View source for Metamaterial

{{Short description|Materials engineered to have properties that have not yet been found in nature}}
[[File:Split-ring resonator array 10K sq nm.jpg|thumb|220px|[[Negative-index metamaterial]] array configuration, which was constructed of copper [[split-ring resonators]] and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3×20×20 unit cells with overall dimensions of {{convert|10|×|100|×|100|mm|2|lk=out|abbr=on}}.<ref name=APhys1>{{cite journal|last=Shelby |first=R. A. |author2=Smith D.R. |author3=Shultz S. |author4=Nemat-Nasser S.C. |title=Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial |journal=Applied Physics Letters |year=2001 |volume=78 |url=http://people.ee.duke.edu/~drsmith/pubs_smith_group/Shelby_APL_(2001).pdf |issue=4 |doi=10.1063/1.1343489 |page=489 |bibcode=2001ApPhL..78..489S |url-status=dead |archive-url=https://web.archive.org/web/20100618193936/http://people.ee.duke.edu/~drsmith/pubs_smith_group/Shelby_APL_%282001%29.pdf |archive-date=June 18, 2010 }}</ref><ref name=comp>{{cite journal|doi=10.1103/PhysRevLett.84.4184 |title=Composite Medium with Simultaneously Negative Permeability and Permittivity |year=2000 |last1=Smith |first1=D. R. |journal=Physical Review Letters |volume=84 |pages=4184–87 |pmid=10990641 |first2=WJ |first3=DC |first4=SC |first5=S |issue=18 |last2=Padilla |last3=Vier |last4=Nemat-Nasser |last5=Schultz |bibcode=2000PhRvL..84.4184S |doi-access=free }}</ref>]]

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

Appropriately designed metamaterials can affect waves of [[electromagnetic radiation]] or [[sound]] in a manner not observed in bulk materials.<ref name="physicsengineering1">{{cite book|last = Engheta|first =Nader |author-link = Nader Engheta |author2=Richard W. Ziolkowski|title = Metamaterials: Physics and Engineering Explorations|publisher = [[Wiley & Sons]]
|date = June 2006|pages = xv, 3–30, 37, 143–50, 215–34, 240–56
|url = https://books.google.com/books?id=51e0UkEuBP4C|isbn = 978-0-471-76102-0}}</ref><ref name="metamaterialplasmonics1" /><ref name="smithmetamaterials1">{{cite web|last=Smith |first=David R. |author-link=David R. Smith (physicist) |title=What are Electromagnetic Metamaterials? |work=Novel Electromagnetic Materials |publisher=The research group of D.R. Smith |date=2006-06-10 |url=http://people.ee.duke.edu/~drsmith/about_metamaterials.html |access-date=2009-08-19 |url-status=dead |archive-url=https://web.archive.org/web/20090720003945/http://people.ee.duke.edu/~drsmith/about_metamaterials.html |archive-date=July 20, 2009 }}</ref> Those that exhibit a negative [[index of refraction]] for particular wavelengths have been the focus of a large amount of research.<ref name="AAAS2">{{Cite journal | last1 = Shelby | first1 = R. A. | last2 = Smith | first2 = D. R. | last3 = Schultz | first3 = S. | doi = 10.1126/science.1058847 | title = Experimental Verification of a Negative Index of Refraction | journal = Science | volume = 292 | issue = 5514 | pages = 77–79 | year = 2001 | pmid =  11292865| bibcode = 2001Sci...292...77S| citeseerx = 10.1.1.119.1617 | s2cid = 9321456 }}</ref><ref name="Pendry2004">{{cite book
 |last         = Pendry
 |first        = John B.
 |author-link   = John Pendry
 |title        = Negative Refraction
 |journal      = [[Contemporary Physics]]
 |volume       = 45
 |issue        = 3
 |pages        = 191–202
 |year         = 2004
 |url          = http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/NegRef_submit.pdf
 |doi          = 10.1080/00107510410001667434
 |access-date   = 2009-08-26
 |isbn         = 978-0-691-12347-9
 |publisher    = Princeton University Press
 |bibcode      = 2004ConPh..45..191P
 |s2cid = 218544892
 |archive-url  = https://web.archive.org/web/20161020150252/http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/NegRef_submit.pdf
 |archive-date = 2016-10-20
 |url-status   = dead
}}</ref><ref name="Veselago1">{{cite journal 
|last=Veselago|first=V. G.
|title=The electrodynamics of substances with simultaneously negative values of ε and μ
|journal= Physics-Uspekhi
|year=1968|volume=10
|issue=4|pages=509–514
|doi=10.1070/PU1968v010n04ABEH003699
|bibcode = 1968SvPhU..10..509V }}
</ref> These materials are known as [[negative-index metamaterial]]s.

Potential applications of metamaterials are diverse and include [[optical filter]]s, [[medical device]]s, remote [[Aerospace engineering|aerospace]] applications, sensor detection and [[Infrastructure security|infrastructure monitoring]], smart [[solar power]] management, Lasers,<ref>{{cite journal |last1=Awad |first1=Ehab |title=A novel metamaterial gain-waveguide nanolaser |journal=Optics & Laser Technology |date=October 2021 |volume=142 |page=107202 |doi=10.1016/j.optlastec.2021.107202 |bibcode=2021OptLT.14207202A |url=https://www.sciencedirect.com/science/article/abs/pii/S0030399221002905}}</ref> [[crowd control]], [[radome]]s, [[Battlespace|high-frequency battlefield communication]] and lenses for high-gain antennas, improving [[Level sensor|ultrasonic sensors]], and even [[Earthquake engineering|shielding structures from earthquakes]].<ref name=control_elastic_waves/><ref name=Thzoverview>

{{cite journal| last =Rainsford| first =Tamath J.| author2 =D. Abbott| title =T-ray sensing applications: review of global developments
|journal =Proc. SPIE| volume = 5649 Smart Structures, Devices, and Systems II| issue =Poster session| pages =826–38| date = 9 March 2005|doi =10.1117/12.607746| series =Smart Structures, Devices, and Systems II| editor1-last =Al-Sarawi| editor1-first =Said F| bibcode =2005SPIE.5649..826R| author-link2 =Derek Abbott| last3 =Abbott| first3 =Derek| s2cid =14374107}}</ref><ref name=Radome>{{cite journal|last =Cotton|first =Micheal G.|title =Applied Electromagnetics|journal =2003 Technical Progress Report (NITA&nbsp;– ITS)|volume =Telecommunications Theory|issue =3|pages =4–5|date =December 2003|url =http://www.its.bldrdoc.gov/pub/ntia-rpt/tpr/2003/telecommunications_theory-03.pdf|archive-url =https://web.archive.org/web/20080916114021/http://www.its.bldrdoc.gov/pub/ntia-rpt/tpr/2003/telecommunications_theory-03.pdf|url-status =dead|archive-date =2008-09-16|access-date =2009-09-14}}</ref><ref name=radiation-properties/> Metamaterials offer the potential to create [[superlens|super-lens]]es.<ref name="Guerra 3555–3557">{{Cite journal |last=Guerra |first=John M. |date=1995-06-26 |title=Super-resolution through illumination by diffraction-born evanescent waves |url=https://aip.scitation.org/doi/10.1063/1.113814 |journal=Applied Physics Letters |volume=66 |issue=26 |pages=3555–3557 |doi=10.1063/1.113814 |bibcode=1995ApPhL..66.3555G |issn=0003-6951}}</ref>  Such a lens can allow imaging below the [[diffraction limit]] that is the minimum [[optical resolution|resolution]] d=λ/(2NA) that can be achieved by conventional lenses having a numerical aperture NA and with illumination wavelength λ. Sub-wavelength optical metamaterials, when integrated with optical recording media, can be used to achieve optical data density higher than limited by diffraction.<ref>{{Cite journal |last1=Guerra |first1=John |last2=Vezenov |first2=Dmitri |last3=Sullivan |first3=Paul |last4=Haimberger |first4=Walter |last5=Thulin |first5=Lukas |date=2002-03-30 |title=Near-Field Optical Recording without Low-Flying Heads: Integral Near-Field Optical (INFO) Media |url=https://doi.org/10.1143/JJAP.41.1866 |journal=Japanese Journal of Applied Physics |language=en |volume=41 |issue=Part 1, No. 3B |pages=1866–1875 |doi=10.1143/jjap.41.1866 |bibcode=2002JaJAP..41.1866G |s2cid=119544019 |issn=0021-4922}}</ref>  A form of 'invisibility' was demonstrated using [[Metamaterial cloaking|gradient-index materials]]. [[Acoustic metamaterials|Acoustic]] and [[seismic metamaterials]] are also research areas.<ref name="control_elastic_waves">{{cite journal| last = Brun| first =M.|author2=S. Guenneau |author3=and A.B. Movchan | title =Achieving control of in-plane elastic waves|journal =[[Appl. Phys. Lett.]]| volume =94 |issue =61903|pages =061903|date =2009-02-09|arxiv =0812.0912|doi =10.1063/1.3068491|bibcode = 2009ApPhL..94f1903B | s2cid =17568906}}</ref><ref name="acousticmeta1107">{{Cite journal | last1 = Guenneau | first1 = S. B. | last2 = Movchan | first2 = A. | last3 = Pétursson | first3 = G. | last4 = Anantha Ramakrishna | first4 = S. | title = Acoustic metamaterials for sound focusing and confinement | doi = 10.1088/1367-2630/9/11/399 | journal = New Journal of Physics | volume = 9 | issue = 11 | page = 399 | year = 2007 | bibcode = 2007NJPh....9..399G| url = https://hal.archives-ouvertes.fr/hal-00186684/document | doi-access = free }}</ref>

Metamaterial research is interdisciplinary and involves such fields as [[electrical engineering]], [[Electromagnetism|electromagnetics]], classical [[optics]], [[solid state physics]], [[microwave engineering|microwave and antenna engineering]], [[optoelectronics]], [[material science]]s, [[nanoscience]] and [[semiconductor]] engineering.<ref name=metamaterialplasmonics1/>
{{toclimit|3}}

==History==
{{main|History of metamaterials}}
Explorations of artificial materials for manipulating [[electromagnetic wave]]s began at the end of the 19th century. Some of the earliest structures that may be considered metamaterials were studied by [[Jagadish Chandra Bose]], who in 1898 researched substances with [[chiral]] properties. Karl Ferdinand Lindman studied [[Dispersion (optics)|wave interaction]] with metallic [[helices]] as artificial [[Chirality (chemistry)|chiral media]] in the early twentieth century.

In the late 1940s, [[Winston E. Kock]] from [[AT&T Bell Laboratories]] developed materials that had similar characteristics to metamaterials. In the 1950s and 1960s, artificial [[dielectric]]s were studied for lightweight [[microwave antenna]]s. Microwave [[Radar-absorbent material|radar absorbers]] were researched in the 1980s and 1990s as applications for artificial chiral media.<ref name=metamaterialplasmonics1/><ref>{{cite journal |title=Birefringent left-handed metamaterials and perfect lenses for vectorial fields |journal=New Journal of Physics |date=2005 |volume=7 |issue=1 |page=220 |doi=10.1088/1367-2630/7/1/220|arxiv=physics/0412128 |doi-access=free |bibcode=2005NJPh....7..220Z |last1=Zharov |first1=Alexander A. |last2=Zharova |first2=Nina A. |last3=Noskov |first3=Roman E. |last4=Shadrivov |first4=Ilya V. |last5=Kivshar |first5=Yuri S. }}</ref><ref>Bowers J. A.; Hyde R. A. et al. "Evanescent electromagnetic wave conversion lenses I, II, III" US Patent and Trademark Office, Grant US-9081202-B2, 14 juli 2015, {{US Patent|9081202}}</ref>

Negative-index materials were first described theoretically by [[Victor Veselago]] in 1967.<ref name=slyusarmeta>{{cite conference|last =Slyusar |first=V.I.|title= Metamaterials on antenna solutions|conference =7th International Conference on Antenna Theory and Techniques ICATT’09 |location =Lviv, Ukraine|date = October 6–9, 2009|pages= 19–24 |url = http://www.slyusar.kiev.ua/019_024_ICATT_2009.pdf}}</ref> He proved that such materials could [[transparency (optics)|transmit light]]. He showed that the [[phase velocity]] could be made anti-parallel to the direction of [[Poynting vector]]. This is contrary to [[wave propagation]] in naturally occurring materials.<ref name="Veselago1" />

In 1995, John M. Guerra fabricated a sub-wavelength transparent grating (later called a photonic metamaterial)  having 50&nbsp;nm lines and spaces, and then coupled it with a standard oil immersion microscope objective (the combination later called a super-lens) to resolve a grating in a silicon wafer also having 50&nbsp;nm lines and spaces. This super-resolved image was achieved with illumination having a wavelength of 650&nbsp;nm in air.<ref name="Guerra 3555–3557"/>

In 2000, [[John Pendry]] was the first to identify a practical way to make a left-handed metamaterial, a material in which the [[right-hand rule]] is not followed.<ref name="slyusarmeta" /> Such a material allows an electromagnetic wave to convey energy (have a [[group velocity]]) against its [[phase velocity]]. Pendry's idea was that metallic wires aligned along the direction of a wave could provide negative [[permittivity]] ([[dielectric function]] ε < 0). Natural materials (such as [[ferroelectricity|ferroelectrics]]) display negative permittivity; the challenge was achieving negative permeability (µ < 0). In 1999 Pendry demonstrated that a split ring (C shape) with its axis placed along the direction of wave propagation could do so. In the same paper, he showed that a periodic array of wires and rings could give rise to a negative refractive index. Pendry also proposed a related negative-permeability design, the [[Swiss roll (metamaterial)|Swiss roll]].

In 2000, [[David R. Smith (physicist)|David R. Smith]] et al. reported the experimental demonstration of functioning electromagnetic metamaterials by horizontally stacking, [[periodic function|periodically]], [[split-ring resonator]]s and thin wire structures. A method was provided in 2002 to realize negative-index metamaterials using artificial lumped-element loaded transmission lines in [[microstrip]] technology. In 2003, complex (both real and imaginary parts of) negative refractive index<ref>AIP News, Number 628 #1, March 13 Physics Today, May 2003, Press conference at APS March Meeting, Austin, Texas, March 4, 2003, New Scientist, vol 177, p. 24.</ref>  and imaging by flat lens<ref>{{cite journal|pmid=14647372|year=2003|last1=Parimi|first1=P. V.|title=Photonic crystals: Imaging by flat lens using negative refraction|journal=Nature|volume=426|issue=6965|pages=404|last2=Lu|first2=W. T.|last3=Vodo|first3=P|last4=Sridhar|first4=S|doi=10.1038/426404a|bibcode=2003Natur.426..404P|s2cid=4411307|doi-access=free}}</ref> using left handed metamaterials were demonstrated. By 2007, experiments that involved [[negative refractive index]] had been conducted by many groups.<ref name="physicsengineering1" /><ref name="radiation-properties" /> At microwave frequencies, the first, imperfect [[cloaking device|invisibility cloak]] was realized in 2006.<ref name="kock1">{{cite journal|author=Kock, W. E.|journal=IRE Proc.|volume=34|year=1946|pages=828–36|title=Metal-Lens Antennas|doi=10.1109/JRPROC.1946.232264|issue=11|s2cid=51658054}}</ref><ref name="kock2">{{cite journal|author=Kock, W.E.|journal=Bell Syst. Tech. J.|volume=27|year=1948|title=Metallic Delay Lenses|pages=58–82|doi=10.1002/j.1538-7305.1948.tb01331.x}}</ref><ref name="caloz">{{cite journal|author1=Caloz, C.|author2=Chang, C.-C.|author3=Itoh, T.|title=Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations|journal=J. Appl. Phys.|url=http://xlab.me.berkeley.edu/MURI/publications/publications_9.pdf|year=2001|volume=90|page=11|doi=10.1063/1.1408261|bibcode=2001JAP....90.5483C|issue=11|access-date=2009-05-17|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="IEEEMTT-V50">{{cite journal|author1=Eleftheriades, G.V. |author2=Iyer A.K. |author3=Kremer, P.C.  |name-list-style=amp |title=Planar Negative Refractive Index Media Using Periodically L-C Loaded Transmission Lines|journal=[[IEEE Transactions on Microwave Theory and Techniques]]|volume=50|pages=2702–12|year=2002|doi=10.1109/TMTT.2002.805197|bibcode = 2002ITMTT..50.2702E|issue =12 }}</ref><ref name="Caloz-V2">{{cite book|author1=Caloz, C.  |author2=Itoh, T. |title=IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313) |chapter=Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip "LH line" |volume=2|page=412|year=2002|doi=10.1109/APS.2002.1016111|isbn =978-0-7803-7330-3|s2cid=108405740 }}</ref>

From the standpoint of governing equations, contemporary researchers can classify the realm of metamaterials into three primary branches:<ref name="c1">{{cite journal |author1=Yang, F.B.; Zhang, Z.R.; Xu, L.J.; Liu, Z.F.; Jin, P.; Zhuang, P.F.; Lei, M.; Liu, J.R.; Jiang, J.-H.; Ouyang, X.P.; Marchesoni, F.; Huang, J.P. |title=Controlling mass and energy diffusion with metamaterials |journal=Rev. Mod. Phys. |date=2024 |volume=96 |issue=1 |page=015002 |arxiv=2309.04711 |doi=10.1103/RevModPhys.96.015002 }}</ref> Electromagnetic/Optical wave metamaterials, other wave metamaterials, and [[diffusion metamaterial]]s. These branches are characterized by their respective governing equations, which include Maxwell's equations (a wave equation describing transverse waves), other wave equations (for longitudinal and transverse waves), and diffusion equations (pertaining to diffusion processes).<ref>{{cite book |author1=Yang, F.B.; Huang, J.P. |title=Diffusionics: Diffusion Process Controlled by Diffusion Metamaterials (to be published in 2024) |publisher=Springer |location=Singapore |url=https://www.amazon.ca/Diffusionics-Diffusion-Process-Controlled-Metamaterials/dp/9819704863}}</ref> For comprehensive information, please refer to Section I.B, "Evolution of metamaterial physics," in Ref.<ref name="c1"/>

==Electromagnetic metamaterials==
{{Electromagnetism|cTopic=[[Classical electromagnetism|Electrodynamics]]}}
An electromagnetic metamaterial affects [[electromagnetic wave]]s that impinge on or interact with its structural features, which are smaller than the wavelength. To behave as a [[Homogeneity (physics)|homogeneous material]] accurately described by an effective [[refractive index]], its features must be much smaller than the wavelength.{{citation needed|date=May 2019}}

The unusual properties of metamaterials arise from the resonant response of each constituent element rather that their spatial arrangement into a lattice. It allows considering the local effective material parameters (permittivity and [[Permeability (electromagnetism)|permeability]]). The resonance effect related to the mutual arrangement of elements is responsible for [[Bragg scattering]], which underlies the physics of [[photonic crystals]], another class of electromagnetic materials. Unlike the local resonances, Bragg scattering and corresponding Bragg stop-band have a low-frequency limit determined by the lattice spacing. The subwavelength approximation ensures that the Bragg stop-bands with the [[spatial dispersion|strong spatial dispersion]] effects are at higher frequencies and can be neglected. The criterion for shifting the local resonance below the lower Bragg stop-band make it possible to build a photonic [[phase transition]] diagram in a parameter space, for example, size and permittivity of the constituent element. Such diagram displays the domain of structure parameters allowing the metamaterial properties observation in the electromagnetic material.<ref>{{cite journal|author=Rybin, M.V.|title= Phase diagram for the transition from photonic crystals to dielectric metamaterials|journal=Nature Communications|pages=10102 |year=2015|doi=10.1038/ncomms10102|pmid= 26626302 |display-authors=etal|volume=6|pmc= 4686770|arxiv= 1507.08901|bibcode= 2015NatCo...610102R}}</ref>

For [[microwave|microwave radiation]], the features are on the order of [[millimeter]]s. Microwave frequency metamaterials are usually constructed as arrays of electrically conductive elements (such as loops of wire) that have suitable [[inductor|inductive]] and [[capacitor|capacitive]] characteristics. Many microwave metamaterials use [[split-ring resonator]]s.<ref name=smithmetamaterials1/><ref name=AAAS2/>

[[Photonic metamaterials]] are structured on the [[nanometers|nanometer]] scale and manipulate light at optical frequencies. [[Photonic crystals]] and frequency-selective surfaces such as [[diffraction grating]]s, [[dielectric mirror]]s and [[optical coating]]s exhibit similarities to [[subwavelength]] structured metamaterials. However, these are usually considered distinct from metamaterials, as their function arises from diffraction or interference and thus cannot be approximated as a homogeneous material.{{Citation needed|date=January 2010}} However, material structures such as photonic crystals are effective in the [[visible light|visible light spectrum]]. The middle of the visible spectrum has a wavelength of approximately 560&nbsp;nm (for sunlight). Photonic crystal structures are generally half this size or smaller, that is <&nbsp;280&nbsp;nm. {{Citation needed|date=January 2011}}

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

Frequency selective surfaces (FSS) can exhibit subwavelength characteristics and are known variously as [[artificial magnetic conductor]]s (AMC) or High Impedance Surfaces (HIS). FSS display inductive and capacitive characteristics that are directly related to their subwavelength structure.<ref name=bandgap>{{Cite journal|last1=Sievenpiper |first1=Dan |title=High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band |journal=[[IEEE Transactions on Microwave Theory and Techniques]] |volume=47 |issue=11 |pages=2059–74 |date=November 1999 |url=http://www.rsl.ku.edu/~eecs501/Hi-Z_surfaces/Sievenpiper1999TMTTpp2059-2074.pdf |doi=10.1109/22.798001 |access-date=2009-11-11 |last2=Lijun Zhang |last3=Broas |first3=R.F.J. |last4=Alexopolous |first4=N.G. |last5=Yablonovitch |first5=E. |bibcode=1999ITMTT..47.2059S |display-authors=1 |url-status=dead |archive-url=https://web.archive.org/web/20110719225821/http://www.rsl.ku.edu/~eecs501/Hi-Z_surfaces/Sievenpiper1999TMTTpp2059-2074.pdf |archive-date=July 19, 2011 }}</ref>

Electromagnetic metamaterials can be divided into different classes, as follows:<ref name=physicsengineering1/><ref name=slyusarmeta/><ref name=metamaterialplasmonics1>
{{cite book
|last = Zouhdi|first = Saïd|author2=Ari Sihvola |author3=Alexey P. Vinogradov |title = Metamaterials and Plasmonics: Fundamentals, Modelling, Applications|publisher = Springer-Verlag|date = December 2008|location = New York|pages=3–10, Chap. 3, 106|url = https://books.google.com/books?id=OqRi4s_EskoC&pg=PA6|isbn = 978-1-4020-9406-4}}</ref><ref name=homogeneous-material>{{cite journal
| last = Pendry| first =John B.| author-link =John Pendry|author2=David R. Smith| title =Reversing Light: Negative Refraction| journal =Physics Today| volume =57| issue =June 37| pages =2 of 9 (originally page 38 of pp. 37–45)| date =June 2004
|url =http://esperia.iesl.forth.gr/~ppm/DALHM/publications/papers/PhysicsTodayv57p37.pdf
|access-date =2009-09-27| doi=10.1063/1.1784272|bibcode = 2004PhT....57f..37P }}</ref>

===Negative refractive index===
[[File:metarefraction.svg|thumb|A comparison of refraction in a left-handed metamaterial to that in a normal material]]
{{Main|Negative-index metamaterial|Negative refraction}}

Negative-index metamaterials (NIM) are characterized by a negative index of refraction. Other terms for NIMs include "left-handed media", "media with a negative refractive index", and "backward-wave media".<ref name=physicsengineering1/> NIMs where the negative index of refraction arises from simultaneously negative permittivity and negative permeability are also known as double negative metamaterials or double negative materials (DNG).<ref name=slyusarmeta/>

Assuming a material well-approximated by a real permittivity and permeability, the relationship between [[permittivity]] <math>\varepsilon_r</math>, [[Permeability (electromagnetism)|permeability]] <math>\mu_r</math> and [[refractive index]] ''n'' is given by <math display=inline> n =\pm\sqrt{\varepsilon_\mathrm{r}\mu_\mathrm{r}}</math>. All known non-metamaterial transparent materials (glass, water, ...) possess positive <math>\varepsilon_r</math> and <math>\mu_r</math>. By convention the positive square root is used for ''n''. However, some engineered metamaterials have <math>\varepsilon_r</math> and <math>\mu_r < 0</math>. Because the product <math>\varepsilon_r\mu_r</math> is positive, ''n'' is [[real number|real]]. Under such circumstances, it is necessary to take the negative square root for ''n''. When both <math>\varepsilon_r</math> and <math>\mu_r</math> are positive (negative), waves travel in the ''forward'' (''backward'') direction. Electromagnetic waves cannot propagate in materials with <math>\varepsilon_r</math> and <math>\mu_r</math> of opposite sign as the refractive index becomes [[Imaginary number|imaginary]]. Such materials are opaque for electromagnetic radiation and examples include [[surface plasmon|plasmonic]] materials such as metals ([[gold]], [[silver]], ...).

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

The foregoing considerations are simplistic for actual materials, which must have complex-valued <math>\varepsilon_r</math> and <math>\mu_r</math>. The real parts of both <math>\varepsilon_r</math> and <math>\mu_r</math> do not have to be negative for a passive material to display negative refraction.<ref>{{cite journal|doi=10.1002/mop.20127|title=A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity|journal=Microwave and Optical Technology Letters|volume=41|pages=315–16|year=2004|issue=4|last1=Depine|first1=Ricardo A.|last2=Lakhtakia|first2=Akhlesh|arxiv=physics/0311029|s2cid=6072651}}</ref><ref>Voznesenskaya, A. and Kabanova, D. (2012) [http://ntv.ifmo.ru/en/article/2413/analiz_prohozhdeniya_luchey_cherez_opticheskie_sistemy,_vklyuchayuschie_elementy_iz_metamaterialov.htm "Analysis of Ray Tracing Through Optical Systems with Metamaterial Elements"], ''Scientific and Technical Journal of Information Technologies, Mechanics and Optics'', Volume 5, Number 12, p. 5.</ref> Indeed, a negative refractive index for circularly polarized waves can also arise from chirality.<ref name=chiralNIMobservationPlum>{{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><ref name=chiralNIMobservationZhang>{{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> Metamaterials with negative ''n'' have numerous interesting properties:<ref name="metamaterialplasmonics1" /><ref name="snglhm">{{cite book|last = Eleftheriades|first = George V.|author2=Keith G. Balmain|title = Negative-refraction metamaterials: fundamental principles and applications|publisher =Wiley|year = 2005|page=340
|url =https://books.google.com/books?id=a4MiyF5_N7MC&pg=PA379|isbn =978-0-471-60146-3|bibcode = 2005nmfp.book.....E}}</ref>
*[[Snell's law]] (''n''<sub>1</sub>sin''θ''<sub>1</sub> = ''n''<sub>2</sub>sin''θ''<sub>2</sub>) still describes refraction, but as ''n''<sub>2</sub> is negative, incident and refracted rays are on the ''same'' side of the surface normal at an interface of positive and negative index materials.
*[[Cherenkov radiation]] points the other way.{{explain|date=August 2019}}
*The time-averaged [[Poynting vector]] is [[antiparallel (mathematics)|antiparallel]] to phase velocity. However, for waves (energy) to propagate, a –''µ'' must be paired with a –''ε'' in order to satisfy the wave number dependence on the material parameters <math>k c = \omega\sqrt{\mu \varepsilon}</math>.

Negative index of refraction derives mathematically from the vector triplet '''E''', '''H''' and '''k'''.<ref name="metamaterialplasmonics1" />

For [[plane wave]]s propagating in electromagnetic metamaterials, the electric field, magnetic field and [[wave vector]] follow a [[left-handed material|left-hand rule]], the reverse of the behavior of conventional optical materials.

To date, only metamaterials exhibit a negative index of refraction.<ref name="physicsengineering1" /><ref name="snglhm" /><ref name="sng-dng">{{Cite journal| last = Alù| first =Andrea and|author2=Nader Engheta | title =Guided Modes in a Waveguide Filled With a Pair of Single-Negative (SNG), Double-Negative (DNG), and/or Double-Positive (DPS) Layers| journal =[[IEEE Transactions on Microwave Theory and Techniques]]| volume =52| issue =1| pages =199–210| date =January 2004
|url =http://repository.upenn.edu/cgi/viewcontent.cgi?article=1001&context=ese_papers
|format = PDF| doi =10.1109/TMTT.2003.821274
|access-date =2010-01-03|bibcode = 2004ITMTT..52..199A | s2cid =234001| author-link2 =Nader Engheta}}</ref>

===Single negative===
Single negative (SNG) metamaterials have either negative relative permittivity (ε<small>r</small>) or negative relative permeability (µ<small>r</small>), but not both.<ref name=slyusarmeta/> They act as metamaterials when combined with a different, complementary SNG, jointly acting as a DNG.

Epsilon negative media (ENG) display a negative ε<small>r</small>  while µ<small>r</small> is positive.<ref name=physicsengineering1/><ref name=snglhm/><ref name=slyusarmeta/> Many plasmas exhibit this characteristic. For example, [[noble metals]] such as gold or silver are ENG in the [[infrared]] and [[visible spectrum]]s.

Mu-negative media (MNG) display a positive ε<small>r </small> and negative µ<small>r</small>.<ref name="physicsengineering1" /><ref name="snglhm" /><ref name=slyusarmeta/> Gyrotropic or gyromagnetic materials exhibit this characteristic. A gyrotropic material is one that has been altered by the presence of a quasistatic [[magnetic field]], enabling a [[magneto-optic effect]].{{citation needed|date=May 2019}} A magneto-optic effect is a phenomenon in which an electromagnetic wave propagates through such a medium. In such a material, left- and right-rotating elliptical polarizations can propagate at different speeds. When light is transmitted through a layer of magneto-optic material, the result is called the [[Faraday effect]]: the [[Polarization (waves)|polarization]] plane can be rotated, forming a [[Faraday rotator]]. The results of such a reflection are known as the [[magneto-optic Kerr effect]] (not to be confused with the [[nonlinear optics|nonlinear]] [[Kerr effect]]). Two gyrotropic materials with reversed rotation directions of the two principal polarizations are called [[optical isomer]]s.

Joining a slab of ENG material and slab of MNG material resulted in properties such as resonances, anomalous tunneling, transparency and zero reflection. Like negative-index materials, SNGs are innately dispersive, so their ε<small>r</small>, µ<small>r</small> and refraction index n, are a function of frequency.<ref name=snglhm/>

=== Hyperbolic ===
Hyperbolic metamaterials (HMMs) behave as a metal for certain polarization or direction of light propagation and behave as a dielectric for the other due to the negative and positive permittivity tensor components, giving extreme [[anisotropy]]. The material's [[dispersion relation]] in wavevector space forms a [[hyperboloid]] and therefore it is called a hyperbolic metamaterial. The extreme anisotropy of HMMs leads to directional propagation of light within and on the surface.<ref>{{cite journal|author=High, A.|title=Visible-frequency hyperbolic metasurface |journal=Nature|pages=192–196 |year=2015|doi=10.1038/nature14477|pmid=26062510 |display-authors=etal|volume=522|issue=7555 |bibcode=2015Natur.522..192H|s2cid=205243865 }}</ref>  HMMs have showed various potential applications, such as sensing, reflection modulator,<ref>Pianelli, A., Kowerdziej, R., Dudek, M., Sielezin, K., Olifierczuk, M., & Parka, J. (2020). Graphene-based hyperbolic metamaterial as a switchable reflection modulator. Optics Express, 28(5), 6708–6718.https://doi.org/10.1364/OE.387065</ref> imaging, steering of optical signals, enhanced plasmon resonance effects.<ref>{{cite journal|author=Takayama, O.|title=Optics with hyperbolic materials. |journal=Journal of the Optical Society of America B |volume=36 |pages=F38–F48 |date=2019|last2=Lavrinenko, A. V. |issue=8 |doi=10.1364/JOSAB.36.000F38 |s2cid=149698994 |url=https://backend.orbit.dtu.dk/ws/files/175847309/Optics_with_hyperbolic_materials_invited_preprint.pdf }}</ref>

=== Bandgap ===
{{Further|Photonic crystal|Electronic band structure|Coupled oscillation}}
Electromagnetic [[bandgap]] metamaterials (EBG or EBM) control light propagation. This is accomplished either with photonic crystals (PC) or left-handed materials (LHM). PCs can prohibit light propagation altogether. Both classes can allow light to propagate in specific, designed directions and both can be designed with bandgaps at desired frequencies.<ref name=physicsengineering3>
{{cite book|last = Engheta|first = Nader|author2=Richard W. Ziolkowski|title = Metamaterials: physics and engineering explorations|publisher = Wiley & Sons|date = 2006|pages = 211–21|format= added this reference on 2009-12-14.|url = https://books.google.com/books?id=51e0UkEuBP4C|isbn = 978-0-471-76102-0}}</ref><ref name=Valenitne-J.>{{Cite journal | last1 = Valentine | first1 = J. | last2 = Zhang | first2 = S. | last3 = Zentgraf | first3 = T. | last4 = Ulin-Avila | first4 = E. | last5 = Genov | first5 = D. A. | last6 = Bartal | first6 = G. | last7 = Zhang | first7 = X. | doi = 10.1038/nature07247 | title = Three-dimensional optical metamaterial with a negative refractive index | journal = Nature | volume = 455 | issue = 7211 | pages = 376–79 | year = 2008 | pmid =  18690249|bibcode = 2008Natur.455..376V | s2cid = 4314138 }}</ref> The period size of EBGs is an appreciable fraction of the wavelength, creating constructive and destructive interference.

PC are distinguished from sub-wavelength structures, such as [[tunable metamaterials]], because the PC derives its properties from its bandgap characteristics. PCs are sized to match the wavelength of light, versus other metamaterials that expose sub-wavelength structure. Furthermore, PCs function by diffracting light. In contrast, metamaterial does not use diffraction.<ref name=PC-01>
{{cite web
 |last=Pendry 
 |first=JB 
 |author-link=John Pendry 
 |title=Metamaterials Generate Novel Electromagnetic Properties 
 |work=UC Berkeley Atomic Physics Seminar 290F 
 |date=2009-04-11 
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 |format=Seminar – lecture series
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 |archive-date=2010-06-27 
}}</ref>

PCs have periodic inclusions that inhibit wave propagation due to the inclusions' destructive interference from scattering. The photonic bandgap property of PCs makes them the electromagnetic analog of electronic semi-conductor crystals.<ref name=Purdue-ebg>
{{cite web| last = Chappell| first =William leads the IDEA laboratory at Purdue University
| title =Metamaterials| work =research in various technologies|year =2005
| url =https://engineering.purdue.edu/IDEAS/Metamaterials.html
| access-date =2009-11-23}}</ref>

EBGs have the goal of creating high quality, low loss, periodic, dielectric structures. An EBG affects photons in the same way semiconductor materials affect electrons. PCs are the perfect bandgap material, because they allow no light propagation.<ref name=PC-in-21st-century>{{cite book| editor =Soukoulis, C. M.| title =Photonic Crystals and Light Localization in the 21st Century
| publisher =Springer London, Limited|date =May 2001| edition =Proceedings of the NATO Advanced Study Institute on Photonic Crystals and Light Localization, Crete, Greece, June 18–30, 2000| location =London| pages =xi |url =https://books.google.com/books?id=y8O7cfQl9ogC&pg=PP1| isbn =978-0-7923-6948-6}}</ref> Each unit of the prescribed periodic structure acts like one atom, albeit of a much larger size.<ref name=physicsengineering1/><ref name=PC-in-21st-century/>

EBGs are designed to prevent the propagation of an allocated [[Bandwidth (signal processing)|bandwidth]] of frequencies, for certain arrival angles and [[Polarization (waves)|polarizations]]. Various geometries and structures have been proposed to fabricate EBG's special properties. In practice it is impossible to build a flawless EBG device.<ref name=physicsengineering1/><ref name=metamaterialplasmonics1/>

EBGs have been manufactured for frequencies ranging from a few gigahertz (GHz) to a few terahertz (THz), radio, microwave and mid-infrared frequency regions. EBG application developments include a [[transmission line]], woodpiles made of square dielectric bars and several different types of low gain [[antenna (radio)|antenna]]s.<ref name=physicsengineering1/><ref name=metamaterialplasmonics1/>

===Double positive medium===
Double positive mediums (DPS) do occur in nature, such as naturally occurring [[dielectric]]s. Permittivity and magnetic permeability are both positive and wave propagation is in the forward direction. Artificial materials have been fabricated which combine DPS, ENG and MNG properties.<ref name=physicsengineering1/><ref name=slyusarmeta/>

===Bi-isotropic and bianisotropic===
Categorizing metamaterials into double or single negative, or double positive, normally assumes that the metamaterial has independent electric and magnetic responses described by ε and µ. However, in many cases, the [[electric field]] causes [[magnetic]] polarization, while the magnetic field induces electrical polarization, known as magnetoelectric coupling. Such media are denoted as [[Bi isotropic|bi-isotropic]]. Media that exhibit magnetoelectric coupling and that are [[anisotropic]] (which is the case for many metamaterial structures<ref name=bi-anisotropic>
{{cite journal| last1 = Marques| first1 =Ricardo |title =Role of bianisotropy in negative permeability and left-handed metamaterials|journal =Physical Review B| volume =65| pages =144440–41| date =2002-04-04|url =http://centro.us.es/gmicronda/Miembros/Ricardo/1-Role-of-bianisotropy.pdf|doi =10.1103/PhysRevB.65.144440| first2 = Francisco| first3 = Rachid| last2 = Medina| last3 = Rafii-El-Idrissi|bibcode = 2002PhRvB..65n4440M| issue = 14 | hdl =11441/59428|url-status =dead|archive-url = https://web.archive.org/web/20110720150321/http://centro.us.es/gmicronda/Miembros/Ricardo/1-Role-of-bianisotropy.pdf|archive-date = 20 July 2011
}}</ref>), are referred to as bi-anisotropic.<ref>{{cite journal| last1 = Rill| first1 =M. S.
|title =Negative-index bianisotropic photonic metamaterial fabricated by direct laser writing and silver shadow evaporation
|journal =Optics Letters| volume =34
|pages =19–21| date =2008-12-22
|doi =10.1364/OL.34.000019| pmid = 19109626| first2 = CE| first3 = M| first4 = G| first5 = S| first6 = M| issue = 1| last2 = Kriegler| last3 = Thiel| last4 = Von Freymann| last5 = Linden| last6 = Wegener| display-authors = 1|arxiv = 0809.2207 |bibcode = 2009OptL...34...19R | s2cid =18596552
}}</ref><ref name=bi-anisotropic-photonic>{{cite journal| last1 = Kriegler| first1 =C. E.
|title =Bianisotropic photonic metamaterials
|journal =IEEE Journal of Selected Topics in Quantum Electronics| volume =999
|pages =1–15|url =http://esperia.iesl.forth.gr/~ppm/PHOME/publications/IEEE_10_1109_2009.pdf
|doi =10.1109/JSTQE.2009.2020809| first2 = Michael Stefan| first3 = Stefan| first4 = Martin| last2 = Rill| last3 = Linden| last4 = Wegener| display-authors = 1| issue = 2| year =2010
|bibcode =2010IJSTQ..16..367K| s2cid =13854440
}}</ref>

Four material parameters are intrinsic to magnetoelectric coupling of bi-isotropic media. They are the [[Electric field|electric ('''E''')]] and [[Magnetic field|magnetic ('''H''')]] field strengths, and [[Electric flux|electric ('''D''')]] and [[magnetic flux|magnetic ('''B''')]] flux densities. These parameters are ε, µ, ''κ'' and χ or permittivity, permeability, strength of chirality, and the Tellegen parameter, respectively. In this type of media, material parameters do not vary with changes along a rotated [[coordinate system]] of measurements. In this sense they are invariant or [[Scalar (physics)|scalar]].<ref name=metamaterialplasmonics1/>

The intrinsic magnetoelectric parameters, ''κ'' and ''χ'', affect the [[Phase (waves)|phase]] of the wave. The effect of the chirality parameter is to split the refractive index. In isotropic media this results in wave propagation only if ε and µ have the same sign. In bi-isotropic media with ''χ'' assumed to be zero, and ''κ'' a non-zero value, different results appear. Either a backward wave or a forward wave can occur. Alternatively, two forward waves or two backward waves can occur, depending on the strength of the chirality parameter.

In the general case, the constitutive relations for bi-anisotropic materials read 
<math>    \mathbf{D} = \varepsilon \mathbf{E} + \xi \mathbf{H},    </math>
<math>    \mathbf{B} = \zeta \mathbf{E} + \mu  \mathbf{H},    </math>
where <math>    \varepsilon   </math> and <math>    \mu   </math> are the permittivity and the permeability tensors, respectively, whereas <math> \xi </math>  and  <math> \zeta </math> are the two magneto-electric tensors.  If the medium is reciprocal,  permittivity and permeability are symmetric tensors, and <math>    \xi=-\zeta^T=-i \kappa^T   </math>, where <math> \kappa </math>  is the chiral tensor describing chiral electromagnetic and reciprocal magneto-electric response.  The chiral tensor can be expressed as <math>    \kappa=\tfrac{1}{3}\operatorname{tr}(\kappa) I+N+J     </math>, where <math>    \operatorname{tr}(\kappa) </math> is the trace of <math>    \kappa   </math>, I is the identity matrix, N is a symmetric trace-free tensor, and J is an antisymmetric tensor. Such decomposition allows us to classify the reciprocal bianisotropic response and we can identify the following three main classes: (i)  chiral media  (<math>  \operatorname{tr}(\kappa)  \neq 0, N \neq 0, J=0  </math>), (ii)  pseudochiral media (<math>  \operatorname{tr}(\kappa)  = 0, N \neq 0, J=0  </math>), (iii) omega media   (<math>  \operatorname{tr}(\kappa)  = 0, N = 0, J \neq 0  </math>).

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

Generally a chiral and/or bianisotropic electromagnetic response is a consequence of 3D geometrical chirality: [[Chirality (electromagnetism)#Intrinsic 3d chirality|3D-chiral]] metamaterials are composed by embedding 3D-chiral structures in a host medium and they show [[chirality (electromagnetism)|chirality-related polarization effects]] such as [[optical activity]] and [[circular dichroism]]. The concept of [[planar chirality|2D chirality]] also exists and a planar object is said to be chiral if it cannot be superposed onto its mirror image unless it is lifted from the plane. 2D-chiral metamaterials that are anisotropic and lossy have been observed to exhibit directionally asymmetric transmission (reflection, absorption) of circularly polarized waves due to circular conversion dichrosim.<ref>
{{Cite journal| last = Fedotov| first =V. A.|author2=Mladyonov, P. L. |author3=Prosvirnin, S. L. |author4=Rogacheva, A. V.  |author5=Chen, Y.  |author6= Zheludev, N. I.  | title =Asymmetric propagation of electromagnetic waves through a planar chiral structure| journal =Physical Review Letters| volume =97| issue =16| page =167401| year =2006| pmid = 17155432| doi =10.1103/PhysRevLett.97.167401| bibcode=2006PhRvL..97p7401F|arxiv = physics/0604234 | s2cid =119436346}}</ref><ref>{{Cite journal| last = Plum| first =E.|author2=Fedotov, V. A. |author3=Zheludev, N. I.  | title =Planar metamaterial with transmission and reflection that depend on the direction of incidence| journal =Applied Physics Letters| volume =94| page =131901| year =2009| doi =10.1063/1.3109780| issue = 13|arxiv = 0812.0696 |bibcode = 2009ApPhL..94m1901P | s2cid =118558819}}</ref> On the other hand, bianisotropic response can arise from geometrical achiral structures possessing neither 2D nor 3D intrinsic chirality. Plum and colleagues investigated magneto-electric coupling due to [[chirality (electromagnetism)#Types of chirality|extrinsic chirality]], where the arrangement of a (achiral) structure together with the radiation wave vector is different from its mirror image, and observed large, tuneable linear optical activity,<ref>{{cite journal|title= Metamaterials: Optical Activity without Chirality |journal=Phys. Rev. Lett.|volume=102|issue=11 |page= 113902|year=2009|doi=10.1103/physrevlett.102.113902|pmid=19392202|bibcode = 2009PhRvL.102k3902P |last1=Plum|first1=E.|last2=Liu|first2=X.-X.|last3=Fedotov|first3=V. A.|last4=Chen|first4=Y.|last5=Tsai|first5=D. P.|last6=Zheludev|first6=N. I.|url=https://eprints.soton.ac.uk/78867/1/4179.pdf}}</ref> nonlinear optical activity,<ref>{{Cite journal| last = Ren| first =M.|author2=Plum, E. |author3=Xu, J. |author4=Zheludev, N. I. | title =Giant nonlinear optical activity in a plasmonic metamaterial| journal =Nature Communications| volume =3| page =833| year =2012| doi =10.1038/ncomms1805 | pmid =22588295| bibcode =2012NatCo...3..833R| doi-access =free}}</ref> specular optical activity<ref>{{Cite journal| last = Plum| first =E.|author2=Fedotov, V. A. |author3=Zheludev, N. I.  | title =Specular optical activity of achiral metasurfaces| journal =Applied Physics Letters| volume =108| page =141905| year =2016| issue =14| doi =10.1063/1.4944775 | bibcode =2016ApPhL.108n1905P| hdl =10220/40854| url =https://eprints.soton.ac.uk/389739/1/specular%2520optical%2520activity%25207rev.pdf}}</ref> and circular conversion dichroism.<ref>{{Cite journal| last = Plum| first =E.|author2=Fedotov, V. A. |author3=Zheludev, N. I.  | title =Extrinsic electromagnetic chirality in metamaterials| journal =Journal of Optics A: Pure and Applied Optics| volume =11| page =074009| year =2009| issue =7| doi =10.1088/1464-4258/11/7/074009 | bibcode =2009JOptA..11g4009P}}</ref> Rizza ''et al.''<ref>{{cite journal|title= One-Dimensional Chirality: Strong Optical Activity in Epsilon-Near-Zero Metamaterials|author1=C. Rizza |author2=Andrea Di Falco |author3=Michael Scalora |author4=Alessandro Ciattoni  |name-list-style=amp |doi= 10.1103/PhysRevLett.115.057401|journal=Phys. Rev. Lett.|volume=115|issue=5 |page= 057401|year=2015|bibcode=2015PhRvL.115e7401R|arxiv = 1503.00490 |pmid=26274441|s2cid=11708854 }}</ref> suggested 1D chiral metamaterials where the effective chiral tensor is not vanishing if the system is geometrically one-dimensional chiral (the mirror image of the entire structure cannot be superposed onto it by using translations without rotations).

3D-chiral metamaterials are constructed from [[chirality (electromagnetism)|chiral]] materials or resonators in which the effective chirality parameter <math>\kappa</math> is non-zero. 
Wave propagation properties in such chiral metamaterials demonstrate that negative refraction can be realized in metamaterials with a strong chirality and positive <math>\varepsilon_r</math> and <math>\mu_r</math>.<ref name=Wang-Chiral-mm>{{Cite journal
|last1 = Wang| first1 =Bingnan| title =Chiral metamaterials: simulations and experiments
|journal =J. Opt. Soc. Am. A| volume =11| pages =114003| date =November 2009
| doi =10.1088/1464-4258/11/11/114003
|last2 = Zhou
|first2 = Jiangfeng
|last3 = Koschny
|first3 = Thomas
|last4 = Kafesaki
|first4 = Maria
|last5 = Soukoulis
|first5 = Costas M|bibcode = 2009JOptA..11k4003W
|display-authors = 1
|issue = 11 }}</ref>
<ref name="TretChiral">{{Cite journal| title=Backward-wave regime and negative refraction in chiral composites |journal = [[Photonics and Nanostructures: Fundamentals and Applications]]|volume=3|doi=10.1016/j.photonics.2005.09.008| year=2005| pages=107–15|arxiv = cond-mat/0509287 |bibcode = 2005PhNan...3..107T| issue=2–3 |last1 = Tretyakov|first1 = S.|last2 = Sihvola|first2 = A.|last3 = Jylhä|first3 = L.|s2cid = 118914130}}</ref> This is because the refractive index <math>n</math> has distinct values for left and right circularly polarized waves, given by

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

It can be seen that a negative index will occur for one polarization if <math>\kappa</math> > <math>\sqrt{\varepsilon_r\mu_r}</math>. In this case, it is not necessary that either or both <math>\varepsilon_r</math> and <math>\mu_r</math> be negative for backward wave propagation.<ref name=metamaterialplasmonics1/> A negative refractive index due to chirality was first observed simultaneously and independently by Plum ''et al.''<ref name=chiralNIMobservationPlum /> and Zhang ''et al.''<ref name=chiralNIMobservationZhang /> in 2009.

=== FSS based ===
{{main|Tunable metamaterials#Frequency selective surface based metamaterials}}

Frequency selective surface-based metamaterials block signals in one waveband and pass those at another waveband. They have become an alternative to fixed frequency metamaterials. They allow for optional changes of frequencies in a single medium, rather than the restrictive limitations of a fixed [[frequency response]].<ref name=Theory-and-Phenomena>{{Cite book| last = Capolino| first =Filippo| title =Theory and Phenomena of Metamaterials| publisher =Taylor & Francis| date =2009|chapter=Chapter 32|chapter-url =https://books.google.com/books?id=0PMnYo8hva8C&pg=PT546| isbn =978-1-4200-5425-5}}</ref>

==Other types==

=== Elastic ===

These metamaterials use different parameters to achieve a negative index of refraction in materials that are not electromagnetic. Furthermore, "a new design for elastic metamaterials that can behave either as liquids or solids over a limited frequency range may enable new applications based on the control of acoustic, elastic and [[seismic waves]]."<ref name=page>
{{cite journal
| doi = 10.1038/nmat3084
| title = Metamaterials: Neither solid nor liquid
| year = 2011
| last1 = Page
| first1 = John
| journal = Nature Materials
| volume = 10
| issue = 8
| pages = 565–66
| pmid = 21778996|bibcode = 2011NatMa..10..565P }}
</ref> They are also called [[mechanical metamaterials]].{{citation needed|date=January 2014}}

=== Acoustic ===
{{Main|Acoustic metamaterials}} {{Continuum mechanics}}

Acoustic metamaterials control, direct and manipulate [[sound]] in the form of [[wikt:Special:Search/sonic|sonic]], [[infrasonic]] or [[Ultrasound|ultrasonic]] waves in [[gas]]es, [[liquid]]s and [[solid]]s. As with electromagnetic waves, sonic waves can exhibit negative refraction.<ref name=acousticmeta1107/>

Control of sound waves is mostly accomplished through the [[bulk modulus]] ''β'', [[mass density]] ''ρ'' and chirality. The bulk modulus and density are analogs of permittivity and permeability in electromagnetic metamaterials. Related to this is the mechanics of [[sound wave]] propagation in a [[lattice model (physics)|lattice]] structure. Also materials have [[mass]] and intrinsic degrees of [[stiffness]]. Together, these form a [[resonant]] system and the mechanical (sonic) resonance may be excited by appropriate sonic frequencies (for example audible [[pulse]]s).

=== Structural ===
Structural metamaterials provide properties such as crushability and light weight. Using [[projection micro-stereolithography]], microlattices can be created using forms much like [[trusses]] and [[girders]]. Materials four orders of magnitude stiffer than conventional [[aerogel]], but with the same density have been created. Such materials can withstand a load of at least 160,000 times their own weight by over-constraining the materials.<ref>{{Cite news|url = http://www.gizmag.com/llnl-ultralight-metamaterial/32589|title = New materials developed that are as light as aerogel, yet 10,000 times stronger|last = Szondy|first = David|date = June 22, 2014|work = Gizmag}}</ref><ref name="cemms">{{cite web |title = Projection Microstereolithography|first = Nicholas|last = Fang|publisher = Department of Mechanical Science & Engineering, University of Illinois|url = http://nano-cemms.illinois.edu/media/uploads/content/111/files/microstereolithography.20101112082545.pdf}}</ref>

A ceramic nanotruss metamaterial can be flattened and revert to its original state.<ref name="Nanotruss">{{cite web|last1 = Fesenmaier|first1 = Kimm|title = Miniature Truss Work|url = https://www.caltech.edu/about/news/miniature-truss-work-42850|website = Caltech|date = 23 May 2014}}</ref>

=== Thermal ===
Typically materials found in nature, when homogeneous, are thermally isotropic. That is to say, heat passes through them at roughly the same rate in all directions. However, thermal metamaterials are anisotropic usually due to their highly organized internal structure. Composite materials with highly aligned internal particles or structures, such as fibers, are examples of this, for example carbon nanotubes (CNT).

=== Nonlinear ===
{{Main|Nonlinear metamaterials}}
Metamaterials may be fabricated that include some form of [[nonlinear]] media, whose properties change with the power of the incident wave. Nonlinear media are essential for [[nonlinear optics]]. Most optical materials have a relatively weak response, meaning that their properties change by only a small amount for large changes in the intensity of the [[electromagnetic field]]. The local electromagnetic fields of the inclusions in nonlinear metamaterials can be much larger than the average value of the field. Besides, remarkable nonlinear effects have been predicted and observed if the metamaterial effective dielectric permittivity is very small (epsilon-near-zero media).<ref>{{cite journal|title=Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity|doi=10.1103/PhysRevA.81.043839|journal=Phys. Rev. A|volume=81|issue=4  |page=043839|year=2010|arxiv = 1002.3321 |bibcode = 2010PhRvA..81d3839C |last1=Ciattoni|first1=A.|last2=Rizza|first2=C.|last3=Palange|first3=E.|s2cid=119182809}}</ref><ref>{{cite journal|title=Singularity-driven second- and third-harmonic generation at epsilon-near-zero crossing points|doi=10.1103/PhysRevA.84.063826|journal=Phys. Rev. A|volume=84|issue=6 |page=063826|year=2011|arxiv = 1107.2354 |bibcode = 2011PhRvA..84f3826V |last1=Vincenti|first1=M. A.|last2=De Ceglia|first2=D.|last3=Ciattoni|first3=A.|last4=Scalora|first4=M.|s2cid=55294978}}</ref><ref>{{cite journal|title=Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers|doi=10.1364/OL.40.001500|pmid=25831369|journal=Opt. Lett. |volume=40|issue=7 |pages=1500–3|year=2015|bibcode = 2015OptL...40.1500C |last1=Capretti|first1=Antonio|last2=Wang|first2=Yu|last3=Engheta|first3=Nader|last4=Dal Negro|first4=Luca}}</ref> In addition, exotic properties such as a negative refractive index, create opportunities to tailor the [[phase matching]] conditions that must be satisfied in any nonlinear optical structure.

=== Hall metamaterials ===
{{Main|Hall effect}}
In 2009, Marc Briane and [[Graeme Milton]]<ref>{{cite journal |last1=Briane |first1=Marc |last2=Milton |first2=Graeme W. |title=Homogenization of the Three-dimensional Hall Effect and Change of Sign of the Hall Coefficient |journal=Archive for Rational Mechanics and Analysis |date=28 November 2008 |volume=193 |issue=3 |pages=715–736 |doi=10.1007/s00205-008-0200-y|s2cid=9367952 |url=https://hal.archives-ouvertes.fr/hal-00130591/file/new.GM.HomHallEff3d.pdf }}</ref> proved mathematically that one can in principle invert the sign of a 3 materials based composite in 3D made out of only positive or negative sign Hall coefficient materials. Later in 2015 Muamer Kadic et al.<ref>{{cite journal |last1=Kadic |first1=Muamer |last2=Schittny |first2=Robert |last3=Bückmann |first3=Tiemo |last4=Kern |first4=Christian |last5=Wegener |first5=Martin |title=Hall-Effect Sign Inversion in a Realizable 3D Metamaterial |journal=Physical Review X |date=22 June 2015 |volume=5 |issue=2 |pages=021030 |doi=10.1103/PhysRevX.5.021030|bibcode=2015PhRvX...5b1030K |arxiv=1503.06118 |s2cid=55414502 }}</ref> showed that a simple perforation of isotropic material can lead to its change of sign of the Hall coefficient. This theoretical claim was finally experimentally demonstrated by Christian Kern et al.<ref>{{cite journal |doi=10.1103/PhysRevLett.118.016601|pmid=28106428|title=Experimental Evidence for Sign Reversal of the Hall Coefficient in Three-Dimensional Metamaterials|journal=Physical Review Letters|volume=118|issue=1|pages=016601|year=2017|last1=Kern|first1=Christian|last2=Kadic|first2=Muamer|last3=Wegener|first3=Martin|bibcode=2017PhRvL.118a6601K|url=https://publikationen.bibliothek.kit.edu/1000064526}}</ref>

In 2015, it was also demonstrated by Christian Kern et al. that an anisotropic perforation of a single material can lead to a yet more unusual effect namely the parallel Hall effect.<ref>{{cite journal |last1=Kern |first1=Christian |last2=Kadic |first2=Muamer |last3=Wegener |first3=Martin |title=Parallel Hall effect from three-dimensional single-component metamaterials |journal=Applied Physics Letters |date=28 September 2015 |volume=107 |issue=13 |pages=132103 |doi=10.1063/1.4932046|bibcode=2015ApPhL.107m2103K |arxiv=1507.04128 |s2cid=119261088 }}</ref> This means that the induced electric field inside a conducting media is no longer orthogonal to the current and the magnetic field but is actually parallel to the latest.

==Frequency bands==

=== Terahertz ===
{{Main|Terahertz metamaterial}}

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

=== Photonic ===
{{Main|Photonic metamaterials}}

Photonic metamaterial interact with optical frequencies ([[mid-infrared]]). The sub-wavelength period distinguishes them from [[photonic band gap]] structures.<ref name=photonic-MM1>{{cite encyclopedia| title =Photonic Metamaterials| encyclopedia =Encyclopedia of Laser Physics and Technology| volume = I & II| pages =1| publisher =Wiley-VCH Verlag| date =2008–18
| url =http://www.rp-photonics.com/photonic_metamaterials.html
| access-date =2009-10-01| author =Paschotta, Rüdiger 
}}</ref><ref name=photonic-MM2>{{cite book| last = Capolino| first =Filippo| title =Applications of Metamaterials|publisher =Taylor & Francis, Inc.| date = 2009|pages =29–1, 25–14, 22–1|url =https://books.google.com/books?id=8M0IqvcsHisC&pg=PT640|isbn =978-1-4200-5423-1|access-date =2009-10-01}}</ref>

=== Tunable ===
{{Main|Tunable metamaterials}}

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

=== Plasmonic ===
{{main|Plasmonic metamaterials}}

Plasmonic metamaterials exploit [[surface plasmons]], which are produced from the interaction of light with metal-[[dielectrics]]. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating [[electromagnetic waves]] or surface waves<ref>{{cite journal|author=Takayama, O.|title=Photonic surface waves on metamaterial interfaces. |journal=Journal of Physics: Condensed Matter|volume=29 |pages=463001 |date=2017|last2= Bogdanov, A. A. |first2=Lavrinenko, A. V. |issue=46 |doi=10.1088/1361-648X/aa8bdd |pmid=29053474 |bibcode=2017JPCM...29T3001T |s2cid=1528860 }}</ref> known as [[surface plasmon polaritons]]. Bulk [[plasma oscillation]]s make possible the effect of negative mass (density).<ref>{{Cite journal|last1=Bormashenko|first1=Edward|last2=Legchenkova|first2=Irina|date=January 2020|title=Negative Effective Mass in Plasmonic Systems|journal=Materials|language=en|volume=13|issue=8|pages=1890|doi=10.3390/ma13081890|pmc=7215794|pmid=32316640|bibcode=2020Mate...13.1890B|doi-access=free}}</ref><ref>{{Cite journal|last1=Bormashenko|first1=Edward|last2=Legchenkova|first2=Irina|last3=Frenkel|first3=Mark|date=January 2020|title=Negative Effective Mass in Plasmonic Systems II: Elucidating the Optical and Acoustical Branches of Vibrations and the Possibility of Anti-Resonance Propagation|journal=Materials|language=en|volume=13|issue=16|pages=3512|doi=10.3390/ma13163512|pmc=7476018|pmid=32784869|bibcode=2020Mate...13.3512B|doi-access=free}}</ref>

== Applications ==

Metamaterials are under consideration for many applications.<ref name= MASSA>{{cite journal |doi= 10.1109/JPROC.2015.2394292 |first1= G.| last1= Oliveri | first2= D.H.| last2= Werner |first3 = A. |last3= Massa | title= Reconfigurable electromagnetics through metamaterials – A review | journal= [[Proceedings of the IEEE]] |volume= 103| issue=7  | pages= 1034–56 |date= 2015|s2cid= 25179597}}</ref> Metamaterial antennas are commercially available.

In 2007, one researcher stated that for metamaterial applications to be realized, energy loss must be reduced, materials must be extended into three-dimensional [[isotropic]] materials and production techniques must be industrialized.<ref name=goals>{{cite web| publisher =DOE /[[Ames Laboratory]]| title =Metamaterials found to work for visible light| date =2007-01-04
| url =http://eurekalert.org/pub_releases/2007-01/dl-mft010407.php?light
| author =Costas Soukoulis 
| access-date =2009-11-07}}</ref>

=== Antennas ===
{{Main|Metamaterial antennas}}

Metamaterial antennas are a class of [[Antenna (radio)|antennas]] that use metamaterials to improve performance.<ref name=radiation-properties/><ref name=slyusarmeta/><ref name=Directive-emission>{{cite journal| doi =10.1103/PhysRevLett.89.213902| title =A Metamaterial for Directive Emission| year =2002| last1 =Enoch| first1 =Stefan| first2 =GéRard| first3 =Pierre| first4 =Nicolas| first5 =Patrick| journal =Physical Review Letters| volume =89| page =213902| pmid =12443413| last2 =Tayeb| last3 =Sabouroux| last4 =Guérin| last5 =Vincent| issue =21| bibcode=2002PhRvL..89u3902E| s2cid =37505778}}</ref><ref name=neg-group-vel-1>{{cite journal| doi =10.1109/TAP.2003.817556| title =Periodically loaded transmission line with effective negative refractive index and negative group velocity| year =2003| last1 =Siddiqui| first1 =O.F.| first3 =G.V.| journal =IEEE Transactions on Antennas and Propagation| volume =51| pages =2619–25| last2 =Mo Mojahedi| last3 =Eleftheriades|bibcode = 2003ITAP...51.2619S| issue =10 }}</ref> Demonstrations showed that metamaterials could enhance an antenna's [[Intensity (physics)|radiated power]].<ref name=radiation-properties/><ref name=Antenna-substrate>{{cite journal|last=Wu |first=B.-I. |author2=W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk and J. A. Kong |title=A Study of Using Metamaterials as Antenna Substrate to Enhance Gain |journal=Progress in Electromagnetics Research |volume=51 |pages=295–28 |year=2005 |doi=10.2528/PIER04070701 |last3=Pacheco |first3=Joe |last4=Chen |first4=Xudong |last5=Grzegorczyk |first5=Tomasz M. |last6=Kong |first6=Jin Au |doi-access=free }}</ref> Materials that can attain negative permeability allow for properties such as small antenna size, high directivity and tunable frequency.<ref name=radiation-properties>{{cite journal|doi = 10.1002/pssb.200674505|title = Radiation properties of a split ring resonator and monopole composite|year = 2007|last1 = Alici|first1 = Kamil Boratay|first2 = Ekmel|journal = Physica Status Solidi B|volume = 244|pages = 1192–96|last2 = Özbay|bibcode = 2007PSSBR.244.1192A|issue = 4 |hdl = 11693/49278|s2cid = 5348103|hdl-access = free}}</ref><ref name=slyusarmeta/>

=== Absorber ===
{{Main|Metamaterial absorber}}
A metamaterial absorber manipulates the loss components of metamaterials' permittivity and magnetic permeability, to absorb large amounts of [[electromagnetic radiation]].<ref>{{cite journal |last1=de Oliveira Neto |first1=A. M. |last2=Beccaro |first2=W. |last3=de Oliveira |first3=A. M. |last4=Justo |first4=J.F. |title=Exploring the Internal Patterns in the Design of Ultrawideband Microwave Absorbers |journal=IEEE Antennas and Wireless Propagation Letters |date=2023 |volume=22 |issue=9 |page=2290-2294 |doi=10.1109/LAWP.2023.3284650}}</ref> This is a useful feature for [[photodetection]]<ref>{{cite journal | last1 = Li | first1 = W. | last2 = Valentine | first2 = J. | year = 2014 | title = Metamaterial Perfect Absorber Based Hot Electron Photodetection | journal = Nano Letters | volume = 14 | issue = 6| pages = 3510–14 | doi=10.1021/nl501090w| pmid = 24837991 | bibcode = 2014NanoL..14.3510L }}</ref><ref>{{Cite journal|last1=Yu|first1=Peng|last2=Wu|first2=Jiang|last3=Ashalley|first3=Eric|last4=Govorov|first4=Alexander|last5=Wang|first5=Zhiming|date=2016|title=Dual-band absorber for multispectral plasmon-enhanced infrared photodetection|journal=Journal of Physics D: Applied Physics|language=en|volume=49|issue=36|pages=365101|doi=10.1088/0022-3727/49/36/365101|issn=0022-3727|bibcode=2016JPhD...49J5101Y|s2cid=123927835 |url=https://discovery.ucl.ac.uk/id/eprint/1522579/1/JPD%20final%20version.pdf}}</ref> and [[solar photovoltaic]] applications.<ref>{{Cite journal|last1=Yu|first1=Peng|last2=Besteiro|first2=Lucas V.|last3=Huang|first3=Yongjun|last4=Wu|first4=Jiang|last5=Fu|first5=Lan|last6=Tan|first6=Hark H.|last7=Jagadish|first7=Chennupati|last8=Wiederrecht|first8=Gary P.|last9=Govorov|first9=Alexander O.|title=Broadband Metamaterial Absorbers|journal=Advanced Optical Materials|pages=1800995|language=en|doi=10.1002/adom.201800995|issn=2195-1071|year=2018|volume=7|issue=3|doi-access=free|hdl=1885/213159|hdl-access=free}}</ref> Loss components are also relevant in applications of negative refractive index (photonic metamaterials, antenna systems) or [[transformation optics]] ([[metamaterial cloaking]], celestial mechanics), but often are not used in these applications.

=== Superlens ===
{{Main|Superlens}}

A ''superlens'' is a two or three-dimensional device that uses metamaterials, usually with negative refraction properties, to achieve resolution beyond the [[diffraction limit]] (ideally, infinite resolution). Such a behaviour is enabled by the capability of double-negative materials to yield negative phase velocity. The diffraction limit is inherent in conventional optical devices or lenses.<ref name=perfect-lens-2000>{{Cite journal|doi =10.1103/PhysRevLett.85.3966|title =Negative Refraction Makes a Perfect Lens|year =2000|last1 =Pendry|first1 =J. B.|journal =Physical Review Letters|volume =85|pages =3966–69|pmid =11041972|issue =18|bibcode=2000PhRvL..85.3966P|s2cid =25803316|doi-access =free}}</ref><ref name=thin-sliver>{{Cite journal| doi =10.1126/science.1108759| title =Sub-Diffraction-Limited Optical Imaging with a Silver Superlens| year =2005| last1 =Fang| first1 =N.| journal =Science| volume =308| pages =534–37| pmid =15845849| last2 =Lee| first2 =H| last3 =Sun| first3 =C| last4 =Zhang| first4 =X| issue =5721|bibcode = 2005Sci...308..534F | s2cid =1085807}}</ref>

=== Cloaking devices ===
{{Main|Metamaterial cloaking}}

Metamaterials are a potential basis for a practical [[cloaking device]]. The [[proof of principle]] was demonstrated on October 19, 2006. No practical cloaks are publicly known to exist.<ref>{{cite news|publisher=Office of News & Communications Duke University |title=First Demonstration of a Working Invisibility Cloak |url=http://www.dukenews.duke.edu/2006/10/cloakdemo.html |access-date=2009-05-05 |url-status=dead |archive-url=https://web.archive.org/web/20090719231753/http://www.dukenews.duke.edu/2006/10/cloakdemo.html |archive-date=July 19, 2009 }}</ref><ref>{{cite journal|title=Metamaterial Electromagnetic Cloak at Microwave Frequencies|author=Schurig, D.|journal=Science|volume=314|issue=5801|doi=10.1126/science.1133628|pmid=17053110|year=2006|bibcode = 2006Sci...314..977S|display-authors=1|last2=Mock|first2=J. J.|last3=Justice|first3=B. J.|last4=Cummer|first4=S. A.|last5=Pendry|first5=J. B.|last6=Starr|first6=A. F.|last7=Smith|first7=D. R.|pages=977–80 |s2cid=8387554|doi-access=free}}</ref><ref>{{cite news|title=Experts test cloaking technology|date=2006-10-19|work=[[BBC News]]|url=http://news.bbc.co.uk/1/hi/sci/tech/6064620.stm|access-date=2008-08-05}}</ref><ref>{{cite web|url=http://www.purdue.edu/uns/x/2007a/070402ShalaevCloaking.html|title=Engineers see progress in creating 'invisibility cloak'|work=purdue.edu}}</ref><ref>{{cite journal|title=Achieving transparency with plasmonic and metamaterial coatings|doi=10.1103/PhysRevE.72.016623|pmid=16090123|journal=Phys. Rev. E|volume=72|issue=1|page=016623|year=2005|arxiv = cond-mat/0502336 |bibcode = 2005PhRvE..72a6623A |last1=Alù|first1=Andrea|last2=Engheta|first2=Nader|s2cid=6004609}}</ref><ref>Merritt, Richard (January 2009) "[http://news.duke.edu/2009/01/invis09.html Next Generation Cloaking Device Demonstrated: Metamaterial renders object 'invisible'"]  {{webarchive |url=https://web.archive.org/web/20090220020959/http://news.duke.edu/2009/01/invis09.html |date=February 20, 2009 }}</ref>

=== Radar cross-section (RCS-)reducing metamaterials ===
Metamaterials have applications in [[stealth technology]], which reduces RCS in any of various ways (e.g., absorption, diffusion, redirection). Conventionally, the RCS has been reduced either by [[radar-absorbent material]] (RAM) or by purpose shaping of the targets such that the scattered energy can be redirected away from the source. While RAMs have narrow frequency band functionality, purpose shaping limits the aerodynamic performance of the target. More recently, metamaterials or metasurfaces are synthesized that can redirect the scattered energy away from the source using either array theory<ref name="A. Modi 19 2">{{cite journal | last1 = Modi | first1 = A. Y. | last2 = Alyahya | first2 = M. A. | last3 = Balanis | first3 = C. A. | last4 = Birtcher | first4 = C. R. | year = 2019| title = Metasurface-Based Method for Broadband RCS Reduction of Dihedral Corner Reflectors with Multiple Bounces | journal = IEEE Transactions on Antennas and Propagation | volume = 67 | issue = 3| page =  1| doi = 10.1109/TAP.2019.2940494 | s2cid = 212649480 }}</ref><ref name="A. Modi 19">{{cite journal | last1 = Modi | first1 = A. Y. | last2 = Balanis | first2 = C. A. | last3 = Birtcher | first3 = C. R. | last4 = Shaman | first4 = H. | year = 2019| title = New Class of RCS-Reduction Metasurfaces Based on Scattering Cancellation Using Array Theory | journal = IEEE Transactions on Antennas and Propagation | volume = 67 | issue = 1| pages = 298–308 | doi = 10.1109/TAP.2018.2878641 | bibcode = 2019ITAP...67..298M | s2cid = 58670543 }}</ref><ref name="A. Modi 17">{{cite journal | doi = 10.1109/TAP.2017.2734069 | volume=65 | issue=10 | title=Novel Design of Ultrabroadband Radar Cross Section Reduction Surfaces Using Artificial Magnetic Conductors | year=2017 | journal=IEEE Transactions on Antennas and Propagation | pages=5406–5417 | last1 = Modi | first1 = Anuj Y. | last2 = Balanis | first2 = Constantine A. | last3 = Birtcher | first3 = Craig R. | last4 = Shaman | first4 = Hussein N.| bibcode=2017ITAP...65.5406M | s2cid=20724998 }}</ref><ref>{{cite journal | doi = 10.2528/PIER10060402 | volume=107 | title=A novel approach for RCS reduction using a combination of artificial magnetic conductors | year=2010 | journal=Progress in Electromagnetics Research | pages=147–159 | last1 = MarÃ | last2 = de Cos | first2 = Elena | last3 = Alvarez Lopez | first3 = Yuri | last4 = Las-Heras | first4 = Fernando| doi-access = free }}</ref> or generalized Snell's law.<ref>{{cite journal | doi =  10.1063/1.4881935 | volume=104 | issue=22 | title=Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces | year=2014 | journal=Applied Physics Letters | page=221110 | last1 = Li | first1 = Yongfeng | last2 = Zhang | first2 = Jieqiu | last3 = Qu | first3 = Shaobo | last4 = Wang | first4 = Jiafu | last5 = Chen | first5 = Hongya | last6 = Xu | first6 = Zhuo | last7 = Zhang | first7 = Anxue| bibcode=2014ApPhL.104v1110L }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |doi-access=free }}</ref> This has led to aerodynamically favorable shapes for the targets with the reduced RCS.

=== Seismic protection ===
{{Main|Seismic metamaterials}}
Seismic metamaterials counteract the adverse effects of seismic waves on man-made structures.<ref name=control_elastic_waves/><ref name=seismic-cloak>{{cite web|last =Johnson| first =R. Colin|title =Metamaterial cloak could render buildings 'invisible' to earthquakes|publisher= EETimes.com|date =2009-07-23
| url =http://www.eetimes.com/showArticle.jhtml?articleID=218600378| access-date =2009-09-09}}</ref><ref name=seismic-cloak-2>{{Cite news| last = Barras| first = Colin| title =Invisibility cloak could hide buildings from quakes| newspaper =New Scientist| page =1| date =2009-06-26
| url =https://www.newscientist.com/article/dn17378-invisibility-cloak-could-hide-buildings-from-quakes.html#| access-date =2009-10-20}}</ref>

=== Sound filtering ===

Metamaterials textured with nanoscale wrinkles could control sound or light signals, such as changing a material's color or improving [[ultrasound]] resolution. Uses include [[Nondestructive testing|nondestructive material testing]], [[medical diagnostics]] and [[sound suppression]]. The materials can be made through a high-precision, multi-layer deposition process. The thickness of each layer can be controlled within a fraction of a wavelength. The material is then compressed, creating precise wrinkles whose spacing can cause scattering of selected frequencies.<ref>{{cite web|url=http://www.kurzweilai.net/wrinkled-metamaterials-for-controlling-light-and-sound-propagation |title=Wrinkled metamaterials for controlling light and sound propagation |publisher=KurzweilAI |date=2014-01-28 |access-date=2014-04-15}}</ref><ref>{{Cite journal | doi = 10.1103/PhysRevLett.112.034301| title = Transforming Wave Propagation in Layered Media via Instability-Induced Interfacial Wrinkling| journal = Physical Review Letters| volume = 112| issue = 3| year = 2014| last1 = Rudykh | first1 = S. | last2 = Boyce | first2 = M. C. | bibcode=2014PhRvL.112c4301R | pmid=24484141 | page=034301| hdl = 1721.1/85082| hdl-access = free}}</ref>

=== Guided mode manipulations ===
Metamaterials can be integrated with [[optical waveguides]] to tailor guided [[electromagnetic waves]] ([[meta-waveguide]]).<ref name=":0">{{Cite journal |last1=Meng |first1=Yuan |last2=Chen |first2=Yizhen |last3=Lu |first3=Longhui |last4=Ding |first4=Yimin |last5=Cusano |first5=Andrea |last6=Fan |first6=Jonathan A. |last7=Hu |first7=Qiaomu |last8=Wang |first8=Kaiyuan |last9=Xie |first9=Zhenwei |last10=Liu |first10=Zhoutian |last11=Yang |first11=Yuanmu |date=2021-11-22 |title=Optical meta-waveguides for integrated photonics and beyond |journal=Light: Science & Applications |language=en |volume=10 |issue=1 |pages=235 |doi=10.1038/s41377-021-00655-x |pmid=34811345 |pmc=8608813 |bibcode=2021LSA....10..235M |issn=2047-7538}}</ref> Subwavelength structures like metamaterials can be integrated with for instance silicon waveguides to develop and polarization beam splitters<ref>{{Cite journal |last1=Halir |first1=Robert |last2=Cheben |first2=Pavel |last3=Luque-González |first3=José Manuel |last4=Sarmiento-Merenguel |first4=Jose Darío |last5=Schmid |first5=Jens H. |last6=Wangüemert-Pérez |first6=Gonzalo |last7=Xu |first7=Dan-Xia |last8=Wang |first8=Shurui |last9=Ortega-Moñux |first9=Alejandro |last10=Molina-Fernández |first10=Íñigo |date=November 2016 |title=Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial |url=https://onlinelibrary.wiley.com/doi/10.1002/lpor.201600213 |journal=Laser & Photonics Reviews |language=en |volume=10 |issue=6 |pages=1039–1046 |doi=10.1002/lpor.201600213 |arxiv=1606.03750 |bibcode=2016LPRv...10.1039H |s2cid=126025926 |issn=1863-8880}}</ref> and optical couplers,<ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Hu |first2=Futai |last3=Liu |first3=Zhoutian |last4=Xie |first4=Peng |last5=Shen |first5=Yijie |last6=Xiao |first6=Qirong |last7=Fu |first7=Xing |last8=Bae |first8=Sang-Hoon |last9=Gong |first9=Mali |date=2019-06-10 |title=Chip-integrated metasurface for versatile and multi-wavelength control of light couplings with independent phase and arbitrary polarization |url=https://opg.optica.org/oe/abstract.cfm?uri=oe-27-12-16425 |journal=Optics Express |language=EN |volume=27 |issue=12 |pages=16425–16439 |doi=10.1364/OE.27.016425 |pmid=31252868 |bibcode=2019OExpr..2716425M |s2cid=189958968 |issn=1094-4087|doi-access=free }}</ref> adding new degrees of freedom of controlling light propagation at nanoscale for integrated photonic devices.<ref>{{Cite journal |last1=Cheben |first1=Pavel |last2=Halir |first2=Robert |last3=Schmid |first3=Jens H. |last4=Atwater |first4=Harry A. |last5=Smith |first5=David R. |date=August 2018 |title=Subwavelength integrated photonics |url=https://www.nature.com/articles/s41586-018-0421-7 |journal=Nature |language=en |volume=560 |issue=7720 |pages=565–572 |doi=10.1038/s41586-018-0421-7 |pmid=30158604 |bibcode=2018Natur.560..565C |s2cid=52117964 |issn=1476-4687}}</ref> Other applications such as integrated mode converters,<ref>{{Cite journal |last1=Li |first1=Zhaoyi |last2=Kim |first2=Myoung-Hwan |last3=Wang |first3=Cheng |last4=Han |first4=Zhaohong |last5=Shrestha |first5=Sajan |last6=Overvig |first6=Adam Christopher |last7=Lu |first7=Ming |last8=Stein |first8=Aaron |last9=Agarwal |first9=Anuradha Murthy|author9-link=Anu Agarwal |last10=Lončar |first10=Marko |last11=Yu |first11=Nanfang |date=July 2017 |title=Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces |url=https://www.nature.com/articles/nnano.2017.50 |journal=Nature Nanotechnology |language=en |volume=12 |issue=7 |pages=675–683 |doi=10.1038/nnano.2017.50 |pmid=28416817 |bibcode=2017NatNa..12..675L |osti=1412777 |issn=1748-3395}}</ref> polarization (de)multiplexers,<ref>{{Cite journal |last1=Guo |first1=Rui |last2=Decker |first2=Manuel |last3=Setzpfandt |first3=Frank |last4=Gai |first4=Xin |last5=Choi |first5=Duk-Yong |last6=Kiselev |first6=Roman |last7=Chipouline |first7=Arkadi |last8=Staude |first8=Isabelle |last9=Pertsch |first9=Thomas |last10=Neshev |first10=Dragomir N. |last11=Kivshar |first11=Yuri S. |date=2017-07-07 |title=High–bit rate ultra-compact light routing with mode-selective on-chip nanoantennas |journal=Science Advances |language=en |volume=3 |issue=7 |pages=e1700007 |doi=10.1126/sciadv.1700007 |issn=2375-2548 |pmc=5517110 |pmid=28776027|bibcode=2017SciA....3E0007G }}</ref> structured light generation,<ref>{{Cite journal |last1=He |first1=Tiantian |last2=Meng |first2=Yuan |last3=Liu |first3=Zhoutian |last4=Hu |first4=Futai |last5=Wang |first5=Rui |last6=Li |first6=Dan |last7=Yan |first7=Ping |last8=Liu |first8=Qiang |last9=Gong |first9=Mali |last10=Xiao |first10=Qirong |date=2021-11-22 |title=Guided mode meta-optics: metasurface-dressed waveguides for arbitrary mode couplers and on-chip OAM emitters with a configurable topological charge |url=https://opg.optica.org/oe/abstract.cfm?uri=oe-29-24-39406 |journal=Optics Express |volume=29 |issue=24 |pages=39406–39418 |doi=10.1364/OE.443186 |issn=1094-4087 |pmid=34809306 |bibcode=2021OExpr..2939406H |doi-access=free |accessdate=2023-02-22}}</ref> and on-chip bio-sensors<ref>{{Cite journal |last1=Flueckiger |first1=Jonas |last2=Schmidt |first2=Shon |last3=Donzella |first3=Valentina |last4=Sherwali |first4=Ahmed |last5=Ratner |first5=Daniel M. |last6=Chrostowski |first6=Lukas |last7=Cheung |first7=Karen C. |date=2016-07-11 |title=Sub-wavelength grating for enhanced ring resonator biosensor |url=https://opg.optica.org/oe/abstract.cfm?uri=oe-24-14-15672 |journal=Optics Express |language=EN |volume=24 |issue=14 |pages=15672–15686 |doi=10.1364/OE.24.015672 |pmid=27410840 |bibcode=2016OExpr..2415672F |issn=1094-4087|doi-access=free }}</ref> can be developed.<ref name=":0" />

==Theoretical models==

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

Several (mathematical) material models [[frequency response]] in DNGs. One of these is the [[Lorentz model]], which describes electron motion in terms of a driven-damped, [[harmonic oscillator]]. The [[Debye relaxation]] model applies when the [[acceleration]] component of the Lorentz mathematical model is small compared to the other components of the equation. The [[Drude model]] applies when the [[restoring force]] component is negligible and the coupling coefficient is generally the [[plasma frequency]]. Other component distinctions call for the use of one of these models, depending on its polarity or purpose.<ref name=physicsengineering1/>

Three-dimensional composites of metal/non-metallic inclusions periodically/randomly embedded in a low permittivity matrix are usually modeled by analytical methods, including mixing formulas and scattering-matrix based methods. The particle is modeled by either an electric dipole parallel to the electric field or a pair of crossed electric and magnetic dipoles parallel to the electric and magnetic fields, respectively, of the applied wave. These dipoles are the leading terms in the multipole series. They are the only existing ones for a homogeneous sphere, whose [[polarizability]] can be easily obtained from the [[Mie scattering]] coefficients. In general, this procedure is known as the "point-dipole approximation", which is a good approximation for metamaterials consisting of composites of electrically small spheres. Merits of these methods include low calculation cost and mathematical simplicity.<ref name=Shore2007>
{{cite journal
 | doi = 10.1029/2007RS003647
 | title = Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers
 | year = 2007
 | last1 = Shore
 | first1 = R. A.
 | author2-link=Arthur D. Yaghjian
 | last2 = Yaghjian
 | first2 = A. D.
 | journal = Radio Science
 | volume = 42
 | issue = 6
 | pages = RS6S21 |bibcode = 2007RaSc...42.6S21S | doi-access = free
 }}
</ref><ref name=Li2012>
{{cite journal
 | doi = 10.1109/tap.2012.2194637
 | title = Traveling waves on three-dimensional periodic arrays of two different magnetodielectric spheres arbitrarily arranged on a simple tetragonal lattice
 | year = 2012
 | last1 = Li
 | first1 = Y.
 | last2 = Bowler
 | first2 = N.
 | journal = IEEE Transactions on Antennas and Propagation
 | volume = 60
 | issue = 6
 | pages = 2727–39 |bibcode = 2012ITAP...60.2727L | s2cid = 21023639
 }}
</ref>

Three conceptions- negative-index medium, [[history of metamaterials#Exceptional phenomena|non-reflecting crystal]] and superlens are foundations of the metamaterial theory. Other [[first principle]]s techniques for analyzing triply-periodic electromagnetic media may be found in [[Photonic crystal#Computing photonic band structure|Computing photonic band structure]]

==Institutional networks==

===MURI===
The Multidisciplinary University Research Initiative (MURI) encompasses dozens of Universities and a few government organizations. Participating universities include UC Berkeley, UC Los Angeles, UC San Diego, Massachusetts Institute of Technology, and Imperial College in London. The sponsors are [[Office of Naval Research]] and the [[Defense Advanced Research Project Agency]].<ref name=MURI-Univ>{{cite web| last =MURI metamaterials| first =UC Berkeley| title =Scalable and Reconfigurable Electromagnetic Metamaterials and Devices| year =2009| url =http://xlab.me.berkeley.edu/MURI/MURI.html| access-date =2009-12-08| archive-date =2009-12-03| archive-url =https://web.archive.org/web/20091203002249/http://xlab.me.berkeley.edu/MURI/MURI.html| url-status =dead}}</ref>

MURI supports research that intersects more than one traditional science and engineering discipline to accelerate both research and translation to applications. As of 2009, 69 academic institutions were expected to participate in 41 research efforts.<ref name=DOD-MURI>{{cite web|last=U.S. Department of Defense |first=Office of the Assistant Secretary of Defense (Public Affairs) |title=DoD Awards $260 Million in University Research Funding |date=2009-05-08 |url=http://www.defense.gov/releases/release.aspx?releaseid=12657 |publisher=DoD |access-date=2009-12-08 |url-status=dead |archive-url=https://web.archive.org/web/20100302010715/http://www.defense.gov/releases/release.aspx?releaseid=12657 |archive-date=March 2, 2010 }}</ref>

===Metamorphose===
The Virtual Institute for Artificial Electromagnetic Materials and Metamaterials "Metamorphose VI AISBL" is an international association to promote artificial electromagnetic materials and metamaterials. It organizes scientific conferences, supports specialized journals, creates and manages research programs, provides training programs (including PhD and training programs for industrial partners); and technology transfer to European Industry.<ref name=Metamorphose-01>

{{cite web| last =Tretyakov| first =Prof. Sergei; President of the Association
|author2=Dr. Vladmir Podlozny |author3=Secretary General | title =Metamorphose| work =Metamaterials research and development| publisher =Metamorphose VI| date =2009-12-13
|url =http://www.metamorphose-vi.org/
|format =See the "About" section of this web site for information about this organization.
|access-date =2009-12-13}}</ref><ref name=Metamorphose-02>

{{Cite journal| last =de Baas| first=A. F.|author2=J. L. Vallés| title =Success stories in the Materials domain| journal =Metamorphose| volume =Networks of Excellence Key for the future of EU research| page =19 | date =2007-02-11| url =http://ec.europa.eu/research/industrial_technologies/pdf/noes-122007_en.pdf| access-date =2009-12-13}}</ref>

==See also==

*[[Electromagnetic metasurface|Metasurface]]
*[[Artificial dielectrics]]—[[macroscopic]] analogues of naturally occurring [[dielectrics]] that came into use with the radar [[Microwave engineering|microwave technologies]] developed between the 1940s and 1970s.
*[[METATOY]] ('''Meta'''material f'''o'''r ra'''y'''s)—composed of super-wavelength structures, such as small arrays of prisms and lenses and can operate over a broad band of frequencies
*[[Magnonics]]
*[[Metamaterials (journal)|''Metamaterials'' (journal)]]
*''[[Metamaterials Handbook]]''
*''[[Metamaterials: Physics and Engineering Explorations]]''

==References==
{{reflist}}

==External links==
{{Sister project links}}
*{{Commons category-inline|Metamaterials}}

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[[Category:Metamaterials| ]]
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