View source for Negative-index metamaterial

{{Short description|Material with a negative refractive index}}
[[File:Artist's rendition of the new light-bending metamaterial.jpg|thumb|170px|A negative-index metamaterial causes light to refract, or bend, differently than in more common positive-index materials such as [[Lens (optics)|glass lens]]es]]

'''Negative-index metamaterial''' or '''negative-index material''' ('''NIM''') is a [[metamaterial]] whose [[refractive index]] for an [[electromagnetic wave]] has a negative value over some [[frequency]] range.<ref name=AAAS2/>

NIMs are constructed of periodic basic parts called [[unit cell]]s, which are usually significantly smaller than the [[wavelength]] of the externally applied [[electromagnetic radiation]]. The unit cells of the first experimentally investigated NIMs were constructed from [[circuit board]] material, or in other words, wires and [[dielectric]]s. In general, these artificially constructed cells are stacked or [[plane (geometry)|planar]] and configured in a particular repeated pattern to compose the individual NIM. For 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).

Specifications 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. In other words, each cell is individually tuned to respond in a certain way, based on the desired output of the NIM.  The aggregate response is mainly determined by each unit cell's ''geometry'' and substantially differs from the response of its constituent materials. In other words, the way the NIM responds is that of a new material, unlike the wires or metals and dielectrics it is made from. Hence, the NIM has become an [[effective medium]]. Also, in effect, this metamaterial has become an “ordered [[macroscopic]] material, synthesized from the bottom up”, and has emergent properties beyond its components.<ref name=emerge>Sihvola, A. (2002)
[http://users.tkk.fi/asihvola/emergence.pdf "Electromagnetic Emergence in Metamaterials: Deconstruction of terminology of complex media"] {{Webarchive|url=https://web.archive.org/web/20120225062122/http://users.tkk.fi/asihvola/emergence.pdf |date=2012-02-25 }}, pp. 3–18 in ''Advances in Electromagnetics of Complex Media and Metamaterials''. Zouhdi, Saïd; Sihvola, Ari and Arsalane, Mohamed (eds.). Kluwer Academic. {{ISBN|978-94-007-1067-2}}.</ref>

Metamaterials that exhibit a negative value for the [[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, double negative (DNG) metamaterials, and other similar names.<ref name=physicsengineering1>In the literature, most widely used designations are "double negative" and "left-handed". 
{{cite book
 |last1=Engheta |first1=N.
 |last2=Ziolkowski |first2=R. W.
 |year=2006
 |title=Metamaterials: Physics and Engineering Explorations
 |at=Chapter 1
 |publisher=[[Wiley & Sons]]
 |isbn=978-0-471-76102-0
|title-link=Metamaterials: Physics and Engineering Explorations
 }}</ref>

==Properties and characteristics==
[[File:Split-ring resonator array 10K sq nm.jpg|thumb|250px|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.<br> The total array consists of 3 by 20×20 unit cells with overall dimensions of 10×100×100 millimeters.<ref name=APhys1>{{cite journal|last1=Shelby |first1=R. A. |last2=Smith |first2=D. R. |last3=Shultz |first3=S. |last4=Nemat-Nasser |first4=S. C. |year=2001 |title=Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial |url=http://people.ee.duke.edu/~drsmith/pubs_smith_group/Shelby_APL_(2001).pdf |journal=[[Applied Physics Letters]] |volume=78 |issue=4 |page=489 |bibcode=2001ApPhL..78..489S |doi=10.1063/1.1343489 |url-status=dead |archive-url=https://web.archive.org/web/20100618193936/http://people.ee.duke.edu/~drsmith/pubs_smith_group/Shelby_APL_(2001).pdf |archive-date=June 18, 2010 }}</ref><ref name="comp"/> The height of 10 millimeters measures a little more than six subdivision marks on the ruler, which is marked in inches.]]

[[Electrodynamics]] of media with negative indices of refraction were first studied by Russian theoretical physicist [[Victor Veselago]] from [[Moscow Institute of Physics and Technology]] in 1967.<ref name=first-paper/> The proposed ''left-handed'' or ''negative-index'' materials were [[theory|theorized]] to exhibit [[Classical optics|optical properties]] opposite to those of [[glass]], [[air]], and other [[optical materials|transparent media]]. Such materials were predicted to exhibit counterintuitive properties like bending or refracting light in unusual and unexpected ways. However, the first practical metamaterial was not constructed until 33 years later and it does support Veselago's concepts.<ref name=AAAS2/><ref name=physicsengineering1/><ref name=first-paper>
{{cite journal
 |last1   = Veselago
 |first1  = V. G.
 |year    = 1968
 |title   = The electrodynamics of substances with simultaneously negative values of ε and μ
 |url     = https://www.academia.edu/5322023
 |journal = [[Soviet Physics Uspekhi]]
 |volume  = 10
 |issue   = 4
 |pages   = 509–514
 |bibcode = 1968SvPhU..10..509V
 |doi     = 10.1070/PU1968v010n04ABEH003699
}}</ref><ref name=NIST-metamat/>

Currently, negative-index metamaterials are being developed to manipulate [[electromagnetic radiation]] in new ways. For example, [[optical]] and [[Electromagnetism|electromagnetic]] properties of natural materials are often altered through [[chemistry]]. With metamaterials, optical and electromagnetic properties can be engineered by changing the [[geometry]] of its [[split-ring resonator|unit cells]]. The unit cells are materials that are ordered in geometric arrangements with dimensions that are fractions of the [[wavelength]] of the radiated [[electromagnetic wave]]. Each artificial unit responds to the radiation from the source. The collective result is the material's response to the electromagnetic [[wave]] that is broader than normal.<ref name=AAAS2/><ref name=physicsengineering1/><ref name=NIST-metamat/>

Subsequently, transmission is altered by adjusting the shape, size, and configurations of the unit cells. This results in control over material parameters known as  [[permittivity]] and [[magnetic permeability]]. These two parameters (or quantities) determine the [[wave propagation|propagation]] of electromagnetic waves in [[matter]]. Therefore, controlling the values of permittivity and permeability means that the [[refractive index]] can be negative or zero as well as conventionally positive. It all depends on the intended [[metamaterial#Classification of electromagnetic metamaterials|application or desired result]]. So, [[optics|optical properties]] can be expanded beyond the capabilities of [[Lens (optics)|lens]]es, mirrors, and other conventional materials. Additionally, one of the effects most studied is the negative index of refraction.<ref name=AAAS2/><ref name=physicsengineering1/><ref name=first-paper/><ref name=NIST-metamat/>

===Reverse propagation===
When a negative index of refraction occurs, propagation of the [[electromagnetic wave]] is reversed. Resolution below the [[diffraction limit]] becomes possible. This is known as [[subwavelength imaging]]. Transmitting a beam of light via an electromagnetically flat surface is another capability. In contrast, [[conventional lens|conventional materials]] are usually curved, and cannot achieve resolution below the diffraction limit. Also,  reversing the electromagnetic waves in a material, in conjunction with other ordinary materials (including air) could result in minimizing losses that would normally occur.<ref name=AAAS2/><ref name=physicsengineering1/><ref name=first-paper/><ref name=NIST-metamat/>

The reverse of the electromagnetic wave, characterized by an antiparallel [[phase velocity]] is also an indicator of negative index of refraction.<ref name=AAAS2/><ref name=first-paper/>

Furthermore, negative-index materials are customized composites. In other words, materials are combined with a desired result in mind. Combinations of materials can be designed to achieve optical properties not seen in nature. The properties of the composite material stem from its [[lattice structure]] constructed from components smaller than the impinging electromagnetic [[wavelength]] separated by distances that are also smaller than the impinging electromagnetic wavelength. Likewise, by fabricating such metamaterials researchers are trying to overcome fundamental limits tied to the [[wavelength]] of [[light]].<ref name=AAAS2/><ref name=physicsengineering1/><ref name=NIST-metamat/>  The unusual and counterintuitive properties currently have practical and commercial use manipulating electromagnetic [[microwave]]s in [[metamaterial antenna|wireless and communication systems]]. Lastly, research continues in the other domains of the [[electromagnetic spectrum]], including [[visible light]].<ref name=NIST-metamat>
{{cite web
 |date=20 August 2009
 |title=Three-Dimensional Plasmonic Metamaterials
 |work=Plasmonic metamaterial research
 |publisher=[[National Institute of Standards and Technology]]
 |url=https://www.nist.gov/cnst/nrg/3d_plasmonic_metamaterials.cfm
 |access-date=2011-01-02
}}</ref><ref name=Chevalier>{{cite web
 |last1=Chevalier |first1=C. T.
 |last2=Wilson |first2=J. D.
 |date=November 2004
 |title=Frequency Bandwidth Optimization of Left-Handed Metamaterial
 |url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050019217_2005000108.pdf
 |publisher=[[Glenn Research Center]]
 |id=NASA/TM—2004-213403
 |access-date=2011-06-11
}}</ref>

==Materials==
The first actual metamaterials worked in the [[microwave]] regime, or centimeter [[wavelengths]], of the [[electromagnetic spectrum]]  (about 4.3&nbsp;GHz). It was constructed of [[split-ring resonator]]s and conducting straight wires (as unit cells). The unit cells were sized from 7 to 10 [[millimeters]].  The unit cells were arranged in a two-dimensional ([[periodic function|periodic]]) repeating pattern which produces a [[crystal|crystal-like]] geometry. Both the unit cells and the [[lattice spacing]] were smaller than the radiated electromagnetic wave. This produced the first left-handed material when both the permittivity and permeability of the material were negative. This system relies on the [[resonance|resonant]] behavior of the unit cells. Below a group of researchers develop an idea for a left-handed metamaterial that does not rely on such resonant behavior.

Research in the microwave range continues with split-ring resonators and conducting wires. Research also continues in the shorter wavelengths with this configuration of materials and the unit cell sizes are scaled down. However, at around [[Terahertz (unit)|200 terahertz]]  issues arise which make using the split ring resonator problematic. "''Alternative materials become more suitable for the terahertz and optical regimes''." At these wavelengths selection of materials and size limitations become important.<ref name=AAAS2/><ref name=APhys1/><ref name=ABoltasseva>
{{cite journal
 |last1=Boltasseva |first1=A.|author-link1=Alexandra Boltasseva
 |last2=Shalaev |first2=V.
 |year=2008
 |title=Fabrication of optical negative-index metamaterials: Recent advances and outlook
 |url=http://cobweb.ecn.purdue.edu/~shalaev/Publication_list_files/e6a11dcdfb53727d92491e50a7856ae2.pdf
 |journal=[[Metamaterials (journal)|Metamaterials]]
 |volume=2 |issue=1
 |pages=1–17
 |bibcode=2008MetaM...2....1B
 |doi=10.1016/j.metmat.2008.03.004
}}</ref><ref name=V2003/> For 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. The researchers believe this produced a negative refraction of 0.6. Nevertheless, this operates at only a single wavelength like its predecessor metamaterials in the microwave regime. Hence, the challenges are to fabricate metamaterials so that they "refract light at ever-smaller wavelengths" and to develop broad band capabilities.<ref name=the-net>
{{cite web
 |date=10 September 2007
 |title=Caught in the "Net" Ames material negatively refracts visible light
 |url=http://www.ornl.gov/info/news/pulse/pulse_v243_07.htm
 |work=DOE Pulse
 |publisher=[[US Department of Energy]]
 |access-date=2012-06-18
}}</ref><ref name=gibson>{{cite web|last=Gibson |first=K. |year=2007 |title=A Visible Improvement |publisher=[[Ames Laboratory]] |url=https://www.ameslab.gov/files/AVisableImprovement2007.pdf |access-date=2012-06-18 |url-status=dead |archive-url=https://web.archive.org/web/20120917014207/https://www.ameslab.gov/files/AVisableImprovement2007.pdf |archive-date=September 17, 2012 }}</ref>

===Artificial transmission-line-media===
{{main|Metamaterial antenna}}

[[File:Artificial transmission-line-media.png|thumb|500px]]
In the [[scientific journal|metamaterial literature]], medium or media refers to [[transmission medium]] or [[optical medium]]. In 2002,  a group of researchers came up with the idea that in contrast to materials that depended on resonant behavior, non-resonant [[phenomena]] could surpass narrow [[bandwidth (signal processing)|bandwidth]] constraints of the wire/[[split-ring resonator]] configuration. This idea translated into a type of medium with broader bandwidth abilities, [[negative refraction]], backward waves, and [[superlens|focusing]] beyond the [[diffraction limit]].

They dispensed with split-ring-resonators and instead used a network of [[L–C loaded]] transmission lines. In metamaterial literature this became known as artificial [[Transmission line|transmission-line]] media. At that time it had the added advantage of being more compact than a unit made of wires and split ring resonators. The network was both scalable (from the [[megahertz]] to the tens of [[gigahertz]] range) and tunable. It also includes a method for focusing the [[frequency|wavelengths of interest]].<ref name=ElefTL02>
{{cite journal
 |last1=Eleftheriades |first1=G.V.
 |last2=Iyer |first2=A.K.
 |last3=Kremer |first3=P.C.
 |author-link=George V. Eleftheriades
 |year=2002
 |title=Planar negative refractive index media using periodically L-C loaded transmission lines
 |url=http://www.waves.utoronto.ca/prof/gelefth/metamaterials_file/GVEAsh_MTT2002_Enhanced.pdf
 |journal=[[IEEE Transactions on Microwave Theory and Techniques]]
 |volume=50 |issue=12 |page=2702
 |bibcode=2002ITMTT..50.2702E
 |doi=10.1109/TMTT.2002.805197
}}</ref>
By 2007 the negative refractive index transmission line was employed as a subwavelength focusing free-space flat lens. That this is a free-space lens is a significant advance. Part of prior research efforts targeted creating a lens that did not need to be embedded in a transmission line.<ref name=Iyer07>{{cite journal
 |last1=Iyer
 |first1=A. K.
 |last2=Eleftheriades
 |first2=G. V.
 |year=2007
 |title=A Multilayer Negative-Refractive-Index Transmission-Line (NRI-TL) Metamaterial Free-Space Lens at ''X''-Band
 |url=http://www.ece.ualberta.ca/~iyer/Papers/Iyer_TAP07.pdf
 |journal=[[IEEE Transactions on Antennas and Propagation]]
 |volume=55
 |issue=10
 |page=2746
 |bibcode=2007ITAP...55.2746I
 |doi=10.1109/TAP.2007.905924
 |s2cid=21922234
 |access-date=2012-08-09
 |archive-date=2013-01-08
 |archive-url=https://web.archive.org/web/20130108010259/http://www.ece.ualberta.ca/~iyer/Papers/Iyer_TAP07.pdf
 |url-status=dead
 }}</ref>

===The optical domain===
{{main|Photonic metamaterial|plasmonic metamaterial}}
Metamaterial components shrink as research explores shorter wavelengths (higher frequencies) of the [[electromagnetic spectrum]] in the [[infrared]] and [[visible spectrum]]s. For example, theory and experiment have investigated smaller horseshoe shaped split ring resonators designed with [[lithographic]] techniques,<ref name=Soukou>{{cite journal
 |last1=Soukoulis |first1=C. M.
 |last2=Kafesaki |first2=M.
 |last3=Economou |first3=E. N.
 |year=2006
 |title=Negative-Index Materials: New Frontiers in Optics
 |url=http://esperia.iesl.forth.gr/~kafesaki/abstracts/AdvMatv18p1941.pdf
 |journal=[[Advanced Materials]]
 |volume=18 |issue=15 |pages=1944 and 1947
 |doi=10.1002/adma.200600106
|bibcode=2006AdM....18.1941S
 |s2cid=54507609
 }}</ref><ref name=at-100-THz>
{{cite journal
 |last1=Linden |first1=S.
 |last2=Enkrich |first2=C.
 |last3=Wegener |first3=M.
 |last4=Zhou |first4=J.
 |last5=Koschny |first5=T.
 |last6=Soukoulis |first6=C. M.
 |year=2004
 |title=Magnetic Response of Metamaterials at 100 Terahertz
 |url=https://publikationen.bibliothek.kit.edu/1000010922/751156
 |journal=[[Science (journal)|Science]]
 |volume=306 |issue=5700 |pages=1351–1353
 |bibcode=2004Sci...306.1351L
 |doi=10.1126/science.1105371
 |pmid=15550664
|s2cid=23557190
 }}</ref> as well as paired [[nanorod|metal nanorods]] or nanostrips,<ref name=nanorod>
{{cite journal
 |last1=Shalaev |first1=V. M.
 |last2=Cai |first2=W.
 |last3=Chettiar |first3=U. K.
 |last4=Yuan |first4=H.-K.
 |last5=Sarychev |first5=A. K.
 |last6=Drachev |first6=V. P.
 |last7=Kildishev |first7=A. V.
 |year=2005
 |title=Negative index of refraction in optical metamaterials
 |url=https://engineering.purdue.edu/~shalaev/Publication_list_files/OLpaper.pdf
 |journal=[[Optics Letters]]
 |volume=30 |issue=24 |pages=3356–8
 |arxiv=physics/0504091
 |bibcode=2005OptL...30.3356S
 |doi=10.1364/OL.30.003356
 |pmid=16389830
|s2cid=14917741
 }}</ref>  and nanoparticles as circuits designed with [[lumped element model]]s <ref name=nanolight>{{cite journal|last1=Engheta |first1=N. |year=2007 |title=Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials |url=http://www.seas.upenn.edu/media/pdf/Nader_Science_Article_Sept_21_2007.pdf |journal=[[Science (journal)|Science]] |volume=317 |issue=5845 |pages=1698–1702 |bibcode=2007Sci...317.1698E |doi=10.1126/science.1133268 |pmid=17885123 |s2cid=1572047 |url-status=dead |archive-url=https://web.archive.org/web/20120222032851/http://www.seas.upenn.edu/media/pdf/Nader_Science_Article_Sept_21_2007.pdf |archive-date=February 22, 2012 }} of this research by [[Nader Engheta]] (PDF format).</ref>

==Applications==
The 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. The materials, devices and systems that are involved with this work could have their properties altered or heightened. Hence, this is already happening with [[metamaterial antenna]]s<ref name=slyusarmeta>Slyusar V.I. (2009) [http://www.slyusar.kiev.ua/019_024_ICATT_2009.pdf "Metamaterials on antenna solutions"]. 7th International Conference on Antenna Theory and Techniques ICATT’09, Lviv, Ukraine, October 6–9, pp. 19–24. {{Webarchive|url=https://web.archive.org/web/20210427232421/http://www.slyusar.kiev.ua/019_024_ICATT_2009.pdf |date=2021-04-27 }}</ref> and related devices which are commercially available. Moreover, in the [[wireless technology|wireless domain]] these metamaterial apparatuses continue to be researched. Other applications are also being researched. These are [[metamaterial absorber|electromagnetic absorbers]] such as [[radar|radar-microwave]] absorbers, electrically small [[resonator]]s, [[waveguide]]s that can go beyond the [[diffraction limit]], [[Metamaterial antenna#Phase compensation due to negative refraction|phase compensators]], advancements in focusing devices (e.g. [[artificial dielectrics|microwave lens]]), and improved electrically small antennas.<ref name=EngZol>
{{cite journal
 |last1=Engheta |first1=N.
 |last2=Ziolkowski |first2=R. W.
 |year=2005
 |title=A positive future for double-negative metamaterials
 |url=http://www2.engr.arizona.edu/~ziolkows/research/papers/Metamaterial_Research/Reviews/MTT_April_2005.pdf
 |journal=[[IEEE Transactions on Microwave Theory and Techniques]]
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 |year    = 2008
 |title   = Planoconcave lens by negative refraction of stacked subwavelength hole arrays
 |journal = [[Optics Express]]
 |volume  = 16
 |issue   = 13
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In the [[optic]]al frequency regime developing the [[superlens]] may allow for imaging below the [[diffraction limit]]. Other potential applications for negative-index metamaterials are optical [[nanolithography]], [[nanotechnology]] circuitry, as well as a near field superlens (Pendry, 2000) that could be useful for biomedical imaging and subwavelength photolithography.<ref name=shalaev>
{{cite journal
 |last1=Shalaev |first1=V. M.
 |year=2007
 |title=Optical negative-index metamaterials
 |url=http://ecn.www.ecn.purdue.edu/~photspec/Optical%20negative-index%20metamaterials.pdf
 |journal=[[Nature Photonics]]
 |volume=1 |issue=1
 |page=41
 |bibcode=2007NaPho...1...41S
 |doi=10.1038/nphoton.2006.49
|s2cid=170678
 }}</ref>

==Manipulating permittivity and permeability==
[[File:Snells law.svg|thumb|300px|[[Refraction]] of light at the interface between two media of different [[refractive index|refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]

To describe any [[electromagnetism|electromagnetic]] properties of a given achiral material such as an [[optical lens]], there are two significant parameters. These are [[permittivity]], <math>\epsilon_r</math>, and [[magnetic permeability|permeability]], <math>\mu_r</math>, which allow accurate prediction of light [[Wave propagation|waves traveling]] within materials, and [[phenomena|electromagnetic phenomena]] that occur at the [[interface (chemistry)|interface]] between two materials.<ref name=PSS-B/>

For example, [[refraction]] is an electromagnetic phenomenon which occurs at the interface between two materials. [[Snell's law]] states that the relationship between the angle of incidence of a beam of [[electromagnetic radiation]] (light) and the resulting angle of refraction rests on the refractive indices, <math>n</math>, of the two media (materials). The refractive index of an achiral medium is given by <math>\scriptstyle n =\pm\sqrt{\epsilon_r\mu_r}</math>.<ref>{{cite book |last1=Ulaby |first1=Fawwaz T. |last2=Ravaioli |first2=Umberto |title=Fundamentals of Applied Electromagnetics |page=363 |edition=7th}}</ref> Hence, it can be seen that the refractive index is dependent on these two parameters. Therefore, if designed or arbitrarily modified values can be inputs for <math>\epsilon_r</math> and <math>\mu_r</math>, then the behavior of propagating electromagnetic waves inside the material can be manipulated at will. This ability then allows for intentional determination of the refractive index.<ref name=PSS-B/>

[[File:Negative refraction.ogv|left|thumb|256px|Video representing negative refraction of light at uniform planar interface.]]

For example, in 1967, [[Victor Veselago]] analytically determined that light will refract in the reverse direction (negatively) at the interface between a material with negative refractive index and a material exhibiting conventional positive [[refractive index]]. This extraordinary material was realized on paper with simultaneous negative values for <math>\epsilon_r</math> and <math>\mu_r</math>, and could therefore be termed a double negative material. However, in Veselago's day a material which exhibits double negative parameters simultaneously seemed impossible because no natural materials exist which can produce this effect. Therefore, his work was ignored for three decades.<ref name=PSS-B/> It was nominated for the Nobel Prize later. 

In general the [[physical properties]] of [[natural material]]s cause limitations. Most [[dielectric]]s only have positive permittivities, <math>\epsilon_r</math> > 0. Metals will exhibit negative permittivity, <math>\epsilon_r</math> < 0 at optical frequencies, and plasmas exhibit negative permittivity values in certain frequency bands. Pendry et al. demonstrated that the [[plasma frequency]] can be made to occur in the lower [[microwave]] frequencies for metals with a material made of metal rods that replaces the [[metal|bulk metal]]. However, in each of these cases permeability remains always positive. At microwave frequencies it is possible for negative μ to occur in some [[ferromagnetic]] materials. But the inherent drawback is they are difficult to find above [[Terahertz radiation|terahertz]] frequencies. In any case, a natural material that can achieve negative values for permittivity and permeability simultaneously has not been found or discovered. Hence, all of this has led to constructing artificial composite materials known as metamaterials in order to achieve the desired results.<ref name=PSS-B>{{Cite journal|last1=Liu |first1=H. |last2=Liu |first2=Y. M. |last3=Li |first3=T. |last4=Wang |first4=S. M. |last5=Zhu |first5=S. N. |last6=Zhang |first6=X. |year=2009 |title=Coupled magnetic plasmons in metamaterials |url=http://xlab.me.berkeley.edu/publications/pdfs/121.PhysStatSolidiB2009_HuiLiu.pdf |journal=[[Physica Status Solidi B]] |volume=246 |issue=7 |pages=1397–1406 |arxiv=0907.4208 |bibcode=2009PSSBR.246.1397L |doi=10.1002/pssb.200844414 |s2cid=16415502 |url-status=dead |archive-url=https://web.archive.org/web/20100624145823/http://xlab.me.berkeley.edu/publications/pdfs/121.PhysStatSolidiB2009_HuiLiu.pdf |archive-date=June 24, 2010 }}</ref>

==Negative index of refraction due to chirality==
In case of [[chirality (electromagnetism)|chiral]] materials, the refractive index <math>n</math> depends not only on permittivity <math>\epsilon_r</math> and permeability <math>\mu_r</math>, but also on the chirality parameter <math>\kappa</math>, resulting in distinct values for left and right circularly polarized waves, given by

:<math>n = \pm\sqrt{\epsilon_r\mu_r} \pm \kappa</math>

A negative index will occur for waves of one circular polarization if <math>\kappa</math> > <math>\sqrt{\epsilon_r\mu_r}</math>. In this case, it is not necessary that either or both <math>\epsilon_r</math> and <math>\mu_r</math> be negative to achieve a negative index of refraction. A negative refractive index due to chirality was predicted by Pendry<ref>{{Cite journal| last = Pendry| first =J. B.| title =A Chiral Route to Negative Refraction| journal =Science| volume =306| year =2004| issue =5700| pages =1353–5| doi =10.1126/science.1104467| bibcode=2004Sci...306.1353P| pmid=15550665 | s2cid =13485411}}</ref> and Tretyakov ''et al.'',<ref>{{Cite journal| last = Tretyakov| first =S.|author2=Nefedov, I. |author3=Shivola, A. |author4=Maslovski, S. |author5=Simovski, C.| title =Waves and Energy in Chiral Nihility| journal =[[Journal of Electromagnetic Waves and Applications]]| volume =17| page =695| year =2003| issue =5| doi =10.1163/156939303322226356| arxiv =cond-mat/0211012| bibcode =2003JEWA...17..695T| s2cid =119507930}}</ref> and first observed simultaneously and independently by Plum ''et al.''<ref>{{Cite journal| last = Plum| first =E.|author2=Zhou, J. |author3=Dong, J. |author4=Fedotov, V. A. |author5=Koschny, T. |author6=Soukoulis, C. M. |author7=Zheludev, N. I.  | title =Metamaterial with negative index due to chirality| journal =Physical Review B| volume =79| page =035407| year =2009| issue =3| doi =10.1103/PhysRevB.79.035407| bibcode =2009PhRvB..79c5407P| s2cid =119259753| url =https://eprints.soton.ac.uk/65777/1/4174.pdf}}</ref> and Zhang ''et al.''<ref>{{Cite journal| last = Zhang| first =S.|author2=Park, Y.-S. |author3=Li, J. |author4=Lu, X. |author5=Zhang, W. |author6=Zhang, X.| title =Negative Refractive Index in Chiral Metamaterials| journal =Physical Review Letters| volume =102| page =023901| year =2009| issue =2| doi =10.1103/PhysRevLett.102.023901| pmid =19257274| bibcode =2009PhRvL.102b3901Z}}</ref> in 2009.

==Physical properties never before produced in nature==
Theoretical articles were published in 1996 and 1999 which showed that synthetic materials could be constructed to purposely exhibit a negative [[permittivity]] and [[magnetic permeability|permeability]].<ref group=note>'''Negative permitivitty''' was explored in group of research papers which included:
* {{cite journal | last1 = Pendry | first1 = J.B. | display-authors = etal | year = 1996 | title = Extremely Low Frequency Plasmons in Metallic Microstructures | journal = [[Phys. Rev. Lett.]] | volume = 76 | issue = 25 | pages = 4773–4776 | doi = 10.1103/physrevlett.76.4773 | pmid = 10061377 | bibcode = 1996PhRvL..76.4773P | s2cid = 35826875 }}
<br>'''Effective permeability''' with large positive and negative values was explored in the following research:
* {{cite journal|last=Pendry|first=J.B.|author2=Holden, A.J.|author3=Robbins, D.J.|author4=Stewart, W.J|title=Magnetism from conductors and enhanced nonlinear phenomena|journal=[[IEEE Transactions on Microwave Theory and Techniques]]|year=1999|volume=47|issue=11|pages=2075–2084|doi=10.1109/22.798002|access-date=2009-07-07|url=http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/magwires.pdf|bibcode=1999ITMTT..47.2075P|citeseerx=10.1.1.564.7060|archive-date=2011-07-17|archive-url=https://web.archive.org/web/20110717081405/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/magwires.pdf|url-status=dead}}
*{{Cite journal |last1=Cai |first1=W. |last2=Chettiar |first2=U. K. |last3=Yuan |first3=H.-K. |last4=de Silva |first4=V. C. |last5=Kildishev |first5=A. V. |last6=Drachev |first6=V. P. |last7=Shalaev |first7=V. M. |year=2007 |title=Metamagnetics with rainbow colors |url=https://engineering.purdue.edu/~shalaev/Publication_list_files/6A90A27E-BDB9-137E-C0F42FDC17844DBB_131194.pdf |journal=Optics Express |volume=15 |issue=6 |pages=3333–3341 |doi=10.1364/OE.15.003333 |pmid=19532574 |bibcode=2007OExpr..15.3333C |author7-link=Shalaev |doi-access=free }}</ref>

These papers, along with [[Victor Veselago|Veselago's]] 1967 theoretical analysis of the properties of negative-index materials, provided the background to fabricate a [[metamaterial]] with negative effective permittivity and permeability.<ref name=Spectroscopy-of-metamaterials-05/><ref name=Physicsworld-Mar-24-2000/><ref>
{{Cite journal
 |last1=Shelby | first1=R. A.
 |last2=Smith |first2=D. R.
 |last3=Schultz |first3=S.
 |year=2001
 |title=Experimental verification of a negative index of refraction
 |journal=[[Science (journal)|Science]]
 |volume=292 |issue=5514 |pages=77–79  
 |bibcode=2001Sci...292...77S
 |doi=10.1126/science.1058847
 |jstor=3082888
 |pmid=11292865
| citeseerx=10.1.1.119.1617
 | s2cid=9321456
 }}</ref> See below.

A [[metamaterial]] developed to exhibit negative-index behavior is typically formed from individual components. Each component responds differently and independently to a radiated [[electromagnetic wave]] as it travels through the material. Since these components are smaller than the radiated [[wavelength]] it is understood that a [[macroscopic]] view includes an [[Effective medium model|effective value]] for both permittivity and permeability.<ref name=Spectroscopy-of-metamaterials-05>
{{Cite journal
 |last1=Padilla |first1=W.J.
 |last2=Smith |first2=D. R.
 |last3=Basov |first3=D. N.
 |year=2006
 |title=Spectroscopy of metamaterials from infrared to optical frequencies
 |url=https://apps.dtic.mil/sti/pdfs/ADA487502.pdf
 |archive-url=https://web.archive.org/web/20110604035404/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA487502&Location=U2&doc=GetTRDoc.pdf
 |url-status=live
 |archive-date=2011-06-04
 |journal=[[Journal of the Optical Society of America B]]
 |volume=23 |issue=3 |pages=404–414
 |bibcode=2006JOSAB..23..404P
 |doi=10.1364/JOSAB.23.000404
}}</ref>

===Composite material===
In the year 2000, [[David R. Smith (physicist)|David R. Smith]]'s team of [[UCSD]] researchers produced a new class of [[composite material]]s 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. This material exhibited unusual [[Physics|physical properties]] that had never been observed in nature. These materials obey the [[laws of physics]], but behave differently from normal materials. In essence these ''negative-index metamaterials'' were noted for having the ability to reverse many of the [[physical properties]] that govern the behavior of ordinary optical materials. One of those unusual properties is the ability to reverse, for the first time, [[Snell's law]] of refraction. Until the demonstration of negative refractive index for microwaves by the UCSD team, the material had been unavailable. Advances during the 1990s in fabrication and computation abilities allowed these first [[metamaterial]]s to be constructed. Thus, the "new" metamaterial was tested for the effects described by [[Victor Veselago]] 30 years earlier. Studies of this experiment, which followed shortly thereafter, announced that other effects had occurred.<ref name=comp/><ref name=Spectroscopy-of-metamaterials-05/><ref name=Physicsworld-Mar-24-2000>{{Cite news| title =Physicists invent "left-handed" material| newspaper =Physicsworld.org| page =01| publisher =[[Institute of Physics]]| date =2000-03-24| url =http://physicsworld.com/cws/article/news/2866| access-date =2010-02-11| archive-date =2010-01-14| archive-url =https://web.archive.org/web/20100114003901/http://physicsworld.com/cws/article/news/2866| url-status =dead}}</ref><ref name=UCSD-press-release/>

With [[antiferromagnet]]s and certain types of insulating [[ferromagnet]]s, effective negative [[magnetic permeability]] is achievable when [[polariton]] resonance exists. To achieve a negative index of refraction, however, permittivity with negative values must occur within the same frequency range. The artificially fabricated [[split-ring resonator]]  is a design that accomplishes this, along with the promise of dampening high losses. With this first introduction of the metamaterial, it appears that the losses incurred were smaller than antiferromagnetic, or ferromagnetic materials.<ref name=comp/>

When first demonstrated in 2000, the composite material (NIM) was limited to transmitting [[Microwave|microwave radiation]] at frequencies of 4 to 7 [[gigahertz]] (4.28–7.49&nbsp;cm wavelengths). This range is between the frequency of household microwave ovens ([[ISM band|~2.45]]&nbsp;[[GHz]], 12.23&nbsp;cm) and military [[radars]] (~10&nbsp;GHz, 3&nbsp;cm). At demonstrated frequencies, pulses of [[electromagnetic radiation]] moving through the material in one direction are composed of constituent waves moving in the opposite direction.<ref name=comp/><ref name=UCSD-press-release>{{cite web|author=McDonald, Kim|title=UCSD Physicists Develop a New Class of Composite Material with 'Reverse' Physical Properties Never Before Seen |url=http://ucsdnews.ucsd.edu/newsrel/science/mccomposite.htm|publisher=UCSD Science and Engineering|date=2000-03-21 |access-date=2010-12-17}}</ref><ref name=Nsf1>{{cite web |author=Program contact: Carmen Huber|title=Physicist Produce Left Handed Composite Material|url=https://www.nsf.gov/pubs/2000/pr0009/pr0009.txt|publisher=[[National Science Foundation]]|date=2000-03-21|access-date=2009-07-10}}</ref>

The metamaterial was constructed as a [[Periodic function|periodic array]] of  [[copper]] split ring and wire conducting elements deposited onto a circuit-board substrate. The design was such that the cells, and the [[lattice spacing]] between the cells, were much smaller than the radiated [[wavelength|electromagnetic wavelength]]. Hence, it behaves as an [[Effective medium model|effective medium]]. The material has become notable because its range of (effective) [[permittivity]] ε<sub>eff</sub> and [[magnetic permeability|permeability]] μ<sub>eff</sub> values have exceeded those found in any ordinary material. Furthermore, the characteristic of negative (effective) permeability evinced by this medium is particularly notable, because it has ''not'' been found in ordinary materials. In addition, the negative values for the magnetic component is directly related to its left-handed nomenclature, and properties (discussed in a section below). The [[split-ring resonator]] (SRR), based on the prior 1999 theoretical article, is the tool employed to achieve negative permeability. This first composite ''metamaterial'' is then composed of split-ring resonators and electrical conducting posts.<ref name=comp/>

Initially, these materials were only demonstrated at wavelengths longer than those in the [[visible spectrum]]. In addition, early NIMs were fabricated from [[Opacity (optics)|opaque]] materials and usually made of non-magnetic constituents. As an illustration, however, if these materials are constructed at [[visible frequencies]], and a [[flashlight]] is shone onto the resulting NIM slab, the material should focus the [[light]] at a point on the other side. This is not possible with a sheet of ordinary opaque material.<ref name=AAAS2/><ref name=comp/><ref name=UCSD-press-release/> In 2007, the [[NIST]] in collaboration with the [[Harry Atwater|Atwater]] Lab at [[Caltech]] created the first NIM active at optical frequencies. More recently ({{as of|2008|lc=on}}), layered "fishnet" NIM materials made of silicon and silver wires have been integrated into optical fibers to create active optical elements.<ref name="Ma, Hyungjin Dissertation">{{cite web | url=http://web.mit.edu/nanophotonics/projects/Dissertation_Hyungjin.pdf#page=56 | title=An Experimental Study of Light-Material Interaction at Subwavelength Scale | publisher=MIT | work=PhD Dissertation | year=2011 | access-date=January 23, 2012 | author=Ma, Hyungjin | page=48}}</ref><ref name="2009 OSA">{{cite journal|title=Ultrafast modulation of optical metamaterials |journal=Optics Express |volume=17 |issue=20 |date=2009-09-28 |bibcode=2009OExpr..1717652C |last2=Wu |first2=Wei |last3=Ponizovskaya |first3=Ekaterina |last4=Chaturvedi |first4=Pratik |last5=Bratkovsky |first5=Alexander M. |last6=Wang |first6=Shih-Yuan |last7=Zhang |first7=Xiang |last8=Wang |first8=Feng |last9=Shen |first9=Y. Ron |pages=17652–7 |doi=10.1364/OE.17.017652 |pmid=19907550 |last1=Cho |first1=D.J. |s2cid=8651163 |doi-access=free }}</ref><ref name="Chaturvedi, Pratik dissertation">{{cite web | url=http://web.mit.edu/nanophotonics/projects/Dissertation_Pratik.pdf | title=Optical Metamaterials: Design, Characterization and Applications | publisher=MIT | work=PhD Dissertation | year=2009 | access-date=January 23, 2012 | author=Chaturvedi, Pratik | page=28}}</ref>

===Simultaneous negative permittivity and permeability===

Negative permittivity ε<sub>eff</sub> < 0 had already been discovered and realized in metals for frequencies all the way up to the [[plasma frequency]], before the first metamaterial. There are two [[requirements]] to achieve a negative value for [[refraction]]. First, is to fabricate a material which can produce negative permeability μ<sub>eff</sub> < 0. Second, negative values for both permittivity and permeability must occur simultaneously over a common range of frequencies.<ref name=AAAS2/><ref name=Spectroscopy-of-metamaterials-05/>

Therefore, for the first metamaterial, the nuts and bolts are one [[split-ring resonator]] electromagnetically combined with one (electric) conducting post. These are designed to resonate at designated frequencies to achieve the desired values. Looking at the make-up of the split ring, the associated [[magnetic field]] pattern from the SRR is [[dipolar]]. This dipolar behavior is notable because this means it mimics nature's [[atom]], but on a much larger scale, such as in this case at 2.5 [[millimeter]]s. Atoms exist on the scale of [[picometer]]s.

The splits in the rings create a [[Dynamics (physics)|dynamic]] where the SRR unit cell can be made [[resonant]] at [[EM radiation|radiated wavelengths]] ''much larger'' than the [[diameter]] of the rings. If the rings were closed, a half wavelength boundary would be [[electromagnet]]ically imposed as a requirement for [[resonance]].<ref name=comp>{{cite journal|doi=10.1103/PhysRevLett.84.4184 |title=Composite Medium with Simultaneously Negative Permeability and Permittivity |first5=S. |last5=Schultz |first4=S. |last4=Nemat-Nasser |first3=D. |last3=Vier |first2=Willie |year=2000 |last2=Padilla |last1=Smith |first1=D. R. |journal=[[Physical Review Letters]] |volume=84 |pages=4184–7 |pmid=10990641 |issue=18 |bibcode=2000PhRvL..84.4184S |doi-access=free }}</ref>

The split in the second ring is oriented opposite to the split in the first ring. It is there to generate a large [[capacitance]], which occurs in the small gap. This capacitance substantially decreases the resonant frequency while concentrating the [[electric field]]. The individual SRR depicted on the right had a resonant frequency of [[Microwave|4.845 GHz]], and the resonance curve, inset in the graph, is also shown. The radiative losses from [[Absorption (electromagnetic radiation)|absorption]] and [[Reflection (physics)|reflection]] are noted to be small, because the unit dimensions are much smaller than the [[free space]], radiated [[wavelength]].<ref name=comp/>

When these units or cells are combined into a [[Split-ring resonator|periodic arrangement]], the [[magnetic coupling]] between the resonators is strengthened, and a ''strong magnetic coupling occurs''. Properties unique in comparison to ordinary or conventional materials begin to emerge. For one thing, this periodic strong coupling creates a material, which now has an effective magnetic permeability μ<sub>eff</sub> in response to the [[Physical optics|radiated-incident]] magnetic field.<ref name=comp/>

===Composite material passband===
Graphing the general [[Dispersion (optics)|dispersion curve]], a region of [[Wave propagation|propagation]] occurs from zero up to a lower [[Frequency band|band edge]], followed by a gap, and then an upper [[passband]]. The presence of a [[MHz|400 MHz]] gap between [[Microwave|4.2 GHz and 4.6 GHz]] implies a band of frequencies where μ<sub>eff</sub> < 0 occurs.

(''Please see the image in the previous section'')

Furthermore, when wires are added [[symmetric]]ally between the split rings, a [[passband]] occurs within the previously [[forbidden band]] of the split ring dispersion curves. That this passband occurs within a previously forbidden region indicates that the negative ε<sub>eff</sub> for this region has combined with the negative μ<sub>eff</sub> to allow propagation, which fits with theoretical predictions. Mathematically, the dispersion relation leads to a band with negative [[group velocity]] everywhere, and a bandwidth that is independent of the [[plasma frequency]], within the stated conditions.<ref name=comp/>

[[Mathematical modeling]] and experiment have both shown that periodically arrayed conducting elements (non-magnetic by nature) respond predominantly to the [[magnetic field|magnetic component]] of [[Physical optics|incident electromagnetic fields]]. The result is an effective medium and negative μ<sub>eff</sub> over a band of frequencies. The permeability was verified to be the region of the forbidden band, where the gap in propagation occurred – from a finite section of material. This was combined with a negative permittivity material, ε<sub>eff</sub> < 0, to form a “left-handed” medium, which formed a propagation band with negative group velocity where previously there was only attenuation. This validated predictions. In addition, a later work determined that this first [[metamaterial]] had a range of frequencies over which the refractive index was predicted to be negative for one direction of [[wave propagation|propagation]] (see ref #<ref name=AAAS2/>). Other predicted [[electrodynamic]] effects were to be investigated in other research.<ref name=comp/>

===Describing a left-handed material===
[[Image:metarefraction.svg|thumb|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').]]
From the conclusions in the above section a left-handed material (LHM) can be defined. It is a material which exhibits simultaneous [[negative numbers|negative values]] for  [[permittivity]], ε, and [[magnetic permeability|permeability]], μ, in an overlapping frequency region. Since the values are derived from the effects of the [[metamaterial|composite medium system]] as a whole, these are defined as effective permittivity, ε<sub>eff</sub>, and effective permeability, μ<sub>eff</sub>. Real values are then derived to denote the value of [[negative refractive index|negative index]] of refraction, and [[wave vector]]s. This means that in practice losses will occur for a given medium used to [[transmission coefficient|transmit]] electromagnetic radiation such as [[microwave]], or [[infrared]] frequencies, or [[visible light]] – for example. In this instance, real values describe either the [[amplitude]] or the [[Intensity (physics)|intensity]] of a transmitted wave relative to an incident wave, while ignoring the negligible loss values.<ref name=APhys1/><ref name=comp/>

==Isotropic negative index in two dimensions==
In the above sections first fabricated [[metamaterial]] was constructed with [[resonate|resonating elements]], which exhibited one direction of [[angle of incidence (optics)|incidence]] and [[polarization (waves)|polarization]]. In other words, this structure exhibited left-handed propagation in one dimension. This was discussed in relation to Veselago's seminal work 33 years earlier (1967). He predicted that intrinsic to a material, which manifests negative values of effective [[permittivity]] and [[magnetic permeability|permeability]], are several types of reversed [[Physical property|physics phenomena]]. Hence, there was then a critical need for a higher-dimensional LHMs to confirm Veselago's theory, as expected. The confirmation would include reversal of [[Snell's law]] (index of refraction), along with other reversed phenomena.

In the beginning of 2001 the existence of a higher-dimensional structure was reported. It was two-dimensional and demonstrated by both experiment and numerical confirmation. It was an [[#Describing a left-handed material|LHM]], a composite constructed of wire strips mounted behind the split-ring resonators (SRRs) in a periodic configuration. It was created for the express purpose of being suitable for further experiments to produce the effects predicted by Veselago.<ref name=APhys1/>

==Experimental verification of a negative index of refraction==
[[File:Left-handed metamaterial array configuration.jpg|thumb|260px|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.<ref name=comp/>]]

A 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. As discussed previously (above), the first [[metamaterial]]  had a range of frequencies over which the refractive index was predicted to be negative for one direction of [[wave propagation|propagation]]. It was reported in May 2000.<ref name=AAAS2/><ref name=first-paper/><ref name="physicsworld-April–2001">{{Cite news| last =Pennicott| first =Katie| title =Magic material flips refractive index| newspaper =[[Physics World]]| publisher =[[Institute of Physics]]| date =2001-04-05| url =http://physicsworld.com/cws/article/news/2692| access-date =2010-02-12| archive-date =2010-01-13| archive-url =https://web.archive.org/web/20100113223429/http://physicsworld.com/cws/article/news/2692| url-status =dead}}</ref>

In 2001, a team of [[researcher]]s constructed a prism composed of metamaterials (negative-index metamaterials) to experimentally test for negative refractive index. The experiment used a waveguide to help transmit the proper frequency and isolate the material. This test achieved its goal because it successfully verified a negative index of refraction.<ref name=AAAS2>

{{cite journal|last=Shelby|first=R. A.|author2=Smith D.R |author3=Shultz S. |title=Experimental Verification of a Negative Index of Refraction|journal=[[Science (journal)|Science]]|year=2001|volume=292
|issue=5514|pages=77–79|doi=10.1126/science.1058847|pmid=11292865|bibcode = 2001Sci...292...77S |citeseerx=10.1.1.119.1617|s2cid=9321456}}</ref><ref name=first-paper/><ref name=Snellslaw1>

{{cite web|author=Bill Casselman|title=The Law of Refraction
|url=http://www.math.ubc.ca/~cass/courses/m309-01a/chu/Fundamentals/snell.htm
|publisher=University of British Columbia, [[Canada]], Department of Mathematics
|year=2009|access-date=2009-07-06|author-link=Bill Casselman (mathematician)
}}</ref><ref name=Opticshistory1>{{cite web|author=Taylor, L.S.|title=An Anecdotal History of Optics from Aristophanes to Zernike|url=http://www.ece.umd.edu/~taylor/optics.htm|publisher=[[University of Maryland]]; Electrical Engineering Department|year=2009|access-date=2009-07-07|archive-date=2011-03-05|archive-url=https://web.archive.org/web/20110305043521/http://www.ece.umd.edu/~taylor/optics.htm|url-status=dead}}</ref><ref name=Newjournalphys1>

{{cite journal|last=Ward|first=David W. |author2=Nelson, Keith A |author3=Webb, Kevin J|title=On the physical origins of the negative index of refraction|journal=New Journal of Physics|year=2005|volume=7| arxiv=physics/0409083
|issue=213|page=213|doi=10.1088/1367-2630/7/1/213|bibcode = 2005NJPh....7..213W |s2cid=119434811 }}</ref><ref name=IEEE1>
{{cite journal|last=Pendry|first=J.B.|author2=Holden, A.J.|author3=Robbins, D.J.|author4=Stewart, W.J|title=Magnetism from conductors and enhanced nonlinear phenomena|journal=[[IEEE Transactions on Microwave Theory and Techniques]]|year=1999|volume=47|issue=11|pages=2075–2084|doi=10.1109/22.798002|access-date=2009-07-07|url=http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/magwires.pdf|bibcode=1999ITMTT..47.2075P|citeseerx=10.1.1.564.7060|archive-url=https://web.archive.org/web/20110717081405/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/magwires.pdf|archive-date=2011-07-17|url-status=dead}}
</ref><ref name=microwave1>{{cite web
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The experimental demonstration of negative refractive index was followed by another demonstration, in 2003, of a reversal of Snell's law, or reversed refraction. However, in this experiment negative index of refraction material is in free space from 12.6 to 13.2&nbsp;GHz. Although the radiated frequency range is about the same, a notable distinction is this experiment is conducted in free space rather than employing waveguides.<ref name=free-space-neg>{{Cite journal|last1=Parazzoli |first1=C.G. |last2=Greegor |first2=R. |last3=Li |first3=K. |last4=Koltenbah |first4=B. |last5=Tanielian |first5=M. |title=Experimental Verification and Simulation of Negative Index of Refraction Using Snell's Law |journal=[[Physical Review Letters]] |volume=90 |issue=10 |pages=107401 (2003) [4 pages] |format=PDF download available to the public. |date=2003-03-11 |url=http://capem.buffalo.edu/rashba/PRL07401.pdf |doi=10.1103/PhysRevLett.90.107401 |bibcode=2003PhRvL..90j7401P |display-authors=1 |url-status=dead |archive-url=https://web.archive.org/web/20110719154737/http://capem.buffalo.edu/rashba/PRL07401.pdf |archive-date=July 19, 2011 |pmid=12689029}}</ref>

Furthering the authenticity of negative refraction, the power flow of a wave transmitted through a dispersive left-handed material was calculated and compared to a dispersive right-handed material. The transmission of an incident field, composed of many frequencies, from an isotropic nondispersive material into an isotropic dispersive media is employed. The direction of power flow for both nondispersive and dispersive media is determined by the time-averaged
[[Poynting vector]]. Negative refraction was shown to be possible for multiple frequency signals by explicit calculation of the Poynting vector in the LHM.<ref name=power-proof-2002>{{Cite journal|last1=Pacheco |first1=J. |format=PDF download is available to the public. |last2=Grzegorczyk |first2=T. |last3=Wu |first3=B.-I. |last4=Zhang |first4=Y. |last5=Kong |first5=J. |title=Power Propagation in Homogeneous Isotropic Frequency-Dispersive Left-Handed Media |journal=[[Phys. Rev. Lett.]] |volume=89 |issue=25 |pages=257401 (2002) [4 pages] |date=2002-12-02 |url=http://web.mit.edu/biwu/www/bib/2002/pacheco_2002_prl.pdf |doi=10.1103/PhysRevLett.89.257401 |access-date=2010-04-19 |pmid=12484915 |bibcode=2002PhRvL..89y7401P |url-status=dead |archive-url=https://web.archive.org/web/20050524214743/http://web.mit.edu/biwu/www/bib/2002/pacheco_2002_prl.pdf |archive-date=May 24, 2005 }}</ref>

===Fundamental electromagnetic properties of the NIM===
In a slab of conventional material with an ordinary [[refractive index]] – a right-handed material (RHM) – the [[wave front]] is transmitted away from the source. In a NIM the wavefront travels toward the source. However, the magnitude and direction of the flow of energy essentially remains the same in both the ordinary material and the NIM. Since the flow of energy remains the same in both materials (media), the impedance of the NIM matches the RHM. Hence, the sign of the intrinsic impedance is still positive in a NIM.<ref name=fund-prop-Caloz/><ref name=fund-prop-Ziolkowski/>

Light incident on a left-handed material, or NIM, will bend to the same side as the incident beam, and for Snell's law to hold, the refraction angle should be negative. In a passive metamaterial medium this determines a negative real and imaginary part of the refractive index.<ref name=physicsengineering1/><ref name=fund-prop-Caloz>{{Cite journal| last1 =Caloz| first1 =C.| last2 =Chang| first2 =C.-C.| last3 =Itoh| first3 =T.| title =Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations| journal =[[Journal of Applied Physics]]| volume =90| issue =11| page =5483| date =2001-12-01| url =http://xlab.me.berkeley.edu/MURI/publications/publications_9.pdf| doi =10.1063/1.1408261| access-date =2009-12-29| bibcode =2001JAP....90.5483C| display-authors =1| archive-date =2021-09-16| archive-url =https://web.archive.org/web/20210916205833/http://xlab.me.berkeley.edu/MURI/publications/publications_9.pdf| url-status =dead}}</ref><ref name=fund-prop-Ziolkowski>{{Cite journal|last=Ziolkowski |first=Richard W |author2=Ehud Heyman |title=Wave propagation in media having negative permittivity and permeability |journal=Physical Review E |volume=64 |page=056625 |date=2001-10-30 |url=http://mesoscopic.mines.edu/mediawiki/images/3/3d/Waveprop_DNG_media.pdf |doi=10.1103/PhysRevE.64.056625 |pmid=11736134 |access-date=2009-12-30 |bibcode=2001PhRvE..64e6625Z |issue=5 |s2cid=38798156 |url-status=dead |archive-url=https://web.archive.org/web/20100717004208/http://mesoscopic.mines.edu/mediawiki/images/3/3d/Waveprop_DNG_media.pdf |archive-date=July 17, 2010 }}</ref>

===Negative refractive index in left-handed materials===
[[Image:Cartesian coordinate system handedness.svg|thumb|200px|The left-handed orientation is shown on the left, and the right-handed on the right.]]
In 1968 [[Victor Veselago]]'s paper showed that the opposite directions of EM [[plane waves]] and the flow of energy was derived from the individual [[Maxwell's equations|Maxwell curl equations]]. In ordinary [[optical]] materials, the curl equation for the [[electric field]] show a "right hand rule" for the directions of the electric field '''E''', the magnetic induction '''B''', and wave propagation, which goes in the direction of [[wave vector| wave vector '''k''']]. However, the direction of energy flow formed by E × H is right-handed only when ''permeability is greater than zero''. This means that when permeability is less than zero, e.g. ''negative'', [[wave propagation]] is reversed (determined by k), and contrary to the direction of energy flow. Furthermore, the relations of vectors '''E''',''' H''', and '''k''' form a "''left-handed" system'' – and it was Veselago who coined the term "left-handed" (LH) material, which is in wide use today (2011). He contended that an LH material has a negative refractive index and relied on the [[steady state|steady-state solutions]] of [[Maxwell's equations]] as a center for his argument.<ref name=PRL-V85-2000>{{Cite journal|last=Smith |first=David R.and |author2=Norman Kroll |title=Negative Refractive Index in Left-Handed Materials |journal=Physical Review Letters |volume=85 |issue=14 |pages=2933–2936 |date=2000-10-02 |pmid=11005971 |url=http://www.pi5.uni-stuttgart.de/lehre/wp2001/prl2000-smith.pdf |doi=10.1103/PhysRevLett.85.2933 |access-date=2010-01-04 |bibcode=2000PhRvL..85.2933S |url-status=dead |archive-url=https://web.archive.org/web/20110719111136/http://www.pi5.uni-stuttgart.de/lehre/wp2001/prl2000-smith.pdf |archive-date=July 19, 2011 }}</ref>

After a 30-year void, when LH materials were finally demonstrated, it could be said that the designation of [[negative refractive index]] is unique to LH systems; even when compared to [[photonic crystal]]s. Photonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase and group velocities. But, negative refraction does not occur in these systems, and not yet realistically in photonic crystals.<ref name=PRL-V85-2000/><ref name=PIERB-V2-2008>{{Cite journal|last1=Srivastava |first1=R. |last2=Srivastava |first2=Shalini |last3=Ojha |first3=Sant Prasad |title=Negative refraction by Photonic Crystal |journal=Progress in Electromagnetics Research B |volume=2 |pages=15–26 |year=2008 |url=http://ceta.mit.edu/pierb/pierb02/02.08042302.pdf |doi=10.2528/PIERB08042302 |access-date=2010-01-04 |display-authors=1 |url-status=dead |archive-url=https://web.archive.org/web/20100719223737/http://ceta.mit.edu/PIERb/pierb02/02.08042302.pdf |archive-date=July 19, 2010 }}</ref><ref name=DARPA>{{cite web
 |last         = Abo-Shaeer
 |first        = Jamil R. 
 |title        = Negative-Index Materials
 |publisher    = [[DARPA]] – [[Defense Science Offices]] (DSO)
 |date         = July 2010
 |url          = http://www.darpa.mil/dso/thrusts/materials/novelmat/nim/index.htm
 |format       = Public Domain – Information presented on the DARPA Web Information Service is considered public information and may be distributed or copied.
 |access-date   = 2010-07-05
 |archive-url  = https://web.archive.org/web/20101224211433/http://www.darpa.mil/dso/thrusts/materials/novelmat/nim/index.htm
 |archive-date = 2010-12-24
 |url-status   = dead
}}</ref>

===Negative refraction at optical frequencies===
The negative refractive index in the optical range was first demonstrated in 2005 by [[Shalaev]] et al. (at the telecom wavelength λ = 1.5 μm)<ref name=nanorod></ref> and by Brueck et al. (at λ = 2 μm) at nearly the same time.<ref name=Brueck>
{{cite journal
 |last1=Zhang |first1=Shuang
 |last2=Fan |first2=Wenjun
 |last3=Panoiu |first3=N. C.
 |last4=Malloy |first4=K. J.
 |last5=Osgood |first5=R. M. |author5-link=Richard M. Osgood Jr.
 |last6=Brueck |first6=S. R. J.
 |year=2005
 |title=Experimental Demonstration of Near-Infrared Negative-Index Metamaterials
 |url=https://engineering.purdue.edu/~shalaev/Publication_list_files/OLpaper.pdf
 |journal=[[Phys. Rev. Lett.]]
 |volume=95 |issue=13
 |pages=137404
 |arxiv=physics/0504208
|doi=10.1103/PhysRevLett.95.137404
 |pmid=16197179
 |bibcode=2005PhRvL..95m7404Z
 |s2cid=15246675
 }}</ref>

In 2006, a Caltech team led by Lezec, Dionne, and Atwater achieved negative refraction in the [[visible spectral regime]].<ref>Caltech Media Relations. [http://media.caltech.edu/press_releases/12959 Negative Refraction of Visible Light Demonstrated; Could Lead to Cloaking Devices] {{webarchive |url=https://web.archive.org/web/20100601205356/http://media.caltech.edu/press_releases/12959 |date=June 1, 2010 }}. March 22, 2007. accessdate – 2010-05-05</ref><ref name=Phys-org-Apr10>{{cite web| last =PhysOrg.com| title =Novel negative-index metamaterial that responds to visible light designed| date =April 22, 2010  
  | url =http://www.physorg.com/news191168001.html| format =Web page| access-date =2010-05-05}}</ref><ref name=PopSci-Apr10>{{cite web
  | last = Dillow| first =Clay| title =New Metamaterial First to Bend Light in the Visible Spectrum
  | publisher =[[Popular Science]]| date =April 23, 2010
  | url =http://www.popsci.com/science/article/2010-04/new-single-layer-metamaterial-bends-light-visible-spectrum| format =Web page| access-date =2010-05-05}}{{Dead link|date=February 2016}}</ref>

==Experimental verification of reversed Cherenkov radiation==
Besides reversed values for [[index of refraction]], Veselago predicted the occurrence of reversed [[Cherenkov radiation]] (also known simply as CR) in a left-handed medium. In 1934 [[Pavel Cherenkov]] discovered a [[coherent radiation]] that occurs when certain types of media are bombarded by fast moving electron beams. In 1937 a theory built around CR stated that when charged particles, such as electrons, travel through a medium at speeds faster than the speed of light in the medium only then will CR radiate. As the CR occurs, electromagnetic radiation is emitted in a cone shape, fanning out in the forward direction.

CR and the 1937 [[theory]] has led to a large array of applications in high energy physics. A notable application are the Cherenkov counters. These are used to determine various properties of a charged particle such as its velocity, charge, direction of motion, and energy. These properties are important in the identification of different particles. For example, the counters were applied in the discovery of the [[antiproton]] and the [[J/psi meson|J/ψ meson]]. Six large [[Cherenkov detector|Cherenkov counters]] were used in the discovery of the J/ψ meson.

It has been difficult to experimentally prove the reversed Cherenkov radiation.<ref name=bw-cr-2009>{{Cite journal
  | last1 = Xi| first1 =Sheng
  | last2 = Chen| first2 = Hongsheng
  | last3 = Jiang | first3 = Tao | last4 = Ran | first4 = Lixin
  | last5 = Huangfu | first5 = Jiangtao | last6 = Wu  | first6 = Bae-Ian
  | last7 = Kong | first7 = Jin | last8 = Chen | first8 = Min
  | title =Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial 
  | journal =[[Phys. Rev. Lett.]]| volume =103| issue =19| pages =194801 (2009)| date =2009-11-02| doi =10.1103/PhysRevLett.103.194801| pmid=20365927 | bibcode=2009PhRvL.103s4801X
  | display-authors = 1| hdl =1721.1/52503
 | s2cid =1501102
 | hdl-access = free}}</ref><ref name=bw-cr-Vwpt-2009>
{{Cite journal|last=Zhang |first=Shuang |author2=Xiang Zhang |title=Flipping a photonic shock wave |journal=Physics |volume=02 |issue=91 |page=03 |date=2009-11-02 |doi=10.1103/Physics.2.91 |bibcode=2009PhyOJ...2...91Z |doi-access=free }}</ref>

==Other optics with NIMs==
Theoretical work, along with [[numerical simulation]]s, began in the early 2000s on the abilities of DNG slabs for [[Superlens|subwavelength focusing]]. The research began with Pendry's proposed "[[Perfect lens]]." Several research investigations that followed Pendry's concluded that the "Perfect lens" was possible in theory but impractical. One direction in subwavelength focusing proceeded with the use of negative-index metamaterials, but based on the enhancements for imaging with surface plasmons. In another direction researchers explored [[paraxial approximation]]s of NIM slabs.<ref name=physicsengineering1/>

==Implications of negative refractive materials==
The existence of negative refractive materials can result in a change in [[electrodynamic]] calculations for the case of ''permeability  μ'' = 1 .  A change  from a conventional refractive index to a negative value gives incorrect results for conventional calculations, because some properties and effects have been altered. When ''permeability  μ'' has values other than 1 this affects [[Snell's law]], the [[Doppler effect]], the [[Cherenkov radiation]], [[Fresnel's equations]], and [[Fermat's principle]].<ref name=V2003>
{{cite journal
|doi=10.1070/PU2003v046n07ABEH001614
|title=Electrodynamics of materials with negative index of refraction
|year=2003
|last1=Veselago
|first1=Viktor G
|journal=[[Physics-Uspekhi]]
|volume=46
|issue=7
|page=764
|bibcode=2003PhyU...46..764V|s2cid=250862458
}}. Reprinted in {{Cite book
  | last = Lim Hock |author2=Ong Chong Kim |author3=Serguei Matitsine 
   | title =Electromagnetic Materials 
  | publisher =World Scientific  | series =Proceedings of the Symposium F  
  | edition = (ICMAT 2003) | date =7–12 December 2003 
  | location =SUNTEC, Singapore | pages = 115–122
  | url =https://books.google.com/books?id=fvzKqPwd098C&pg=PA115 
  | isbn =978-981-238-372-3
  }}</ref>

The [[refractive index]] is basic to the science of optics. Shifting the refractive index to a negative value may be a cause to revisit or reconsider the interpretation of some [[Convention (norm)|norms]], or [[optics|basic laws]].<ref name=shalaev/>

==US patent on left-handed composite media==
The first US patent for a fabricated metamaterial, titled "Left handed composite media" by [[David R. Smith (physicist)|David R. Smith]], [[Sheldon Schultz]], [[Norman Kroll]] and [[Richard A. Shelby]], was issued in 2004. The invention achieves simultaneous negative permittivity and permeability over a common band of frequencies. The material can integrate media which is already composite or continuous, but which will produce negative permittivity and permeability within the same spectrum of frequencies. Different types of continuous or composite may be deemed appropriate when combined for the desired effect. However, the inclusion of a periodic array of conducting elements is preferred. The array scatters [[electromagnetic radiation]] at [[wavelengths]] longer than the size of the element and lattice spacing. The array is then viewed as an [[effective medium]].<ref name=US-patent-6791432>Smith, David; Schultz, Sheldon; Kroll, Norman; Shelby, Richard A. "Left handed composite media" {{US Patent|6791432}}
Publication date 2001-03-16, Issue date 2004-03-14.</ref>

==See also==
{{div col|colwidth=22em}}
*[[History of metamaterials]]
*[[Superlens]]
*[[Metamaterial cloaking]]
*[[Photonic metamaterials]]
*[[Metamaterial antenna]]
*[[Nonlinear metamaterials]]
*[[Photonic crystal]]
*[[Seismic metamaterials]]
*[[Split-ring resonator]]
*[[Acoustic metamaterials]]
*[[Metamaterial absorber]]
*[[Metamaterial]]
*[[Plasmonic metamaterials]]
*[[Terahertz metamaterials]]
*[[Tunable metamaterials]]
*[[Transformation optics]]
*[[Theories of cloaking]]
{{div col end}}

;'''Academic journals'''
*[[Metamaterials (journal)|''Metamaterials'']]

;'''Metamaterials books'''
*''[[Metamaterials Handbook]]''
*''[[Metamaterials: Physics and Engineering Explorations]]''

==Notes==
{{USGovernment}} -[[NIST]]

{{Reflist|group=note}}

==References==
{{reflist|30em}}

==Further reading==
*{{cite book| last =S. Anantha Ramakrishna| author2 =Tomasz M. Grzegorczyk| title =Physics and Applications of Negative Refractive Index Materials| publisher =CRC Press| year =2008| url =http://www.fulviofrisone.com/attachments/article/404/6875x_c001.pdf| doi =10.1201/9781420068764.ch1| isbn =978-1-4200-6875-7| url-status =dead| archive-url =https://web.archive.org/web/20160303224255/http://www.fulviofrisone.com/attachments/article/404/6875x_c001.pdf| archive-date =2016-03-03}}
*{{cite journal
 | doi= 10.1088/0034-4885/68/2/R06
 | title= Physics of negative refractive index materials
 | year= 2005
 | last1= Ramakrishna
 | first1= S Anantha
 | journal= Reports on Progress in Physics
 | volume= 68
 | issue= 2
 | page= 449|bibcode = 2005RPPh...68..449R | s2cid= 250829241
 }}

*{{cite journal
 | doi= 10.1103/PhysRevLett.76.4773
 | url= http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/lfplslet.pdf
 | title= Extremely Low Frequency Plasmons in Metallic Mesostructures
 | year= 1996
 | last1= Pendry
 | first1= J.
 | last2= Holden
 | first2= A.
 | last3= Stewart
 | first3= W.
 | last4= Youngs
 | first4= I.
 | journal= Physical Review Letters
 | volume= 76
 | issue= 25
 | pages= 4773–4776
 | pmid= 10061377
 | bibcode= 1996PhRvL..76.4773P
 | access-date= 2011-08-18
 | archive-url= https://web.archive.org/web/20110717081513/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/lfplslet.pdf
 | archive-date= 2011-07-17
 | url-status= dead
 }}

*{{cite journal
 |doi=10.1088/0953-8984/10/22/007
 |url=http://esperia.iesl.forth.gr/~ppm/DALHM/bibliography/LHMpdfs/pendry_jocoma10_4785_98.pdf
 |title=Low frequency plasmons in thin-wire structures
 |year=1998
 |last1=Pendry
 |first1=J B
 |last2=Holden
 |first2=A J
 |last3=Robbins
 |first3=D J
 |last4=Stewart
 |first4=W J
 |journal=Journal of Physics: Condensed Matter
 |volume=10
 |issue=22
 |pages=4785–4809|bibcode = 1998JPCM...10.4785P |s2cid=250891354
 }}  Also see the [https://web.archive.org/web/20110928090729/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/wires.pdf Preprint-author's copy].
*{{cite journal|doi=10.1016/S1369-7021(06)71573-5 |title=Negative refractive index metamaterials |year=2006 |last1=Padilla |first1=Willie J. |last2=Basov |first2=Dimitri N. |last3=Smith |first3=David R. |journal=Materials Today |volume=9 |issue=7–8 |page=28 |doi-access=free }}
*{{cite journal|last1=Bayindir|first1=Mehmet|last2=Aydin|first2=K.|last3=Ozbay|first3=E.|last4=Markoš|first4=P.|last5=Soukoulis|first5=C. M.|title=Transmission properties of composite metamaterials in free space|journal=Applied Physics Letters|volume=81|issue=1|page=120|date=2002-07-01|url=http://yoksis.bilkent.edu.tr/pdf/10.1063-1.1492009.pdf|doi= 10.1063/1.1492009|bibcode = 2002ApPhL..81..120B |hdl=11693/24684|hdl-access=free}}{{Dead link|date=February 2016}}

==External links==
*[http://online.itp.ucsb.edu/online/qo02/pendry/ Manipulating the Near Field with Metamaterials] Slide show, with audio available, by Dr. John Pendry, Imperial College, London
*{{cite book|last=Laszlo Solymar|author2=Ekaterina Shamonina|title=Waves in Metamaterials|url=https://books.google.com/books?id=014CA0-PaqYC&q=Waves+in+Metamaterials|publisher=Oxford University Press, USA. March 2009.|isbn= 978-0-19-921533-1|date=2009-03-15}}
*{{cite web|url=http://www.math.ubc.ca/~cass/courses/m309-01a/chu/Fundamentals/snell.htm|title=Illustrating the Law of Refraction}}
*{{cite news|last = Young|first = Andrew T.|location = SDSU San Diego, CA|title = An Introduction to Mirages|year = 1999–2009|url = http://mintaka.sdsu.edu/GF/mirages/mirintro.html
|access-date = 2009-08-12}}
*{{cite journal|last1=Garrett|first1=C.|last2=McCumber|first2=D.|title=Light pulse and anamolous dispersion|journal=Phys. Rev. A|volume=1|issue=2|pages=305–313|date=1969-09-25|url=http://www.physics.princeton.edu/~mcdonald/examples/optics/garrett_pra_1_305_70.pdf|doi=10.1103/PhysRevA.1.305|bibcode=1970PhRvA...1..305G|display-authors=1}}{{dead link|date=February 2018 |bot=InternetArchiveBot |fix-attempted=yes }}
*[http://www.utexas.edu/research/cemd/nim/News.html List of science website news stories on Left Handed Materials]
*{{Cite journal| last = Caloz| first =Christophe| title =Perspectives on EM metamaterials| journal =[[Materials Today]]| volume =12| issue =3| pages =12–20| date =March 2009| doi =10.1016/S1369-7021(09)70071-9 |doi-access=free}}

{{DEFAULTSORT:Negative Index Metamaterials}}
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