials were predicted to exhibit counterintuitive properties like bending or refracting light in unusual and unexpected ways.\nHowever, the first practical metamaterial was not constructed until 33 years later and it does support Veselago's concepts.\nCurrently, negative-index metamaterials are being developed to manipulate [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) in new ways.\nFor example, [optical](https://bliptext.com/articles/optical) and [electromagnetic](https://bliptext.com/articles/electromagnetism) properties of natural materials are often altered through [chemistry](https://bliptext.com/articles/chemistry).\nWith metamaterials, optical and electromagnetic properties can be engineered by changing the [geometry](https://bliptext.com/articles/geometry) of its [unit cells](https://bliptext.com/articles/split-ring-resonator).\nThe unit cells are materials that are ordered in geometric arrangements with dimensions that are fractions of the [wavelength](https://bliptext.com/articles/wavelength) of the radiated [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave).\nEach artificial unit responds to the radiation from the source.\nThe collective result is the material's response to the electromagnetic [wave](https://bliptext.com/articles/wave) that is broader than normal.\nSubsequently, transmission is altered by adjusting the shape, size, and configurations of the unit cells.\nThis results in control over material parameters known as [permittivity](https://bliptext.com/articles/permittivity) and [magnetic permeability](https://bliptext.com/articles/magnetic-permeability).\nThese two parameters (or quantities) determine the [propagation](https://bliptext.com/articles/wave-propagation) of electromagnetic waves in [matter](https://bliptext.com/articles/matter).\nTherefore, controlling the values of permittivity and permeability means that the [refractive index](https://bliptext.com/articles/refractive-index) can be negative or zero as well as conventionally positive.\nIt all depends on the intended [application or desired result](https://bliptext.com/articles/metamaterial).\nSo, [optical properties](https://bliptext.com/articles/optics) can be expanded beyond the capabilities of [lenses](https://bliptext.com/articles/lens-optics), mirrors, and other conventional materials.\nAdditionally, one of the effects most studied is the negative index of refraction.\n# [A split-ring resonator array arranged to produce a negative index of refraction, constructed of copper split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3 by 20×20 unit cells with overall dimensions of 10×100×100 millimeters. The height of 10 millimeters measures a little more than six subdivision marks on the ruler, which is marked in inches. | upload.wikimedia.org/wikipedia/commons/8/82/Split-ring///resonator///array///10K///sq///nm.jpg]\n\n## Reverse propagation\nWhen a negative index of refraction occurs, propagation of the [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave) is reversed.\nResolution below the [diffraction limit](https://bliptext.com/articles/diffraction-limit) becomes possible.\nThis is known as [subwavelength imaging](https://bliptext.com/articles/subwavelength-imaging).\nTransmitting a beam of light via an electromagnetically flat surface is another capability.\nIn contrast, [conventional materials](https://bliptext.com/articles/conventional-lens) are usually curved, and cannot achieve resolution below the diffraction limit.\nAlso, reversing the electromagnetic waves in a material, in conjunction with other ordinary materials (including air) could result in minimizing losses that would normally occur.\nThe reverse of the electromagnetic wave, characterized by an antiparallel [phase velocity](https://bliptext.com/articles/phase-velocity) is also an indicator of negative index of refraction.\nFurthermore, negative-index materials are customized composites.\nIn other words, materials are combined with a desired result in mind.\nCombinations of materials can be designed to achieve optical properties not seen in nature.\nThe properties of the composite material stem from its [lattice structure](https://bliptext.com/articles/lattice-structure) constructed from components smaller than the impinging electromagnetic [wavelength](https://bliptext.com/articles/wavelength) separated by distances that are also smaller than the impinging electromagnetic [wavelength](https://bliptext.com/articles/wavelength).\nLikewise, by fabricating such metamaterials researchers are trying to overcome fundamental limits tied to the [wavelength](https://bliptext.com/articles/wavelength) of [light](https://bliptext.com/articles/light).\nThe unusual and counterintuitive properties currently have practical and commercial use manipulating electromagnetic [microwaves](https://bliptext.com/articles/microwave) in [wireless and communication systems](https://bliptext.com/articles/metamaterial-antenna).\nLastly, research continues in the other domains of the [electromagnetic spectrum](https://bliptext.com/articles/electromagnetic-spectrum), including [visible light](https://bliptext.com/articles/visible-light).\n\n# Materials\nThe first actual metamaterials worked in the [microwave](https://bliptext.com/articles/microwave) regime, or centimeter [wavelengths](https://bliptext.com/articles/wavelengths), of the [electromagnetic spectrum](https://bliptext.com/articles/electromagnetic-spectrum) (about 4.3 GHz).\nIt was constructed of [split-ring resonators](https://bliptext.com/articles/split-ring-resonator) and conducting straight wires (as unit cells).\nThe unit cells were sized from 7 to 10 [millimeters](https://bliptext.com/articles/millimeters).\nThe unit cells were arranged in a two-dimensional ([periodic](https://bliptext.com/articles/periodic-function)) repeating pattern which produces a [crystal-like](https://bliptext.com/articles/crystal) geometry.\nBoth the unit cells and the [lattice spacing](https://bliptext.com/articles/lattice-spacing) were smaller than the radiated electromagnetic wave.\nThis produced the first left-handed material when both the permittivity and permeability of the material were negative.\nThis system relies on the [resonant](https://bliptext.com/articles/resonance) behavior of the unit cells.\nBelow a group of researchers develop an idea for a left-handed metamaterial that does not rely on such resonant behavior.\nResearch in the microwave range continues with split-ring resonators and conducting wires.\nResearch also continues in the shorter wavelengths with this configuration of materials and the unit cell sizes are scaled down.\nHowever, at around [200 terahertz](https://bliptext.com/articles/terahertz-unit) issues arise which make using the split ring resonator problematic.\n\"Alternative materials become more suitable for the terahertz and optical regimes.\"\nAt these wavelengths selection of materials and size limitations become important.\nFor example, in 2007 a 100 nanometer mesh wire design made of silver and woven in a repeating pattern transmitted beams at the 780 nanometer wavelength, the far end of the visible spectrum.\nThe researchers believe this produced a negative refraction of 0.6.\nNevertheless, this operates at only a single wavelength like its predecessor metamaterials in the microwave regime.\nHence, the challenges are to fabricate metamaterials so that they \"refract light at ever-smaller wavelengths\" and to develop broad band capabilities.\n\n## Artificial transmission-line-media\nIn the [metamaterial literature](https://bliptext.com/articles/scientific-journal), medium or media refers to [transmission medium](https://bliptext.com/articles/transmission-medium) or [optical medium](https://bliptext.com/articles/optical-medium).\nIn 2002, a group of researchers came up with the idea that in contrast to materials that depended on resonant behavior, non-resonant [phenomena](https://bliptext.com/articles/phenomena) could surpass narrow [bandwidth](https://bliptext.com/articles/bandwidth-signal-processing) constraints of the wire/[split-ring resonator](https://bliptext.com/articles/split-ring-resonator) configuration.\nThis idea translated into a type of medium with broader bandwidth abilities, [negative refraction](https://bliptext.com/articles/negative-refraction), backward waves, and [focusing](https://bliptext.com/articles/superlens) beyond the [diffraction limit](https://bliptext.com/articles/diffraction-limit).\nThey dispensed with split-ring-resonators and instead used a network of [L–C loaded](https://bliptext.com/articles/l-c-loaded) transmission lines.\nIn metamaterial literature this became known as artificial [transmission-line](https://bliptext.com/articles/transmission-line) media.\nAt that time it had the added advantage of being more compact than a unit made of wires and split ring resonators.\nThe network was both scalable (from the [megahertz](https://bliptext.com/articles/megahertz) to the tens of [gigahertz](https://bliptext.com/articles/gigahertz) range) and tunable.\nIt also includes a method for focusing the [wavelengths of interest](https://bliptext.com/articles/frequency).\nBy 2007 the negative refractive index transmission line was employed as a subwavelength focusing free-space flat lens.\nThat this is a free-space lens is a significant advance.\nPart of prior research efforts targeted creating a lens that did not need to be embedded in a transmission line.\n# [500px | upload.wikimedia.org/wikipedia/commons/8/86/Artificial///transmission-line-media.png]\n\n## The optical domain\nMetamaterial components shrink as research explores shorter wavelengths (higher frequencies) of the [electromagnetic spectrum](https://bliptext.com/articles/electromagnetic-spectrum) in the [infrared](https://bliptext.com/articles/infrared) and [visible spectrums](https://bliptext.com/articles/visible-spectrum).\nFor example, theory and experiment have investigated smaller horseshoe shaped split ring resonators designed with [lithographic](https://bliptext.com/articles/lithographic) techniques, as well as paired [metal nanorods](https://bliptext.com/articles/nanorod) or nanostrips, and nanoparticles as circuits designed with [lumped element models](https://bliptext.com/articles/lumped-element-model)\n\n# Applications\nThe science of negative-index materials is being matched with conventional devices that broadcast, transmit, shape, or receive electromagnetic signals that travel over cables, wires, or air.\nThe materials, devices and systems that are involved with this work could have their properties altered or heightened.\nHence, this is already happening with [metamaterial antennas](https://bliptext.com/articles/metamaterial-antenna) and related devices which are commercially available.\nMoreover, in the [wireless domain](https://bliptext.com/articles/wireless-technology) these metamaterial apparatuses continue to be researched.\nOther applications are also being researched.\nThese are [electromagnetic absorbers](https://bliptext.com/articles/metamaterial-absorber) such as [radar-microwave](https://bliptext.com/articles/radar) absorbers, electrically small [resonators](https://bliptext.com/articles/resonator), [waveguides](https://bliptext.com/articles/waveguide) that can go beyond the [diffraction limit](https://bliptext.com/articles/diffraction-limit), [phase compensators](https://bliptext.com/articles/metamaterial-antenna), advancements in focusing devices (e.g. [microwave lens](https://bliptext.com/articles/artificial-dielectrics)), and improved electrically small antennas.\nIn the [optical](https://bliptext.com/articles/optic) frequency regime developing the [superlens](https://bliptext.com/articles/superlens) may allow for imaging below the [diffraction limit](https://bliptext.com/articles/diffraction-limit).\nOther potential applications for negative-index metamaterials are optical [nanolithography](https://bliptext.com/articles/nanolithography), [nanotechnology](https://bliptext.com/articles/nanotechnology) circuitry, as well as a near field superlens (Pendry, 2000) that could be useful for biomedical imaging and subwavelength photolithography.\n\n# Manipulating permittivity and permeability\nTo describe any [electromagnetic](https://bliptext.com/articles/electromagnetism) properties of a given achiral material such as an [optical lens](https://bliptext.com/articles/optical-lens), there are two significant parameters.\nThese are [permittivity](https://bliptext.com/articles/permittivity), \\epsilon_r, and [permeability](https://bliptext.com/articles/magnetic-permeability), \\mu_r, which allow accurate prediction of light [waves traveling](https://bliptext.com/articles/wave-propagation) within materials, and [electromagnetic phenomena](https://bliptext.com/articles/phenomena) that occur at the [interface](https://bliptext.com/articles/interface-chemistry) between two materials.\nFor example, [refraction](https://bliptext.com/articles/refraction) is an electromagnetic phenomenon which occurs at the interface between two materials.\n[Snell's law](https://bliptext.com/articles/snell-s-law) states that the relationship between the angle of incidence of a beam of [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) (light) and the resulting angle of refraction rests on the refractive indices, n, of the two media (materials).\nThe refractive index of an achiral medium is given by.\nHence, it can be seen that the refractive index is dependent on these two parameters.\nTherefore, if designed or arbitrarily modified values can be inputs for \\epsilon_r and \\mu_r, then the behavior of propagating electromagnetic waves inside the material can be manipulated at will.\nThis ability then allows for intentional determination of the refractive index.\nFor example, in 1967, [Victor Veselago](https://bliptext.com/articles/victor-veselago) analytically determined that light will refract in the reverse direction (negatively) at the interface between a material with negative [refractive index](https://bliptext.com/articles/refractive-index) and a material exhibiting conventional positive [refractive index](https://bliptext.com/articles/refractive-index).\nThis extraordinary material was realized on paper with simultaneous negative values for \\epsilon_r and \\mu_r, and could therefore be termed a double negative material.\nHowever, in Veselago's day a material which exhibits double negative parameters simultaneously seemed impossible because no natural materials exist which can produce this effect.\nTherefore, his work was ignored for three decades.\nIt was nominated for the Nobel Prize later.\nIn general the [physical properties](https://bliptext.com/articles/physical-properties) of [natural materials](https://bliptext.com/articles/natural-material) cause limitations.\nMost [dielectrics](https://bliptext.com/articles/dielectric) only have positive permittivities, \\epsilon_r > 0.\nMetals will exhibit negative permittivity, \\epsilon_r < 0 at optical frequencies, and plasmas exhibit negative permittivity values in certain frequency bands.\nPendry et al. demonstrated that the [plasma frequency](https://bliptext.com/articles/plasma-frequency) can be made to occur in the lower [microwave](https://bliptext.com/articles/microwave) frequencies for metals with a material made of metal rods that replaces the [bulk metal](https://bliptext.com/articles/metal).\nHowever, in each of these cases permeability remains always positive.\nAt microwave frequencies it is possible for negative μ to occur in some [ferromagnetic](https://bliptext.com/articles/ferromagnetic) materials.\nBut the inherent drawback is they are difficult to find above [terahertz](https://bliptext.com/articles/terahertz-radiation) frequencies.\nIn any case, a natural material that can achieve negative values for permittivity and permeability simultaneously has not been found or discovered.\nHence, all of this has led to constructing artificial composite materials known as metamaterials in order to achieve the desired results.\n# [Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal. | upload.wikimedia.org/wikipedia/commons/d/d1/Snells///law.svg]\n\n# Negative index of refraction due to chirality\nIn case of [chiral](https://bliptext.com/articles/chirality-electromagnetism) materials, the refractive index n depends not only on permittivity \\epsilon_r and permeability \\mu_r, but also on the [chiral](https://bliptext.com/articles/chirality-electromagnetism)ity parameter \\kappa, resulting in distinct values for left and right circularly polarized waves, given by\nA negative index will occur for waves of one circular polarization if \\kappa >.\nIn this case, it is not necessary that either or both \\epsilon_r and \\mu_r be negative to achieve a negative index of refraction.\nA negative refractive index due to chirality was predicted by Pendry and Tretyakov et al., and first observed simultaneously and independently by Plum et al. and Zhang et al. in 2009.\n\n# Physical properties never before produced in nature\nTheoretical articles were published in 1996 and 1999 which showed that synthetic materials could be constructed to purposely exhibit a negative [permittivity](https://bliptext.com/articles/permittivity) and [permeability](https://bliptext.com/articles/magnetic-permeability).\nThese papers, along with [Veselago's](https://bliptext.com/articles/victor-veselago) 1967 theoretical analysis of the properties of negative-index materials, provided the background to fabricate a [metamaterial](https://bliptext.com/articles/metamaterial) with negative effective permittivity and permeability.\nSee below.\nA [metamaterial](https://bliptext.com/articles/metamaterial) developed to exhibit negative-index behavior is typically formed from individual components.\nEach component responds differently and independently to a radiated [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave) as it travels through the material.\nSince these components are smaller than the radiated [wavelength](https://bliptext.com/articles/wavelength) it is understood that a [macroscopic](https://bliptext.com/articles/macroscopic) view includes an [effective value](https://bliptext.com/articles/effective-medium-model) for both permittivity and permeability.\n\n## Composite material\nIn the year 2000, [David R. Smith](https://bliptext.com/articles/david-r-smith-physicist)'s team of [UCSD](https://bliptext.com/articles/ucsd) researchers produced a new class of [composite materials](https://bliptext.com/articles/composite-material) by depositing a structure onto a circuit-board substrate consisting of a series of thin copper split-rings and ordinary wire segments strung parallel to the rings.\nThis material exhibited unusual [physical properties](https://bliptext.com/articles/physics) that had never been observed in nature.\nThese materials obey the [laws of physics](https://bliptext.com/articles/laws-of-physics), but behave differently from normal materials.\nIn essence these negative-index metamaterials were noted for having the ability to reverse many of the [physical properties](https://bliptext.com/articles/physical-properties) that govern the behavior of ordinary optical materials.\nOne of those unusual properties is the ability to reverse, for the first time, [Snell's law](https://bliptext.com/articles/snell-s-law) of refraction.\nUntil the demonstration of negative refractive index for microwaves by the UCSD team, the material had been unavailable.\nAdvances during the 1990s in fabrication and computation abilities allowed these first [metamaterials](https://bliptext.com/articles/metamaterial) to be constructed.\nThus, the \"new\" metamaterial was tested for the effects described by [Victor Veselago](https://bliptext.com/articles/victor-veselago) 30 years earlier.\nStudies of this experiment, which followed shortly thereafter, announced that other effects had occurred.\nWith [antiferromagnets](https://bliptext.com/articles/antiferromagnet) and certain types of insulating [ferromagnets](https://bliptext.com/articles/ferromagnet), effective negative [magnetic permeability](https://bliptext.com/articles/magnetic-permeability) is achievable when [polariton](https://bliptext.com/articles/polariton) resonance exists.\nTo achieve a negative index of refraction, however, permittivity with negative values must occur within the same frequency range.\nThe artificially fabricated [split-ring resonator](https://bliptext.com/articles/split-ring-resonator) is a design that accomplishes this, along with the promise of dampening high losses.\nWith this first introduction of the metamaterial, it appears that the losses incurred were smaller than antiferromagnetic, or ferromagnetic materials.\nWhen first demonstrated in 2000, the composite material (NIM) was limited to transmitting [microwave radiation](https://bliptext.com/articles/microwave) at frequencies of 4 to 7 [gigahertz](https://bliptext.com/articles/gigahertz) (4.28–7.49 cm wavelengths).\nThis range is between the frequency of household microwave ovens ([~2.45](https://bliptext.com/articles/ism-band) [GHz](https://bliptext.com/articles/ghz), 12.23 cm) and military [radars](https://bliptext.com/articles/radars) (~10 [GHz](https://bliptext.com/articles/ghz), 3 cm).\nAt demonstrated frequencies, pulses of [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) moving through the material in one direction are composed of constituent waves moving in the opposite direction.\nThe metamaterial was constructed as a [periodic array](https://bliptext.com/articles/periodic-function) of [copper](https://bliptext.com/articles/copper) split ring and wire conducting elements deposited onto a circuit-board substrate.\nThe design was such that the cells, and the [lattice spacing](https://bliptext.com/articles/lattice-spacing) between the cells, were much smaller than the radiated [electromagnetic wavelength](https://bliptext.com/articles/wavelength).\nHence, it behaves as an [effective medium](https://bliptext.com/articles/effective-medium-model).\nThe material has become notable because its range of (effective) [permittivity](https://bliptext.com/articles/permittivity) εeff and [permeability](https://bliptext.com/articles/magnetic-permeability) μeff values have exceeded those found in any ordinary material.\nFurthermore, the characteristic of negative (effective) permeability evinced by this medium is particularly notable, because it has not been found in ordinary materials.\nIn addition, the negative values for the magnetic component is directly related to its left-handed nomenclature, and properties (discussed in a section below).\nThe [split-ring resonator](https://bliptext.com/articles/split-ring-resonator) (SRR), based on the prior 1999 theoretical article, is the tool employed to achieve negative permeability.\nThis first composite metamaterial is then composed of split-ring resonators and electrical conducting posts.\nInitially, these materials were only demonstrated at wavelengths longer than those in the [visible spectrum](https://bliptext.com/articles/visible-spectrum).\nIn addition, early NIMs were fabricated from [opaque](https://bliptext.com/articles/opacity-optics) materials and usually made of non-magnetic constituents.\nAs an illustration, however, if these materials are constructed at [visible frequencies](https://bliptext.com/articles/visible-frequencies), and a [flashlight](https://bliptext.com/articles/flash[light](https://bliptext.com/articles/light)) is shone onto the resulting NIM slab, the material should focus the [light](https://bliptext.com/articles/light) at a point on the other side.\nThis is not possible with a sheet of ordinary opaque material.\nIn 2007, the [NIST](https://bliptext.com/articles/nist) in collaboration with the [Atwater](https://bliptext.com/articles/harry-atwater) Lab at [Caltech](https://bliptext.com/articles/caltech) created the first NIM active at optical frequencies.\nMore recently, layered \"fishnet\" NIM materials made of silicon and silver wires have been integrated into optical fibers to create active optical elements.\n\n## Simultaneous negative permittivity and permeability\nNegative permittivity εeff < 0 had already been discovered and realized in metals for frequencies all the way up to the [plasma frequency](https://bliptext.com/articles/plasma-frequency), before the first metamaterial.\nThere are two [requirements](https://bliptext.com/articles/requirements) to achieve a negative value for [refraction](https://bliptext.com/articles/refraction).\nFirst, is to fabricate a material which can produce negative permeability μeff < 0.\nSecond, negative values for both permittivity and permeability must occur simultaneously over a common range of frequencies.\nTherefore, for the first metamaterial, the nuts and bolts are one [split-ring resonator](https://bliptext.com/articles/split-ring-resonator) electromagnetically combined with one (electric) conducting post.\nThese are designed to resonate at designated frequencies to achieve the desired values.\nLooking at the make-up of the split ring, the associated [magnetic field](https://bliptext.com/articles/magnetic-field) pattern from the SRR is [dipolar](https://bliptext.com/articles/dipolar).\nThis dipolar behavior is notable because this means it mimics nature's [atom](https://bliptext.com/articles/atom), but on a much larger scale, such as in this case at 2.5 [millimeters](https://bliptext.com/articles/millimeter).\nAtoms exist on the scale of [picometers](https://bliptext.com/articles/picometer).\nThe splits in the rings create a [dynamic](https://bliptext.com/articles/dynamics-physics) where the SRR unit cell can be made [resonant](https://bliptext.com/articles/resonant) at [radiated wavelengths](https://bliptext.com/articles/em-radiation) much larger than the [diameter](https://bliptext.com/articles/diameter) of the rings.\nIf the rings were closed, a half wavelength boundary would be [electromagnetically](https://bliptext.com/articles/electromagnet) imposed as a requirement for [resonance](https://bliptext.com/articles/resonance).\nThe split in the second ring is oriented opposite to the split in the first ring.\nIt is there to generate a large [capacitance](https://bliptext.com/articles/capacitance), which occurs in the small gap.\nThis capacitance substantially decreases the resonant frequency while concentrating the [electric field](https://bliptext.com/articles/electric-field).\nThe individual SRR depicted on the right had a resonant frequency of [4.845 GHz](https://bliptext.com/articles/microwave), and the resonance curve, inset in the graph, is also shown.\nThe radiative losses from [absorption](https://bliptext.com/articles/absorption-electromagnetic-radiation) and [reflection](https://bliptext.com/articles/reflection-physics) are noted to be small, because the unit dimensions are much smaller than the [free space](https://bliptext.com/articles/free-space), radiated [wavelength](https://bliptext.com/articles/wavelength).\nWhen these units or cells are combined into a [periodic arrangement](https://bliptext.com/articles/split-ring-resonator), the [magnetic coupling](https://bliptext.com/articles/magnetic-coupling) between the resonators is strengthened, and a strong [magnetic coupling](https://bliptext.com/articles/magnetic-coupling) occurs.\nProperties unique in comparison to ordinary or conventional materials begin to emerge.\nFor one thing, this periodic strong coupling creates a material, which now has an effective magnetic permeability μeff in response to the [radiated-incident](https://bliptext.com/articles/physical-optics) magnetic field.\n\n## Composite material passband\nGraphing the general [dispersion curve](https://bliptext.com/articles/dispersion-optics), a region of [propagation](https://bliptext.com/articles/wave-propagation) occurs from zero up to a lower [band edge](https://bliptext.com/articles/frequency-band), followed by a gap, and then an upper [passband](https://bliptext.com/articles/passband).\nThe presence of a [400 MHz](https://bliptext.com/articles/mhz) gap between [4.2 GHz and 4.6 GHz](https://bliptext.com/articles/microwave) implies a band of frequencies where μeff < 0 occurs.\n(Please see the image in the previous section)\nFurthermore, when wires are added [symmetrically](https://bliptext.com/articles/symmetric) between the split rings, a [passband](https://bliptext.com/articles/passband) occurs within the previously [forbidden band](https://bliptext.com/articles/forbidden-band) of the split ring dispersion curves.\nThat 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, which fits with theoretical predictions.\nMathematically, the dispersion relation leads to a band with negative [group velocity](https://bliptext.com/articles/group-velocity) everywhere, and a bandwidth that is independent of the [plasma frequency](https://bliptext.com/articles/plasma-frequency), within the stated conditions.\n[Mathematical modeling](https://bliptext.com/articles/mathematical-modeling) and experiment have both shown that periodically arrayed conducting elements (non-magnetic by nature) respond predominantly to the [magnetic component](https://bliptext.com/articles/magnetic-field) of [incident electromagnetic fields](https://bliptext.com/articles/physical-optics).\nThe result is an effective medium and negative μeff over a band of frequencies.\nThe permeability was verified to be the region of the forbidden band, where the gap in propagation occurred – from a finite section of material.\nThis 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.\nThis validated predictions.\nIn addition, a later work determined that this first [metamaterial](https://bliptext.com/articles/metamaterial) had a range of frequencies over which the refractive index was predicted to be negative for one direction of [propagation](https://bliptext.com/articles/wave-propagation) (see ref # ).\nOther predicted [electrodynamic](https://bliptext.com/articles/electrodynamic) effects were to be investigated in other research.\n\n## Describing a left-handed material\nFrom the conclusions in the above section a left-handed material (LHM) can be defined.\nIt is a material which exhibits simultaneous [negative values](https://bliptext.com/articles/negative-numbers) for [permittivity](https://bliptext.com/articles/permittivity), ε, and [permeability](https://bliptext.com/articles/magnetic-permeability), μ, in an overlapping frequency region.\nSince the values are derived from the effects of the [composite medium system](https://bliptext.com/articles/metamaterial) as a whole, these are defined as effective permittivity, εeff, and effective permeability, μeff.\nReal values are then derived to denote the value of [negative index](https://bliptext.com/articles/negative-refractive-index) of refraction, and [wave vectors](https://bliptext.com/articles/wave-vector).\nThis means that in practice losses will occur for a given medium used to [transmit](https://bliptext.com/articles/transmission-coefficient) electromagnetic radiation such as [microwave](https://bliptext.com/articles/microwave), or [infrared](https://bliptext.com/articles/infrared) frequencies, or [visible light](https://bliptext.com/articles/visible-light) – for example.\nIn this instance, real values describe either the [amplitude](https://bliptext.com/articles/amplitude) or the [intensity](https://bliptext.com/articles/intensity-physics) of a transmitted wave relative to an incident wave, while ignoring the negligible loss values.\n# [A comparison of refraction in a negative-index metamaterial to that in a conventional material having the same, but positive refractive index. The incident beam θ enters from air and refracts in a normal (θ') or metamaterial (-θ'). | upload.wikimedia.org/wikipedia/commons/1/15/metarefraction.svg]\n\n# Isotropic negative index in two dimensions\nIn the above sections first fabricated [metamaterial](https://bliptext.com/articles/metamaterial) was constructed with [resonating elements](https://bliptext.com/articles/resonate), which exhibited one direction of [incidence](https://bliptext.com/articles/angle-of-incidence-optics) and [polarization](https://bliptext.com/articles/polarization-waves).\nIn other words, this structure exhibited left-handed propagation in one dimension.\nThis was discussed in relation to Veselago's seminal work 33 years earlier (1967).\nHe predicted that intrinsic to a material, which manifests negative values of effective [permittivity](https://bliptext.com/articles/permittivity) and [permeability](https://bliptext.com/articles/magnetic-permeability), are several types of reversed [physics phenomena](https://bliptext.com/articles/physical-property).\nHence, there was then a critical need for a higher-dimensional LHMs to confirm Veselago's theory, as expected.\nThe confirmation would include reversal of [Snell's law](https://bliptext.com/articles/snell-s-law) (index of refraction), along with other reversed phenomena.\nIn the beginning of 2001 the existence of a higher-dimensional structure was reported.\nIt was two-dimensional and demonstrated by both experiment and numerical confirmation.\nIt was an [LHM](https://bliptext.com/articles/), a composite constructed of wire strips mounted behind the split-ring resonators (SRRs) in a periodic configuration.\nIt was created for the express purpose of being suitable for further experiments to produce the effects predicted by Veselago.\n\n# Experimental verification of a negative index of refraction\nA theoretical work published in 1967 by Soviet physicist Victor Veselago showed that a refractive index with negative values is possible and that this does not violate the laws of physics.\nAs discussed previously (above), the first [metamaterial](https://bliptext.com/articles/metamaterial) had a range of frequencies over which the refractive index was predicted to be negative for one direction of [propagation](https://bliptext.com/articles/wave-propagation).\nIt was reported in May 2000.\nIn 2001, a team of [researchers](https://bliptext.com/articles/researcher) constructed a prism composed of metamaterials (negative-index metamaterials) to experimentally test for negative refractive index.\nThe experiment used a waveguide to help transmit the proper frequency and isolate the material.\nThis test achieved its goal because it successfully verified a negative index of refraction.\nThe experimental demonstration of negative refractive index was followed by another demonstration, in 2003, of a reversal of Snell's law, or reversed refraction.\nHowever, in this experiment negative index of refraction material is in free space from 12.6 to 13.2 GHz.\nAlthough the radiated frequency range is about the same, a notable distinction is this experiment is conducted in free space rather than employing waveguides.\nFurthering 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.\nThe transmission of an incident field, composed of many frequencies, from an isotropic nondispersive material into an isotropic dispersive media is employed.\nThe direction of power flow for both nondispersive and dispersive media is determined by the time-averaged\n[Poynting vector](https://bliptext.com/articles/poynting-vector).\nNegative refraction was shown to be possible for multiple frequency signals by explicit calculation of the Poynting vector in the LHM.\n# [Split-ring resonator consisting of an inner square with a split on one side embedded in an outer square with a split on the other side. Split-ring resonators are on the front and right surfaces of the square grid, and single vertical wires are on the back and left surfaces. | upload.wikimedia.org/wikipedia/commons/f/fb/Left-handed///metamaterial///array///configuration.jpg]\n\n## Fundamental electromagnetic properties of the NIM\nIn a slab of conventional material with an ordinary [refractive index](https://bliptext.com/articles/refractive-index) – a right-handed material (RHM) – the [wave front](https://bliptext.com/articles/wave-front) is transmitted away from the source.\nIn a NIM the wavefront travels toward the source.\nHowever, the magnitude and direction of the flow of energy essentially remains the same in both the ordinary material and the NIM.\nSince the flow of energy remains the same in both materials (media), the impedance of the NIM matches the RHM.\nHence, the sign of the intrinsic impedance is still positive in a NIM.\nLight 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.\nIn a passive metamaterial medium this determines a negative real and imaginary part of the refractive index.\n\n## Negative refractive index in left-handed materials\nIn 1968 [Victor Veselago](https://bliptext.com/articles/victor-veselago)'s paper showed that the opposite directions of EM [plane waves](https://bliptext.com/articles/plane-waves) and the flow of energy was derived from the individual [Maxwell curl equations](https://bliptext.com/articles/maxwell-s-equations).\nIn ordinary [optical](https://bliptext.com/articles/optical) materials, the curl equation for the [electric field](https://bliptext.com/articles/electric-field) show a \"right hand rule\" for the directions of the [electric field](https://bliptext.com/articles/electric-field) **E**, the magnetic induction **B**, and wave propagation, which goes in the direction of wave vector **k**.\nHowever, the direction of energy flow formed by E × H is right-handed only when permeability is greater than zero.\nThis means that when permeability is less than zero, e.g. negative, [wave propagation](https://bliptext.com/articles/wave-propagation) is reversed (determined by k), and contrary to the direction of energy flow.\nFurthermore, 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).\nHe contended that an LH material has a negative refractive index and relied on the [steady-state solutions](https://bliptext.com/articles/steady-state) of [Maxwell's equations](https://bliptext.com/articles/maxwell-s-equations) as a center for his argument.\nAfter a 30-year void, when LH materials were finally demonstrated, it could be said that the designation of [negative refractive index](https://bliptext.com/articles/negative-refractive-index) is unique to LH systems; even when compared to [photonic crystals](https://bliptext.com/articles/photonic-crystal).\nPhotonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase and group velocities.\nBut, negative refraction does not occur in these systems, and not yet realistically in photonic crystals.\n# [The left-handed orientation is shown on the left, and the right-handed on the right. | upload.wikimedia.org/wikipedia/commons/e/e2/Cartesian///coordinate///system///handedness.svg]\n\n## Negative refraction at optical frequencies\nThe negative refractive index in the optical range was first demonstrated in 2005 by [Shalaev](https://bliptext.com/articles/shalaev) et al. (at the telecom wavelength λ = 1.5 μm) and by Brueck et al. (at λ = 2 μm) at nearly the same time.\nIn 2006, a Caltech team led by Lezec, Dionne, and Atwater achieved negative refraction in the [visible spectral regime](https://bliptext.com/articles/visible-spectral-regime).\n\n# Reversed Cherenkov radiation\nBesides reversed values for the [index of refraction](https://bliptext.com/articles/index-of-refraction), Veselago predicted the occurrence of reversed [Cherenkov radiation](https://bliptext.com/articles/cherenkov-radiation) in a left-handed medium.\nWhereas ordinary Cherenkov radiation is emitted in a cone around the direction in which a charged particle is travelling through the medium, reversed Cherenkov radiation is emitted in a cone around the opposite direction.\nReversed Cherenkov radiation was first experimentally demonstrated indirectly in 2009, using a phased electromagnetic dipole array to model a moving charged particle.\nReversed Cherenkov radiation emitted by actual charged particles was first observed in 2017.\n\n# Other optics with NIMs\nTheoretical work, along with [numerical simulations](https://bliptext.com/articles/numerical-simulation), began in the early 2000s on the abilities of DNG slabs for [subwavelength focusing](https://bliptext.com/articles/superlens).\nThe research began with Pendry's proposed \"[Perfect lens](https://bliptext.com/articles/perfect-lens).\"\nSeveral research investigations that followed Pendry's concluded that the \"Perfect lens\" was possible in theory but impractical.\nOne direction in subwavelength focusing proceeded with the use of negative-index metamaterials, but based on the enhancements for imaging with surface plasmons.\nIn another direction researchers explored [paraxial approximations](https://bliptext.com/articles/paraxial-approximation) of NIM slabs.\n\n# Implications of negative refractive materials\nThe existence of negative refractive materials can result in a change in [electrodynamic](https://bliptext.com/articles/electrodynamic) calculations for the case of permeability μ = 1.\nA change from a conventional refractive index to a negative value gives incorrect results for conventional calculations, because some properties and effects have been altered.\nWhen permeability μ has values other than 1 this affects [Snell's law](https://bliptext.com/articles/snell-s-law), the [Doppler effect](https://bliptext.com/articles/doppler-effect), the [Cherenkov radiation](https://bliptext.com/articles/cherenkov-radiation), [Fresnel's equations](https://bliptext.com/articles/fresnel-s-equations), and [Fermat's principle](https://bliptext.com/articles/fermat-s-principle).\nThe [refractive index](https://bliptext.com/articles/refractive-index) is basic to the science of optics.\nShifting the refractive index to a negative value may be a cause to revisit or reconsider the interpretation of some [norms](https://bliptext.com/articles/convention-norm), or [basic laws](https://bliptext.com/articles/optics).\n\n# US patent on left-handed composite media\nThe first US patent for a fabricated metamaterial, titled \"Left handed composite media\" by [David R. Smith](https://bliptext.com/articles/david-r-smith-physicist), [Sheldon Schultz](https://bliptext.com/articles/sheldon-schultz), [Norman Kroll](https://bliptext.com/articles/norman-kroll) and [Richard A. Shelby](https://bliptext.com/articles/richard-a-shelby), was issued in 2004.\nThe invention achieves simultaneous negative permittivity and permeability over a common band of frequencies.\nThe material can integrate media which is already composite or continuous, but which will produce negative permittivity and permeability within the same spectrum of frequencies.\nDifferent types of continuous or composite may be deemed appropriate when combined for the desired effect.\nHowever, the inclusion of a periodic array of conducting elements is preferred.\nThe array scatters [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) at [wavelengths](https://bliptext.com/articles/wavelengths) longer than the size of the element and lattice spacing.\nThe array is then viewed as an [effective medium](https://bliptext.com/articles/effective-medium).","current_revision":null,"created_by":"kACnuQmH5k9Nr5VNVEpVeg7XpvUmMctD","created_at":"2025-01-26T12:04:10.960Z","updated_at":"2025-01-26T12:04:10.960Z","search_vector":"'index':3 'metamateri':4 'negat':2 'negative-index':1","search_content":" \n \n\n# \n**Negative-index [metamaterial](https://bliptext.com/articles/metamaterial)** or **negative-index material** (**NIM**) is a [metamaterial](https://bliptext.com/articles/metamaterial) whose [refractive index](https://bliptext.com/articles/refractive-index) for an [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave) has a negative value over some [frequency](https://bliptext.com/articles/frequency) range.\nNIMs are constructed of periodic basic parts called [unit cells](https://bliptext.com/articles/unit-cell), which are usually significantly smaller than the [wavelength](https://bliptext.com/articles/wavelength) of the externally applied [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation).\nThe unit cells of the first experimentally investigated NIMs were constructed from [circuit board](https://bliptext.com/articles/circuit-board) material, or in other words, wires and [dielectrics](https://bliptext.com/articles/dielectric).\nIn general, these artificially constructed cells are stacked or [planar](https://bliptext.com/articles/plane-geometry) and configured in a particular repeated pattern to compose the individual NIM.\nFor instance, the unit cells of the first NIMs were stacked horizontally and vertically, resulting in a pattern that was repeated and intended (see below images).\nSpecifications for the response of each unit cell are predetermined prior to construction and are based on the intended response of the entire, newly constructed, material.\nIn other words, each cell is individually tuned to respond in a certain way, based on the desired output of the NIM.\nThe aggregate response is mainly determined by each unit cell's geometry and substantially differs from the response of its constituent materials.\nIn other words, the way the NIM responds is that of a new material, unlike the wires or metals and dielectrics it is made from.\nHence, the NIM has become an [effective medium](https://bliptext.com/articles/effective-medium).\nAlso, in effect, this metamaterial has become an “ordered [macroscopic](https://bliptext.com/articles/macroscopic) material, synthesized from the bottom up”, and has emergent properties beyond its components.\nMetamaterials that exhibit a negative value for the [refractive index](https://bliptext.com/articles/refractive-index) are often referred to by any of several terminologies: left-handed media or left-handed material (LHM), backward-wave media (BW media), media with negative [refractive index](https://bliptext.com/articles/refractive-index), double negative (DNG) metamaterials, and other similar names.\n# [A negative-index metamaterial causes light to refract, or bend, differently than in more common positive-index materials such as glass lenses | upload.wikimedia.org/wikipedia/commons/c/c3/Artist%27s///rendition///of///the///new///light-bending///metamaterial.jpg]\n\n# Properties and characteristics\n[Electrodynamics](https://bliptext.com/articles/electrodynamics) of media with negative indices of refraction were first studied by Russian theoretical physicist [Victor Veselago](https://bliptext.com/articles/victor-veselago) from [Moscow Institute of Physics and Technology](https://bliptext.com/articles/moscow-institute-of-physics-and-technology) in 1967.\nThe proposed left-handed or negative-index materials were [theorized](https://bliptext.com/articles/theory) to exhibit [optical properties](https://bliptext.com/articles/classical-optics) opposite to those of [glass](https://bliptext.com/articles/glass), [air](https://bliptext.com/articles/air), and other [transparent media](https://bliptext.com/articles/optical-materials).\nSuch materials were predicted to exhibit counterintuitive properties like bending or refracting light in unusual and unexpected ways.\nHowever, the first practical metamaterial was not constructed until 33 years later and it does support Veselago's concepts.\nCurrently, negative-index metamaterials are being developed to manipulate [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) in new ways.\nFor example, [optical](https://bliptext.com/articles/optical) and [electromagnetic](https://bliptext.com/articles/electromagnetism) properties of natural materials are often altered through [chemistry](https://bliptext.com/articles/chemistry).\nWith metamaterials, optical and electromagnetic properties can be engineered by changing the [geometry](https://bliptext.com/articles/geometry) of its [unit cells](https://bliptext.com/articles/split-ring-resonator).\nThe unit cells are materials that are ordered in geometric arrangements with dimensions that are fractions of the [wavelength](https://bliptext.com/articles/wavelength) of the radiated [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave).\nEach artificial unit responds to the radiation from the source.\nThe collective result is the material's response to the electromagnetic [wave](https://bliptext.com/articles/wave) that is broader than normal.\nSubsequently, transmission is altered by adjusting the shape, size, and configurations of the unit cells.\nThis results in control over material parameters known as [permittivity](https://bliptext.com/articles/permittivity) and [magnetic permeability](https://bliptext.com/articles/magnetic-permeability).\nThese two parameters (or quantities) determine the [propagation](https://bliptext.com/articles/wave-propagation) of electromagnetic waves in [matter](https://bliptext.com/articles/matter).\nTherefore, controlling the values of permittivity and permeability means that the [refractive index](https://bliptext.com/articles/refractive-index) can be negative or zero as well as conventionally positive.\nIt all depends on the intended [application or desired result](https://bliptext.com/articles/metamaterial).\nSo, [optical properties](https://bliptext.com/articles/optics) can be expanded beyond the capabilities of [lenses](https://bliptext.com/articles/lens-optics), mirrors, and other conventional materials.\nAdditionally, one of the effects most studied is the negative index of refraction.\n# [A split-ring resonator array arranged to produce a negative index of refraction, constructed of copper split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3 by 20×20 unit cells with overall dimensions of 10×100×100 millimeters. The height of 10 millimeters measures a little more than six subdivision marks on the ruler, which is marked in inches. | upload.wikimedia.org/wikipedia/commons/8/82/Split-ring///resonator///array///10K///sq///nm.jpg]\n\n## Reverse propagation\nWhen a negative index of refraction occurs, propagation of the [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave) is reversed.\nResolution below the [diffraction limit](https://bliptext.com/articles/diffraction-limit) becomes possible.\nThis is known as [subwavelength imaging](https://bliptext.com/articles/subwavelength-imaging).\nTransmitting a beam of light via an electromagnetically flat surface is another capability.\nIn contrast, [conventional materials](https://bliptext.com/articles/conventional-lens) are usually curved, and cannot achieve resolution below the diffraction limit.\nAlso, reversing the electromagnetic waves in a material, in conjunction with other ordinary materials (including air) could result in minimizing losses that would normally occur.\nThe reverse of the electromagnetic wave, characterized by an antiparallel [phase velocity](https://bliptext.com/articles/phase-velocity) is also an indicator of negative index of refraction.\nFurthermore, negative-index materials are customized composites.\nIn other words, materials are combined with a desired result in mind.\nCombinations of materials can be designed to achieve optical properties not seen in nature.\nThe properties of the composite material stem from its [lattice structure](https://bliptext.com/articles/lattice-structure) constructed from components smaller than the impinging electromagnetic [wavelength](https://bliptext.com/articles/wavelength) separated by distances that are also smaller than the impinging electromagnetic [wavelength](https://bliptext.com/articles/wavelength).\nLikewise, by fabricating such metamaterials researchers are trying to overcome fundamental limits tied to the [wavelength](https://bliptext.com/articles/wavelength) of [light](https://bliptext.com/articles/light).\nThe unusual and counterintuitive properties currently have practical and commercial use manipulating electromagnetic [microwaves](https://bliptext.com/articles/microwave) in [wireless and communication systems](https://bliptext.com/articles/metamaterial-antenna).\nLastly, research continues in the other domains of the [electromagnetic spectrum](https://bliptext.com/articles/electromagnetic-spectrum), including [visible light](https://bliptext.com/articles/visible-light).\n\n# Materials\nThe first actual metamaterials worked in the [microwave](https://bliptext.com/articles/microwave) regime, or centimeter [wavelengths](https://bliptext.com/articles/wavelengths), of the [electromagnetic spectrum](https://bliptext.com/articles/electromagnetic-spectrum) (about 4.3 GHz).\nIt was constructed of [split-ring resonators](https://bliptext.com/articles/split-ring-resonator) and conducting straight wires (as unit cells).\nThe unit cells were sized from 7 to 10 [millimeters](https://bliptext.com/articles/millimeters).\nThe unit cells were arranged in a two-dimensional ([periodic](https://bliptext.com/articles/periodic-function)) repeating pattern which produces a [crystal-like](https://bliptext.com/articles/crystal) geometry.\nBoth the unit cells and the [lattice spacing](https://bliptext.com/articles/lattice-spacing) were smaller than the radiated electromagnetic wave.\nThis produced the first left-handed material when both the permittivity and permeability of the material were negative.\nThis system relies on the [resonant](https://bliptext.com/articles/resonance) behavior of the unit cells.\nBelow a group of researchers develop an idea for a left-handed metamaterial that does not rely on such resonant behavior.\nResearch in the microwave range continues with split-ring resonators and conducting wires.\nResearch also continues in the shorter wavelengths with this configuration of materials and the unit cell sizes are scaled down.\nHowever, at around [200 terahertz](https://bliptext.com/articles/terahertz-unit) issues arise which make using the split ring resonator problematic.\n\"Alternative materials become more suitable for the terahertz and optical regimes.\"\nAt these wavelengths selection of materials and size limitations become important.\nFor example, in 2007 a 100 nanometer mesh wire design made of silver and woven in a repeating pattern transmitted beams at the 780 nanometer wavelength, the far end of the visible spectrum.\nThe researchers believe this produced a negative refraction of 0.6.\nNevertheless, this operates at only a single wavelength like its predecessor metamaterials in the microwave regime.\nHence, the challenges are to fabricate metamaterials so that they \"refract light at ever-smaller wavelengths\" and to develop broad band capabilities.\n\n## Artificial transmission-line-media\nIn the [metamaterial literature](https://bliptext.com/articles/scientific-journal), medium or media refers to [transmission medium](https://bliptext.com/articles/transmission-medium) or [optical medium](https://bliptext.com/articles/optical-medium).\nIn 2002, a group of researchers came up with the idea that in contrast to materials that depended on resonant behavior, non-resonant [phenomena](https://bliptext.com/articles/phenomena) could surpass narrow [bandwidth](https://bliptext.com/articles/bandwidth-signal-processing) constraints of the wire/[split-ring resonator](https://bliptext.com/articles/split-ring-resonator) configuration.\nThis idea translated into a type of medium with broader bandwidth abilities, [negative refraction](https://bliptext.com/articles/negative-refraction), backward waves, and [focusing](https://bliptext.com/articles/superlens) beyond the [diffraction limit](https://bliptext.com/articles/diffraction-limit).\nThey dispensed with split-ring-resonators and instead used a network of [L–C loaded](https://bliptext.com/articles/l-c-loaded) transmission lines.\nIn metamaterial literature this became known as artificial [transmission-line](https://bliptext.com/articles/transmission-line) media.\nAt that time it had the added advantage of being more compact than a unit made of wires and split ring resonators.\nThe network was both scalable (from the [megahertz](https://bliptext.com/articles/megahertz) to the tens of [gigahertz](https://bliptext.com/articles/gigahertz) range) and tunable.\nIt also includes a method for focusing the [wavelengths of interest](https://bliptext.com/articles/frequency).\nBy 2007 the negative refractive index transmission line was employed as a subwavelength focusing free-space flat lens.\nThat this is a free-space lens is a significant advance.\nPart of prior research efforts targeted creating a lens that did not need to be embedded in a transmission line.\n# [500px | upload.wikimedia.org/wikipedia/commons/8/86/Artificial///transmission-line-media.png]\n\n## The optical domain\nMetamaterial components shrink as research explores shorter wavelengths (higher frequencies) of the [electromagnetic spectrum](https://bliptext.com/articles/electromagnetic-spectrum) in the [infrared](https://bliptext.com/articles/infrared) and [visible spectrums](https://bliptext.com/articles/visible-spectrum).\nFor example, theory and experiment have investigated smaller horseshoe shaped split ring resonators designed with [lithographic](https://bliptext.com/articles/lithographic) techniques, as well as paired [metal nanorods](https://bliptext.com/articles/nanorod) or nanostrips, and nanoparticles as circuits designed with [lumped element models](https://bliptext.com/articles/lumped-element-model)\n\n# Applications\nThe science of negative-index materials is being matched with conventional devices that broadcast, transmit, shape, or receive electromagnetic signals that travel over cables, wires, or air.\nThe materials, devices and systems that are involved with this work could have their properties altered or heightened.\nHence, this is already happening with [metamaterial antennas](https://bliptext.com/articles/metamaterial-antenna) and related devices which are commercially available.\nMoreover, in the [wireless domain](https://bliptext.com/articles/wireless-technology) these metamaterial apparatuses continue to be researched.\nOther applications are also being researched.\nThese are [electromagnetic absorbers](https://bliptext.com/articles/metamaterial-absorber) such as [radar-microwave](https://bliptext.com/articles/radar) absorbers, electrically small [resonators](https://bliptext.com/articles/resonator), [waveguides](https://bliptext.com/articles/waveguide) that can go beyond the [diffraction limit](https://bliptext.com/articles/diffraction-limit), [phase compensators](https://bliptext.com/articles/metamaterial-antenna), advancements in focusing devices (e.g. [microwave lens](https://bliptext.com/articles/artificial-dielectrics)), and improved electrically small antennas.\nIn the [optical](https://bliptext.com/articles/optic) frequency regime developing the [superlens](https://bliptext.com/articles/superlens) may allow for imaging below the [diffraction limit](https://bliptext.com/articles/diffraction-limit).\nOther potential applications for negative-index metamaterials are optical [nanolithography](https://bliptext.com/articles/nanolithography), [nanotechnology](https://bliptext.com/articles/nanotechnology) circuitry, as well as a near field superlens (Pendry, 2000) that could be useful for biomedical imaging and subwavelength photolithography.\n\n# Manipulating permittivity and permeability\nTo describe any [electromagnetic](https://bliptext.com/articles/electromagnetism) properties of a given achiral material such as an [optical lens](https://bliptext.com/articles/optical-lens), there are two significant parameters.\nThese are [permittivity](https://bliptext.com/articles/permittivity), \\epsilon_r, and [permeability](https://bliptext.com/articles/magnetic-permeability), \\mu_r, which allow accurate prediction of light [waves traveling](https://bliptext.com/articles/wave-propagation) within materials, and [electromagnetic phenomena](https://bliptext.com/articles/phenomena) that occur at the [interface](https://bliptext.com/articles/interface-chemistry) between two materials.\nFor example, [refraction](https://bliptext.com/articles/refraction) is an electromagnetic phenomenon which occurs at the interface between two materials.\n[Snell's law](https://bliptext.com/articles/snell-s-law) states that the relationship between the angle of incidence of a beam of [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) (light) and the resulting angle of refraction rests on the refractive indices, n, of the two media (materials).\nThe refractive index of an achiral medium is given by.\nHence, it can be seen that the refractive index is dependent on these two parameters.\nTherefore, if designed or arbitrarily modified values can be inputs for \\epsilon_r and \\mu_r, then the behavior of propagating electromagnetic waves inside the material can be manipulated at will.\nThis ability then allows for intentional determination of the refractive index.\nFor example, in 1967, [Victor Veselago](https://bliptext.com/articles/victor-veselago) analytically determined that light will refract in the reverse direction (negatively) at the interface between a material with negative [refractive index](https://bliptext.com/articles/refractive-index) and a material exhibiting conventional positive [refractive index](https://bliptext.com/articles/refractive-index).\nThis extraordinary material was realized on paper with simultaneous negative values for \\epsilon_r and \\mu_r, and could therefore be termed a double negative material.\nHowever, in Veselago's day a material which exhibits double negative parameters simultaneously seemed impossible because no natural materials exist which can produce this effect.\nTherefore, his work was ignored for three decades.\nIt was nominated for the Nobel Prize later.\nIn general the [physical properties](https://bliptext.com/articles/physical-properties) of [natural materials](https://bliptext.com/articles/natural-material) cause limitations.\nMost [dielectrics](https://bliptext.com/articles/dielectric) only have positive permittivities, \\epsilon_r > 0.\nMetals will exhibit negative permittivity, \\epsilon_r n1. Since the velocity is lower in the second medium (v2 .\nIn this case, it is not necessary that either or both \\epsilon_r and \\mu_r be negative to achieve a negative index of refraction.\nA negative refractive index due to chirality was predicted by Pendry and Tretyakov et al., and first observed simultaneously and independently by Plum et al. and Zhang et al. in 2009.\n\n# Physical properties never before produced in nature\nTheoretical articles were published in 1996 and 1999 which showed that synthetic materials could be constructed to purposely exhibit a negative [permittivity](https://bliptext.com/articles/permittivity) and [permeability](https://bliptext.com/articles/magnetic-permeability).\nThese papers, along with [Veselago's](https://bliptext.com/articles/victor-veselago) 1967 theoretical analysis of the properties of negative-index materials, provided the background to fabricate a [metamaterial](https://bliptext.com/articles/metamaterial) with negative effective permittivity and permeability.\nSee below.\nA [metamaterial](https://bliptext.com/articles/metamaterial) developed to exhibit negative-index behavior is typically formed from individual components.\nEach component responds differently and independently to a radiated [electromagnetic wave](https://bliptext.com/articles/electromagnetic-wave) as it travels through the material.\nSince these components are smaller than the radiated [wavelength](https://bliptext.com/articles/wavelength) it is understood that a [macroscopic](https://bliptext.com/articles/macroscopic) view includes an [effective value](https://bliptext.com/articles/effective-medium-model) for both permittivity and permeability.\n\n## Composite material\nIn the year 2000, [David R. Smith](https://bliptext.com/articles/david-r-smith-physicist)'s team of [UCSD](https://bliptext.com/articles/ucsd) researchers produced a new class of [composite materials](https://bliptext.com/articles/composite-material) by depositing a structure onto a circuit-board substrate consisting of a series of thin copper split-rings and ordinary wire segments strung parallel to the rings.\nThis material exhibited unusual [physical properties](https://bliptext.com/articles/physics) that had never been observed in nature.\nThese materials obey the [laws of physics](https://bliptext.com/articles/laws-of-physics), but behave differently from normal materials.\nIn essence these negative-index metamaterials were noted for having the ability to reverse many of the [physical properties](https://bliptext.com/articles/physical-properties) that govern the behavior of ordinary optical materials.\nOne of those unusual properties is the ability to reverse, for the first time, [Snell's law](https://bliptext.com/articles/snell-s-law) of refraction.\nUntil the demonstration of negative refractive index for microwaves by the UCSD team, the material had been unavailable.\nAdvances during the 1990s in fabrication and computation abilities allowed these first [metamaterials](https://bliptext.com/articles/metamaterial) to be constructed.\nThus, the \"new\" metamaterial was tested for the effects described by [Victor Veselago](https://bliptext.com/articles/victor-veselago) 30 years earlier.\nStudies of this experiment, which followed shortly thereafter, announced that other effects had occurred.\nWith [anti[ferromagnets](https://bliptext.com/articles/ferromagnet)](https://bliptext.com/articles/antiferromagnet) and certain types of insulating [ferromagnets](https://bliptext.com/articles/ferromagnet), effective negative [magnetic permeability](https://bliptext.com/articles/magnetic-permeability) is achievable when [polariton](https://bliptext.com/articles/polariton) resonance exists.\nTo achieve a negative index of refraction, however, permittivity with negative values must occur within the same frequency range.\nThe artificially fabricated [split-ring resonator](https://bliptext.com/articles/split-ring-resonator) is a design that accomplishes this, along with the promise of dampening high losses.\nWith this first introduction of the metamaterial, it appears that the losses incurred were smaller than antiferromagnetic, or ferromagnetic materials.\nWhen first demonstrated in 2000, the composite material (NIM) was limited to transmitting [microwave radiation](https://bliptext.com/articles/microwave) at frequencies of 4 to 7 [gigahertz](https://bliptext.com/articles/gigahertz) (4.28–7.49 cm wavelengths).\nThis range is between the frequency of household microwave ovens ([~2.45](https://bliptext.com/articles/ism-band) [GHz](https://bliptext.com/articles/ghz), 12.23 cm) and military [radars](https://bliptext.com/articles/radars) (~10 [GHz](https://bliptext.com/articles/ghz), 3 cm).\nAt demonstrated frequencies, pulses of [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) moving through the material in one direction are composed of constituent waves moving in the opposite direction.\nThe metamaterial was constructed as a [periodic array](https://bliptext.com/articles/periodic-function) of [copper](https://bliptext.com/articles/copper) split ring and wire conducting elements deposited onto a circuit-board substrate.\nThe design was such that the cells, and the [lattice spacing](https://bliptext.com/articles/lattice-spacing) between the cells, were much smaller than the radiated [electromagnetic wavelength](https://bliptext.com/articles/wavelength).\nHence, it behaves as an [effective medium](https://bliptext.com/articles/effective-medium-model).\nThe material has become notable because its range of (effective) [permittivity](https://bliptext.com/articles/permittivity) εeff and [permeability](https://bliptext.com/articles/magnetic-permeability) μeff values have exceeded those found in any ordinary material.\nFurthermore, the characteristic of negative (effective) permeability evinced by this medium is particularly notable, because it has not been found in ordinary materials.\nIn addition, the negative values for the magnetic component is directly related to its left-handed nomenclature, and properties (discussed in a section below).\nThe [split-ring resonator](https://bliptext.com/articles/split-ring-resonator) (SRR), based on the prior 1999 theoretical article, is the tool employed to achieve negative permeability.\nThis first composite metamaterial is then composed of split-ring resonators and electrical conducting posts.\nInitially, these materials were only demonstrated at wavelengths longer than those in the [visible spectrum](https://bliptext.com/articles/visible-spectrum).\nIn addition, early NIMs were fabricated from [opaque](https://bliptext.com/articles/opacity-optics) materials and usually made of non-magnetic constituents.\nAs an illustration, however, if these materials are constructed at [visible frequencies](https://bliptext.com/articles/visible-frequencies), and a [flash[light](https://bliptext.com/articles/light)](https://bliptext.com/articles/flash[light](https://bliptext.com/articles/light)) is shone onto the resulting NIM slab, the material should focus the [light](https://bliptext.com/articles/light) at a point on the other side.\nThis is not possible with a sheet of ordinary opaque material.\nIn 2007, the [NIST](https://bliptext.com/articles/nist) in collaboration with the [Atwater](https://bliptext.com/articles/harry-atwater) Lab at [Caltech](https://bliptext.com/articles/caltech) created the first NIM active at optical frequencies.\nMore recently, layered \"fishnet\" NIM materials made of silicon and silver wires have been integrated into optical fibers to create active optical elements.\n\n## Simultaneous negative permittivity and permeability\nNegative permittivity εeff < 0 had already been discovered and realized in metals for frequencies all the way up to the [plasma frequency](https://bliptext.com/articles/plasma-frequency), before the first metamaterial.\nThere are two [requirements](https://bliptext.com/articles/requirements) to achieve a negative value for [refraction](https://bliptext.com/articles/refraction).\nFirst, is to fabricate a material which can produce negative permeability μeff < 0.\nSecond, negative values for both permittivity and permeability must occur simultaneously over a common range of frequencies.\nTherefore, for the first metamaterial, the nuts and bolts are one [split-ring resonator](https://bliptext.com/articles/split-ring-resonator) electromagnetically combined with one (electric) conducting post.\nThese are designed to resonate at designated frequencies to achieve the desired values.\nLooking at the make-up of the split ring, the associated [magnetic field](https://bliptext.com/articles/magnetic-field) pattern from the SRR is [dipolar](https://bliptext.com/articles/dipolar).\nThis dipolar behavior is notable because this means it mimics nature's [atom](https://bliptext.com/articles/atom), but on a much larger scale, such as in this case at 2.5 [millimeters](https://bliptext.com/articles/millimeter).\nAtoms exist on the scale of [picometers](https://bliptext.com/articles/picometer).\nThe splits in the rings create a [dynamic](https://bliptext.com/articles/dynamics-physics) where the SRR unit cell can be made [resonant](https://bliptext.com/articles/resonant) at [radiated wavelengths](https://bliptext.com/articles/em-radiation) much larger than the [diameter](https://bliptext.com/articles/diameter) of the rings.\nIf the rings were closed, a half wavelength boundary would be [electromagnetically](https://bliptext.com/articles/electromagnet) imposed as a requirement for [resonance](https://bliptext.com/articles/resonance).\nThe split in the second ring is oriented opposite to the split in the first ring.\nIt is there to generate a large [capacitance](https://bliptext.com/articles/capacitance), which occurs in the small gap.\nThis capacitance substantially decreases the resonant frequency while concentrating the [electric field](https://bliptext.com/articles/electric-field).\nThe individual SRR depicted on the right had a resonant frequency of [4.845 GHz](https://bliptext.com/articles/microwave), and the resonance curve, inset in the graph, is also shown.\nThe radiative losses from [absorption](https://bliptext.com/articles/absorption-electromagnetic-radiation) and [reflection](https://bliptext.com/articles/reflection-physics) are noted to be small, because the unit dimensions are much smaller than the [free space](https://bliptext.com/articles/free-space), radiated [wavelength](https://bliptext.com/articles/wavelength).\nWhen these units or cells are combined into a [periodic arrangement](https://bliptext.com/articles/split-ring-resonator), the [magnetic coupling](https://bliptext.com/articles/magnetic-coupling) between the resonators is strengthened, and a strong [magnetic coupling](https://bliptext.com/articles/magnetic-coupling) occurs.\nProperties unique in comparison to ordinary or conventional materials begin to emerge.\nFor one thing, this periodic strong coupling creates a material, which now has an effective magnetic permeability μeff in response to the [radiated-incident](https://bliptext.com/articles/physical-optics) magnetic field.\n\n## Composite material passband\nGraphing the general [dispersion curve](https://bliptext.com/articles/dispersion-optics), a region of [propagation](https://bliptext.com/articles/wave-propagation) occurs from zero up to a lower [band edge](https://bliptext.com/articles/frequency-band), followed by a gap, and then an upper [passband](https://bliptext.com/articles/passband).\nThe presence of a [400 MHz](https://bliptext.com/articles/mhz) gap between [4.2 GHz and 4.6 GHz](https://bliptext.com/articles/microwave) implies a band of frequencies where μeff < 0 occurs.\n(Please see the image in the previous section)\nFurthermore, when wires are added [symmetrically](https://bliptext.com/articles/symmetric) between the split rings, a [passband](https://bliptext.com/articles/passband) occurs within the previously [forbidden band](https://bliptext.com/articles/forbidden-band) of the split ring dispersion curves.\nThat 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, which fits with theoretical predictions.\nMathematically, the dispersion relation leads to a band with negative [group velocity](https://bliptext.com/articles/group-velocity) everywhere, and a bandwidth that is independent of the [plasma frequency](https://bliptext.com/articles/plasma-frequency), within the stated conditions.\n[Mathematical modeling](https://bliptext.com/articles/mathematical-modeling) and experiment have both shown that periodically arrayed conducting elements (non-magnetic by nature) respond predominantly to the [magnetic component](https://bliptext.com/articles/magnetic-field) of [incident electromagnetic fields](https://bliptext.com/articles/physical-optics).\nThe result is an effective medium and negative μeff over a band of frequencies.\nThe permeability was verified to be the region of the forbidden band, where the gap in propagation occurred – from a finite section of material.\nThis 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.\nThis validated predictions.\nIn addition, a later work determined that this first [metamaterial](https://bliptext.com/articles/metamaterial) had a range of frequencies over which the refractive index was predicted to be negative for one direction of [propagation](https://bliptext.com/articles/wave-propagation) (see ref # ).\nOther predicted [electrodynamic](https://bliptext.com/articles/electrodynamic) effects were to be investigated in other research.\n\n## Describing a left-handed material\nFrom the conclusions in the above section a left-handed material (LHM) can be defined.\nIt is a material which exhibits simultaneous [negative values](https://bliptext.com/articles/negative-numbers) for [permittivity](https://bliptext.com/articles/permittivity), ε, and [permeability](https://bliptext.com/articles/magnetic-permeability), μ, in an overlapping frequency region.\nSince the values are derived from the effects of the [composite medium system](https://bliptext.com/articles/metamaterial) as a whole, these are defined as effective permittivity, εeff, and effective permeability, μeff.\nReal values are then derived to denote the value of [negative index](https://bliptext.com/articles/negative-refractive-index) of refraction, and [wave vectors](https://bliptext.com/articles/wave-vector).\nThis means that in practice losses will occur for a given medium used to [transmit](https://bliptext.com/articles/transmission-coefficient) electromagnetic radiation such as [microwave](https://bliptext.com/articles/microwave), or [infrared](https://bliptext.com/articles/infrared) frequencies, or [visible light](https://bliptext.com/articles/visible-light) – for example.\nIn this instance, real values describe either the [amplitude](https://bliptext.com/articles/amplitude) or the [intensity](https://bliptext.com/articles/intensity-physics) of a transmitted wave relative to an incident wave, while ignoring the negligible loss values.\n# [A comparison of refraction in a negative-index metamaterial to that in a conventional material having the same, but positive refractive index. The incident beam θ enters from air and refracts in a normal (θ') or metamaterial (-θ'). | upload.wikimedia.org/wikipedia/commons/1/15/metarefraction.svg]\n\n# Isotropic negative index in two dimensions\nIn the above sections first fabricated [metamaterial](https://bliptext.com/articles/metamaterial) was constructed with [resonating elements](https://bliptext.com/articles/resonate), which exhibited one direction of [incidence](https://bliptext.com/articles/angle-of-incidence-optics) and [polarization](https://bliptext.com/articles/polarization-waves).\nIn other words, this structure exhibited left-handed propagation in one dimension.\nThis was discussed in relation to Veselago's seminal work 33 years earlier (1967).\nHe predicted that intrinsic to a material, which manifests negative values of effective [permittivity](https://bliptext.com/articles/permittivity) and [permeability](https://bliptext.com/articles/magnetic-permeability), are several types of reversed [physics phenomena](https://bliptext.com/articles/physical-property).\nHence, there was then a critical need for a higher-dimensional LHMs to confirm Veselago's theory, as expected.\nThe confirmation would include reversal of [Snell's law](https://bliptext.com/articles/snell-s-law) (index of refraction), along with other reversed phenomena.\nIn the beginning of 2001 the existence of a higher-dimensional structure was reported.\nIt was two-dimensional and demonstrated by both experiment and numerical confirmation.\nIt was an [LHM](https://bliptext.com/articles/), a composite constructed of wire strips mounted behind the split-ring resonators (SRRs) in a periodic configuration.\nIt was created for the express purpose of being suitable for further experiments to produce the effects predicted by Veselago.\n\n# Experimental verification of a negative index of refraction\nA theoretical work published in 1967 by Soviet physicist Victor Veselago showed that a refractive index with negative values is possible and that this does not violate the laws of physics.\nAs discussed previously (above), the first [metamaterial](https://bliptext.com/articles/metamaterial) had a range of frequencies over which the refractive index was predicted to be negative for one direction of [propagation](https://bliptext.com/articles/wave-propagation).\nIt was reported in May 2000.\nIn 2001, a team of [researchers](https://bliptext.com/articles/researcher) constructed a prism composed of metamaterials (negative-index metamaterials) to experimentally test for negative refractive index.\nThe experiment used a waveguide to help transmit the proper frequency and isolate the material.\nThis test achieved its goal because it successfully verified a negative index of refraction.\nThe experimental demonstration of negative refractive index was followed by another demonstration, in 2003, of a reversal of Snell's law, or reversed refraction.\nHowever, in this experiment negative index of refraction material is in free space from 12.6 to 13.2 GHz.\nAlthough the radiated frequency range is about the same, a notable distinction is this experiment is conducted in free space rather than employing waveguides.\nFurthering 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.\nThe transmission of an incident field, composed of many frequencies, from an isotropic nondispersive material into an isotropic dispersive media is employed.\nThe direction of power flow for both nondispersive and dispersive media is determined by the time-averaged\n[Poynting vector](https://bliptext.com/articles/poynting-vector).\nNegative refraction was shown to be possible for multiple frequency signals by explicit calculation of the Poynting vector in the LHM.\n# [Split-ring resonator consisting of an inner square with a split on one side embedded in an outer square with a split on the other side. Split-ring resonators are on the front and right surfaces of the square grid, and single vertical wires are on the back and left surfaces. | upload.wikimedia.org/wikipedia/commons/f/fb/Left-handed///metamaterial///array///configuration.jpg]\n\n## Fundamental electromagnetic properties of the NIM\nIn a slab of conventional material with an ordinary [refractive index](https://bliptext.com/articles/refractive-index) – a right-handed material (RHM) – the [wave front](https://bliptext.com/articles/wave-front) is transmitted away from the source.\nIn a NIM the wavefront travels toward the source.\nHowever, the magnitude and direction of the flow of energy essentially remains the same in both the ordinary material and the NIM.\nSince the flow of energy remains the same in both materials (media), the impedance of the NIM matches the RHM.\nHence, the sign of the intrinsic impedance is still positive in a NIM.\nLight 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.\nIn a passive metamaterial medium this determines a negative real and imaginary part of the refractive index.\n\n## Negative refractive index in left-handed materials\nIn 1968 [Victor Veselago](https://bliptext.com/articles/victor-veselago)'s paper showed that the opposite directions of EM [plane waves](https://bliptext.com/articles/plane-waves) and the flow of energy was derived from the individual [Maxwell curl equations](https://bliptext.com/articles/maxwell-s-equations).\nIn ordinary [optical](https://bliptext.com/articles/optical) materials, the curl equation for the [electric field](https://bliptext.com/articles/electric-field) show a \"right hand rule\" for the directions of the [electric field](https://bliptext.com/articles/electric-field) **E**, the magnetic induction **B**, and wave propagation, which goes in the direction of wave vector **k**.\nHowever, the direction of energy flow formed by E × H is right-handed only when permeability is greater than zero.\nThis means that when permeability is less than zero, e.g. negative, [wave propagation](https://bliptext.com/articles/wave-propagation) is reversed (determined by k), and contrary to the direction of energy flow.\nFurthermore, 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).\nHe contended that an LH material has a negative refractive index and relied on the [steady-state solutions](https://bliptext.com/articles/steady-state) of [Maxwell's equations](https://bliptext.com/articles/maxwell-s-equations) as a center for his argument.\nAfter a 30-year void, when LH materials were finally demonstrated, it could be said that the designation of [negative refractive index](https://bliptext.com/articles/negative-refractive-index) is unique to LH systems; even when compared to [photonic crystals](https://bliptext.com/articles/photonic-crystal).\nPhotonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase and group velocities.\nBut, negative refraction does not occur in these systems, and not yet realistically in photonic crystals.\n# [The left-handed orientation is shown on the left, and the right-handed on the right. | upload.wikimedia.org/wikipedia/commons/e/e2/Cartesian///coordinate///system///handedness.svg]\n\n## Negative refraction at optical frequencies\nThe negative refractive index in the optical range was first demonstrated in 2005 by [Shalaev](https://bliptext.com/articles/shalaev) et al. (at the telecom wavelength λ = 1.5 μm) and by Brueck et al. (at λ = 2 μm) at nearly the same time.\nIn 2006, a Caltech team led by Lezec, Dionne, and Atwater achieved negative refraction in the [visible spectral regime](https://bliptext.com/articles/visible-spectral-regime).\n\n# Reversed Cherenkov radiation\nBesides reversed values for the [index of refraction](https://bliptext.com/articles/index-of-refraction), Veselago predicted the occurrence of reversed [Cherenkov radiation](https://bliptext.com/articles/cherenkov-radiation) in a left-handed medium.\nWhereas ordinary Cherenkov radiation is emitted in a cone around the direction in which a charged particle is travelling through the medium, reversed Cherenkov radiation is emitted in a cone around the opposite direction.\nReversed Cherenkov radiation was first experimentally demonstrated indirectly in 2009, using a phased electromagnetic dipole array to model a moving charged particle.\nReversed Cherenkov radiation emitted by actual charged particles was first observed in 2017.\n\n# Other optics with NIMs\nTheoretical work, along with [numerical simulations](https://bliptext.com/articles/numerical-simulation), began in the early 2000s on the abilities of DNG slabs for [subwavelength focusing](https://bliptext.com/articles/superlens).\nThe research began with Pendry's proposed \"[Perfect lens](https://bliptext.com/articles/perfect-lens).\"\nSeveral research investigations that followed Pendry's concluded that the \"Perfect lens\" was possible in theory but impractical.\nOne direction in subwavelength focusing proceeded with the use of negative-index metamaterials, but based on the enhancements for imaging with surface plasmons.\nIn another direction researchers explored [paraxial approximations](https://bliptext.com/articles/paraxial-approximation) of NIM slabs.\n\n# Implications of negative refractive materials\nThe existence of negative refractive materials can result in a change in [electrodynamic](https://bliptext.com/articles/electrodynamic) calculations for the case of permeability μ = 1.\nA change from a conventional refractive index to a negative value gives incorrect results for conventional calculations, because some properties and effects have been altered.\nWhen permeability μ has values other than 1 this affects [Snell's law](https://bliptext.com/articles/snell-s-law), the [Doppler effect](https://bliptext.com/articles/doppler-effect), the [Cherenkov radiation](https://bliptext.com/articles/cherenkov-radiation), [Fresnel's equations](https://bliptext.com/articles/fresnel-s-equations), and [Fermat's principle](https://bliptext.com/articles/fermat-s-principle).\nThe [refractive index](https://bliptext.com/articles/refractive-index) is basic to the science of optics.\nShifting the refractive index to a negative value may be a cause to revisit or reconsider the interpretation of some [norms](https://bliptext.com/articles/convention-norm), or [basic laws](https://bliptext.com/articles/optics).\n\n# US patent on left-handed composite media\nThe first US patent for a fabricated metamaterial, titled \"Left handed composite media\" by [David R. Smith](https://bliptext.com/articles/david-r-smith-physicist), [Sheldon Schultz](https://bliptext.com/articles/sheldon-schultz), [Norman Kroll](https://bliptext.com/articles/norman-kroll) and [Richard A. Shelby](https://bliptext.com/articles/richard-a-shelby), was issued in 2004.\nThe invention achieves simultaneous negative permittivity and permeability over a common band of frequencies.\nThe material can integrate media which is already composite or continuous, but which will produce negative permittivity and permeability within the same spectrum of frequencies.\nDifferent types of continuous or composite may be deemed appropriate when combined for the desired effect.\nHowever, the inclusion of a periodic array of conducting elements is preferred.\nThe array scatters [electromagnetic radiation](https://bliptext.com/articles/electromagnetic-radiation) at [wavelengths](https://bliptext.com/articles/wavelengths) longer than the size of the element and lattice spacing.\nThe array is then viewed as an [effective medium](https://bliptext.com/articles/effective-medium).","revisionCount":0},"hasMore":false,"nextCursor":null}

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