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A '''nonlinear metamaterial''' is an artificially constructed material that can exhibit properties not yet found in nature. Its response to [[electromagnetic radiation]] can be characterized by its [[permittivity]] and [[magnetic permeability|material permeability]]. The product of the permittivity and permeability results in the [[refractive index]]. Unlike natural materials, nonlinear metamaterials can produce a negative refractive index. These can also produce a more pronounced nonlinear response than naturally occurring materials.

Nonlinear metamaterials are a [[periodic function|periodic]], nonlinear,  [[transmission medium]]. These are a type of [[negative index metamaterial]] where the [[nonlinear]]ity is available because the microscopic [[electric field]] of the [[wiktionary:inclusion|inclusion]]s can be larger  than the macroscopic [[electric field]] of the [[EM radiation|electromagnetic (EM) source]]. This then becomes a useful tool which allows for enhancing the [[nonlinear optics|nonlinear behavior]] of the [[metamaterial]]. A dominant nonlinear response, however, can be derived from the [[Hysteresis| hysteresis-type]] dependence of the material's [[magnetic permeability]] on the magnetic component of the incident [[electromagnetic wave]] (light) propagating through the material. Furthermore, the hysteresis-type dependence of the magnetic permeability on the [[field intensity]] allows changing the material from left to right-handed and back.

[[Nonlinear system|Nonlinear]] media are essential for [[nonlinear optics]].  However most [[optical]] materials  have a relatively weak nonlinear response, meaning that their properties only change by a small amount for large changes in intensity of the [[electromagnetic field]].  Nonlinear metamaterials can overcome this limitation, since the local fields of the resonant structures can be much larger than the average value of the field<ref name=intro-nonlinear-mm>
{{cite book
 | last1=Krowne | first1=C. M.
 | last2=Zhang | first2=Y.
 | year=2007
 | title=Physics of Negative Refraction and Negative Index Materials: Optical and Electronic Aspects and Diversified Approaches
 | url=https://books.google.com/books?id=AjdbPVfK7rkC&q=nonlinear+metamaterials&pg=PT255
 | publisher=[[Springer-Verlag]]
 | pages=331, 332
 | isbn=978-3-540-72131-4
}}</ref><ref name=nonlinear-properties>
{{cite journal
 | last1=Zharov | first1=A. A.
 | last2=Shadrivov | first2=I.
 | last3=Kivshar | first3=Y.
 | year=2003
 | title=Nonlinear properties of left-handed metamaterials
 | journal=[[Physical Review Letters]]
 | volume=91 | issue=3 | pages=037401
 | arxiv=cond-mat/0303443
 | doi=10.1103/PhysRevLett.91.037401 | bibcode=2003PhRvL..91c7401Z | pmid=12906453
| s2cid=17817365
 }}</ref><ref name=Shadrivov>
{{cite journal
|doi=10.1117/2.1200811.1390
|url=http://spie.org/x31810.xml?ArticleID=x31810
|title=Nonlinear metamaterials: a new degree of freedom
|year=2008|
last1=Shadrivov
|first1=Ilya
|journal=SPIE Newsroom|citeseerx=10.1.1.497.6901}}</ref> - in this respect metamaterials are similar to other composite media, such e.g. as [[Vladimir_M._Shalaev#Random_composites | random metal-dielectric composites]], including fractal clusters and semicoutinouos/percolation metal films, where the areas with  enhanced local light fields<ref>D.P. Tsai, J. Kovacs, Zh. Wang, M. Moskovits, V.M. Shalaev, J.S. Suh, and R. Botet, [https://engineering.purdue.edu/~shalaev/Publication_list_files/Photon_Scanning_Tunneling-1994.pdf Photon Scanning Tunneling Microscopy Images of Optical Excitations of Fractal Metal Colloid Clusters], Physical Review Letters, v. 72, pp. 4149–4152, (1994)</ref> - “hot spots”{{efn|sometimes referred to as [[Vladimir M. Shalaev | Shalaev]]'s "hot spots": see e.g. <ref>A. Otto, [https://onlinelibrary.wiley.com/doi/abs/10.1002/jrs.1524 On the significance of Shalaev's 'hot spots' in ensemble and single‐molecule SERS by adsorbates on metallic films at the percolation threshold], J. Raman Spectroscopy, v. 37, pp. 937–947 (2006)</ref>.}} - produce giant linear and non-linear optical responses.<ref>V. M. Shalaev, [http://www.sciencedirect.com/science/article/pii/0370157395000763 Electromagnetic Properties of Small-Particle Composites], Physics Reports, v. 272, pp. 61–137 (1996)</ref><ref>A.K. Sarychev, V.M. Shalaev, [https://engineering.purdue.edu/~shalaev/Publication_list_files/PhysRep.pdf Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites], Physics Reports, v. 335, pp. 275–371 (2000)</ref><ref>V. M. Shalaev, [https://www.springer.com/us/book/9783540656159 Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films], Springer (2000)</ref><ref>M.I. Stockman, V.M. Shalaev, M. Moskovits, R. Botet, T.F. George, [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.46.2821 Enhanced Raman scattering by fractal clusters: Scale-invariant theory], Physical Review B, v. 46, pp. 2821–2830 (1992)</ref>
{{notelist}}

==Overview of metamaterials==
Metamaterials are incarnations of materials first proposed by a Russian theorist, [[Victor Veselago]] in 1967.

''Nonlinear metamaterials'', a type of [[metamaterial]], are being developed in order to manipulate [[electromagnetic radiation]] in new ways. Optical and electromagnetic properties of natural materials are often altered through chemistry. With metamaterials optical and electromagnetic properties can be engineered through the geometry of its unit cells. The unit cells are materials that are ordered in geometric arrangements with dimensions that are fractions of the wavelength of the radiated [[electromagnetic wave]].<ref name=smith>
{{NIST-PD
|article=Metamaterials Invisibility Cloaks and Superlenses
|url=https://www.nist.gov/public_affairs/colloquia/20101015.cfm
|accessdate=2011-08-13}}</ref><ref name=plasmonicMM>
{{NIST-PD
|article=Three-Dimensional Plasmonic Metamaterials
|url=https://www.nist.gov/cnst/nrg/3d_plasmonic_metamaterials.cfm
|author=Henri Lezec
|accessdate=2011-08-13}}</ref>

By having the freedom to alter effects by adjusting the configurations and sizes of the unit cells, control over [[permittivity]] and [[magnetic permeability]] can be achieved. These two parameters (or quantities) determine the propagation of electromagnetic waves in matter. Therefore, the achievable electromagnetic and optical effects can be extended.

Optical properties can be expanded beyond the capabilities of lenses, mirrors, and other conventional materials. One of the effects most studied is the [[negative index of refraction]] first proposed by Victor Veselago in 1967. [[Negative index material]]s, exhibit optical properties opposite to those of glass, air, and the other conventional materials. At the correct frequencies,  the negative index materials refract electromagnetic waves in novel ways, to a zero index or negative index. Also, energy can propagate in the opposite direction which can result in compensation mechanisms, among other possibilities.<ref name=plasmonicMM/><ref name="v1967">
{{cite journal|author=V. G. Veselago|year=1968|title=The electrodynamics of substances with simultaneously negative values of ε and μ|url=http://www.turpion.org/php/paper.phtml?journal_id=pu&paper_id=3699|journal=Sov. Phys. Usp.|volume=10|issue=4|pages=509–14|bibcode=1968SvPhU..10..509V|doi=10.1070/PU1968v010n04ABEH003699}}</ref><ref name="Bolta">
{{cite journal|last1=Boltasseva|first1=A|author-link1=Alexandra Boltasseva |last2=Shalaev|first2=V|year=2008|title=Fabrication of optical negative-index metamaterials…|url=http://cobweb.ecn.purdue.edu/~shalaev/Publication_list_files/e6a11dcdfb53727d92491e50a7856ae2.pdf|format=Free PDF download|journal=Metamaterials|volume=2|issue=1|pages=1–17|bibcode=2008MetaM...2....1B|doi=10.1016/j.metmat.2008.03.004}}</ref><ref name=SRRpendry>
{{cite journal
 |doi         = 10.1109/22.798002
 |url         = http://www.cmth.ph.ic.ac.uk/photonics/Newphotonics/pdf/magwires.pdf
 |format      = Free PDF download
 |title       = Magnetism from conductors and enhanced nonlinear phenomena
 |year        = 1999
 |last1       = Pendry
 |first1      = J.B.
 |last2       = Holden
 |first2      = A.J.
 |last3       = Robbins
 |first3      = D.J.
 |last4       = Stewart
 |first4      = W.J.
 |journal     = IEEE Transactions on Microwave Theory and Techniques
 |volume      = 47
 |issue       = 11
 |pages       = 2075–2084
 |bibcode     = 1999ITMTT..47.2075P
 |url-status     = dead
 |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
|citeseerx         = 10.1.1.564.7060
 }}</ref>

===Interactions===
Materials which scatter [[light]] or other [[electromagnetic waves]] create a general [[physical process]] where the different [[frequencies]] of light are forced to deviate from a straight trajectory. It is because, physically, the material is non-uniform at one, or more, or many places.<ref name=srr-mw-tunable/>

Furthermore, the [[optical science]]s make predictions about the path of light traversing through a material. When light deviates from its predicted (reflected) path, this also is considered [[scattering]]. The [[split ring resonator]]s which make up metamaterials are engineered to scatter light at [[resonance]]. Moreover, these resonant scattering elements are purposely designed at a uniform size throughout the material. This uniform size is much smaller than the [[wavelength]] of the [[frequency]] of light [[Wave propagation|propagating]] through the material.<ref name=srr-mw-tunable/>

Since the repeating, scattering, resonant elements, which make up the [[engineered]] material are much smaller than the frequency of propagating light,  metamaterials can now, also,  be described in terms of [[macroscopic]] quantities. This description is simply another way to view metamaterials. And these are [[permittivity|electric permittivity]],  ''' ''ε'''''  and [[magnetic permeability]],  '''''μ'''''.<ref name=srr-mw-tunable/><ref name=Lazarides2010/>

Hence, by designing the individual, [[geometrical]]ly shaped unit of the material, called a cell,  as the right kind of composite, it becomes a material with ''macroscopic properties that do not occur in nature''.<ref name=srr-mw-tunable/><ref name=Lazarides2010/>

Of particular interest regarding '''''nonlinear metamaterials''''', is the artificially induced  macroscopic property known as [[negative refractive index]]. This effect is created by [[Negative index metamaterials]] (NIMs), which are [[employed]] for use as ''nonlinear metamaterials''.<ref name=intro-nonlinear-mm/><ref name=srr-mw-tunable/><ref name=Lazarides2010/><ref name=x-mission-prop2002/><ref name=Opt-exp-v14-is20-2006/><ref name=Opt-exp-v15-is6-2007/> In NIMs, nonlinear phenomena such as [[second-harmonic generation]] and [[parametric oscillator|parametric amplification]] can take on highly unusual characteristics. Namely, the fact that the [[wavevector]] and the [[Poynting vector]] of a wave propagating in a NIM are counter-directed alters the [[phase (waves)|phase-matching]] conditions for the interacting waves, resulting in backward propagating waves as well as considerably changed [[Manley-Rowe relations]] and the distribution in space of the interacting fields' intensity.<ref name="Popov_Shalaev">A.K. Popov and V.M.Shalaev, [https://link.springer.com/article/10.1007/s00340-006-2167-4 Negative-index metamaterials: second-harmonic generation, Manley-Rowe relations and parametric amplification], Applied Physics B, v. 84, pp. 131–37 (2006)</ref>

==Non-linear properties of left-handed metamaterials==
Previous studies of left-handed or [[negative index metamaterials]] were focused on the [[superposition property|linear properties]] of the medium during [[wave propagation]]. In such cases, the view was that magnetic permeability and material permittivity are each not dependent on the intensity of the electromagnetic field. However, creating tunable structures requires knowledge of non-linear properties where the intensity of the [[electromagnetic field]] alters the permittivity, or permeability, or both, which in turn affects the range of [[Transmission coefficient|transmission spectra]] or [[Reflection coefficient|stop band spectra]]. Hence, the effective permeability is dependent on the [[macroscopic]] magnetic field intensity. As the field intensity is varied, switching between its positive and negative values can occur. Consequently, the material can switch from being left-handed to being right-handed, or vice versa.<ref name=nonlinear-properties/><ref name=x-mission-prop2002/>

A composite structure consisting of a square lattice of the periodic arrays of conducting wires and split-ring resonators, produces an enhanced magnetic response. Without the correct magnetic response, it is not possible to produce a left-handed material.<ref name=nonlinear-properties/><ref name=x-mission-prop2002>
{{cite journal
 | last=Bayindir | first=M.
 | year=2002
 | title=Transmission properties of composite metamaterials in free space
 | url=http://www.fen.bilkent.edu.tr/~ozbay/Papers/60-02apl-LHMbayndir.pdf
 | journal=[[Applied Physics Letters]]
 | volume=81 | issue=1 | pages=120–122
 | doi=10.1063/1.1492009
 | access-date=2009-12-28
|bibcode = 2002ApPhL..81..120B |display-authors=etal| hdl=11693/11213
 | hdl-access=free
 }}</ref>

===Tunable split-ring resonators for nonlinear negative-index metamaterials===
Variable capacitance diodes are incorporated into the split-ring cell producing a dynamic tunable system.<ref name=Opt-exp-v14-is20-2006>
{{cite journal
 | last1=Shadrivov | first1=I. V.
 | last2=Morrison | first2=S. K.
 | last3=Kivshar |first3=Y. S.
 | year=2006
 | title=Tunable split-ring resonators for nonlinear negative-index metamaterials
 | url=http://www.rsphysse.anu.edu.au/nonlinear/papers/pdf/OE_2006_14_09344.pdf
 | format=Free PDF download
 | journal=[[Optics Express]]
 | volume=14 | issue=20 | pages=9344–9349
 | arxiv=physics/0608044
 | doi=10.1364/OE.14.009344
| pmid=19529318
 |bibcode = 2006OExpr..14.9344S | hdl=10440/1057
 | s2cid=16175210
 }}</ref>

===Reconfigurable refractive index (infrared)===
[[Infrared|Source radiation]] of near infrared [[wavelength]]s are applied to a [[metamaterial]] system. The [[index of refraction]] can be reconfigured to exhibit negative values, zero, or positive values.<ref name=Opt-exp-v15-is6-2007>
{{cite journal
 | last=Werner | first=D. H.
 | year=2007
 | title=Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices
 | url=http://cobweb.ecn.purdue.edu/~shalaev/Publication_list_files/liquid_crystal.pdf
 | journal=[[Optics Express]]
 | volume=15 | issue=6 | pages=3342–3347
 | doi=10.1364/OE.15.003342
 | pmid=19532575
 | access-date=2010-02-26
|bibcode = 2007OExpr..15.3342W |display-authors=etal| doi-access=free
 }}</ref>

===SRR microwave nonlinear tunable metamaterial===
Fabrication and [[experiment]]al studies of the properties of the ''first nonlinear tunable metamaterial'' were operating at [[microwave]] frequencies. Such a metamaterial was fabricated by modifying the properties of [[Split-ring resonator|SRRs]] and introducing [[varactor]] diodes in each SRR element of the composite structure such that the whole structure becomes dynamically tunable by varying the [[amplitude]] of the propagating [[electromagnetic waves]]. In particular, the power dependent transmission of the left-handed and magnetic metamaterials at higher powers were demonstrated, as well as the generation of particular harmonics, as was [[theoretical]]ly suggested earlier.<ref name=srr-mw-tunable>
{{cite journal
 | last=Shadrivov | first=I. V.
 | year=2008
 | title=Tunable transmission and harmonic generation in nonlinear metamaterials
 | journal=[[Applied Physics Letters]]
 | volume=93 | issue=16 | pages=9303–3
 | arxiv=0805.0028
 | doi=10.1063/1.2999634
|bibcode = 2008ApPhL..93p1903S | s2cid=118574962
 |display-authors=etal}}</ref>

====SRR microwave nonlinear magnetic metamaterials====
The fabrication and experimental studies of the properties of the''nonlinear tunable magnetic metamaterial'' were operating at microwave frequencies. Varactor diodes are symmetrically introduced, which results in dynamic tunability for the whole structure. Since the magnetic component of the interaction determines the application, the power dependency is demonstrated. Nonlinearity-dependent enhancement or suppression of the transmission turns out to be dynamically tunable.<ref name=srr-mw-nonlinear-magnetic>
{{cite journal
 | last=Shadrivov | first=Ilya V.
 | year=2008
 | title=Nonlinear magnetic metamaterials
 | url=http://dspace-sub.anu.edu.au:8080/jspui/bitstream/10440/410/1/Shadrivov_Nonlinear2008.pdf
 | journal=[[Optics Express]]
 | volume=16 | issue=25 |pages=20266–71
 | doi=10.1364/OE.16.020266
 | pmid=19065165
 | access-date=2009-12-05
|bibcode = 2008OExpr..1620266S |display-authors=etal| citeseerx=10.1.1.221.5805
 | hdl=10440/410
 }}</ref>

====SRR microwave nonlinear electric metamaterials====
A new type of nonlinear metamaterials, is proposed and designed, exhibiting a resonant electric response at microwave frequencies. By introducing a varactor diode as a nonlinear element within each resonator,  the frequency of the electric mode stop band is shifted by changing the incident power without affecting the magnetic response. These elements could be combined with the previously developed nonlinear magnetic metamaterials in order to create negative index media with a control over both electric and magnetic nonlinearities.<ref name=mw-nonlinear-electric/>

Nonlinear resonators are designed in a similar fashion. A strong nonlinear electric response is obtained.<ref name=mw-nonlinear-electric>
{{cite journal
 | last1=Powell | first1=D. A.
 | last2=Shadrivov |first2=I. V.
 | last3=Kivshar |first3=Y. S.
 | year=2009
 | title=Nonlinear electric metamaterials
 | url=http://www.rsphysse.anu.edu.au/nonlinear/papers/pdf/APL_2009_95_84102.pdf
 | journal=[[Applied Physics Letters]]
 | volume=95 | issue=8 | pages=084102
 | doi=10.1063/1.3212726
 | access-date=2009-12-05
|bibcode = 2009ApPhL..95h4102P |arxiv = 0905.3930 | hdl=1885/95056
 | s2cid=18640642
 }}</ref>

===Sub-diffraction limit for non-linear metamaterial lens===
By covering a thin flat nonlinear lens on the sources, the sub-diffraction-limit observation can be achieved by measuring either the near-field distribution or the far-field radiation of the sources at the harmonic frequencies and calculating the IFT to obtain the sub-wavelength imaging. The higher order harmonics are used, the higher resolution is obtained.<ref name=nonlinear-lens>
{{cite arXiv
 | last=Wang | first=Z.
 | year=2009
 | title=Sub-diffraction-limit Observation Realized by Nonlinear Metamaterial Lens
 | class=physics.optics
 | eprint=0905.0263 
|display-authors=etal}}</ref>

===Non-linear electric metamaterial===
A new type of nonlinear metamaterial is designed, and analyzed with a dominant negative electric response. Introducing nonlinearity into the electric response makes it tunable while leaving the magnetic response unchanged. A nonlinear NIM containing tunable electric and magnetic elements, which can respond independently is possible.<ref name=nonlin-electric-MM>
{{cite journal
 | last1=Powell | first1=D. A.
 | last2=Shadrivov | first2=I. V.
 | last3=Kivshar | first3=Y. S.
 | year=2009
 | title=Nonlinear electric metamaterials
 | url=http://www.rsphysse.anu.edu.au/nonlinear/papers/pdf/APL_2009_95_84102.pdf
 | journal=[[Applied Physics Letters]]
 | volume=95 | issue=8 | pages=084102
 | doi=10.1063/1.3212726
 | access-date=2009-10-14
|bibcode = 2009ApPhL..95h4102P |arxiv = 0905.3930 | hdl=1885/95056
 | s2cid=18640642
 }}</ref>

===EM field shielding by non-linear metamaterials===
It is well known that over certain frequencies, typical metals can reflect electromagnetic
(EM) fields and can thus be used as electromagnetic shielding materials. However, conventional ''linear'' LHMs cannot be used to shield electromagnetic fields. This is drastically modified when nonlinearity of the magnetic response is taken into account, creating a controllable shielding effect in LHMs, accompanied by a parametric reflection.<ref name=shielding-again>
{{cite journal
 | last1=Feng | first1=S.
 | last2=Halterman |first2=K.
 | year=2008
 | title=Parametrically Shielding Electromagnetic Fields by Nonlinear Metamaterials
 | journal=[[Physical Review Letters]]
 | volume=100 | issue=6 | pages=063901
 | arxiv=0710.4337
 | doi=10.1103/PhysRevLett.100.063901
 | pmid=18352472 | bibcode=2008PhRvL.100f3901F
| s2cid=8537671
 }}</ref>

==Meta-dimer metamaterial==
A meta-dimer is composed of two spatially separated SRRs, with the two SRRs identical in each unit cell.  The proximity of the SRRs in the dimer results in relatively strong coupling between them.  A metamaterial comprising a large number of such metadimers can be utilized as an actively tunable medium at optical wavelengths.  If either or both of the SRRs in the meta-dimer become nonlinear, the metamaterial itself acquires nonlinear properties. This can allow for nonlinear behavior, such as tunability in real time. [http://www.nature.com/nphoton/journal/v3/n3/abs/nphoton.2009.4.html  Stereometamaterials] are also a type of meta-dimer.<ref name=Lazarides2010>
{{cite journal
 | last=Lazaridesa | first=N.
 | year=2010
 | title=Multistability and localization in coupled nonlinear split–ring resonators
 | journal=[[Physics Letters A]]
 | volume=374 | issue=19 | pages=2095–2097
 | arxiv=0909.2503
 | doi=10.1016/j.physleta.2010.03.008
|bibcode = 2010PhLA..374.2095L | s2cid=13570718
 |display-authors=etal}}</ref>

==See also==
{{Col-begin}}
{{Col-break}}
*[[History of metamaterials]]
*[[Negative index metamaterials]]
*[[Superlens]]
*[[Metamaterial cloaking]]
*[[Photonic metamaterials]]
*[[Metamaterial antennas]]
*[[Photonic crystal]]
*[[Seismic metamaterials]]
*[[Split-ring resonator]]
*[[Acoustic metamaterials]]
*[[Metamaterial absorber]]
*[[Metamaterial]]
{{Col-break}}
*[[Plasmonic metamaterials]]
*[[Terahertz metamaterials]]
*[[Tunable metamaterials]]
*[[Transformation optics]]
*[[Theories of cloaking]]
::::'''Academic journals'''
*[[Metamaterials (journal)]]
::::'''Metamaterials books'''
*[[Metamaterials Handbook]]
*[[Metamaterials: Physics and Engineering Explorations]]
{{Col-break}}
'''Metamaterials scientists'''
*[[John Pendry]]
*[[David R. Smith (physicist)|David R. Smith]]
*[[Richard W. Ziolkowski]]
*[[Nader Engheta]]
*Ulf Leonhardt
*[[Vladimir Shalaev]]
{{col-end}}

==References==
{{reflist|2}}

==Further reading==
*{{Cite journal
 | last1=Lapine | first1=M.
 | last2=Gorkunov |first2=M.
 | year=2004
 | title=Three-wave coupling of microwaves in metamaterial with nonlinear resonant conductive elements
 | journal=[[Physical Review E]]
 | volume=70 | issue=6 | pages=06660
 | doi=10.1103/PhysRevE.70.066601
| pmid=15697520
 |bibcode = 2004PhRvE..70f6601L }}
*{{cite journal
 | last1=Shadrivov | first1=I. V.
 | last2=Morrison | first2=S. K.
 | last3=Kivshar |first3=Y. S.
 | year=2006
 | title=Tunable split-ring resonators for nonlinear negative-index metamaterials
 | url=http://www.rsphysse.anu.edu.au/nonlinear/papers/pdf/OE_2006_14_09344.pdf
 | format=Free PDF download
 | journal=[[Optics Express]]
 | volume=14 | issue=20 | pages=9344–9349
 | arxiv=physics/0608044
 | doi=10.1364/OE.14.009344
| pmid=19529318
 |bibcode = 2006OExpr..14.9344S | hdl=10440/1057
 | s2cid=16175210
 }}
*{{cite journal
|doi=10.1117/2.1200811.1390
|url=http://spie.org/x31810.xml?ArticleID=x31810
|format=Free online article from [[SPIE]]
|title=Nonlinear metamaterials: a new degree of freedom
|year=2008
|last1=Shadrivov
|first1=Ilya
|journal=SPIE Newsroom|citeseerx=10.1.1.497.6901
}}

[[Category:Electric and magnetic fields in matter]]
[[Category:Metamaterials]]