Editing Plasmon

{{Short description|Quasiparticle of charge oscillations in condensed matter}}
{{Hatnote|Not to be confused with [[plasmaron]]. For the brand of dried milk biscuit, see [[Plasmon biscuit]].}}
{{Condensed matter physics|expanded=Quasiparticles}}
{{Technical|date=March 2015}}

In [[physics]], a '''plasmon''' is a [[quantum]] of [[plasma oscillation]]. Just as [[light]] (an optical oscillation) consists of [[photons]], the plasma oscillation consists of plasmons. The plasmon can be considered as a [[quasiparticle]] since it arises from the quantization of plasma oscillations, just like [[phonon]]s are quantizations of mechanical vibrations. Thus, plasmons are collective (a discrete number) oscillations of the [[Free electron model|free electron gas]] density. For example, at optical frequencies, plasmons can [[Coupling (physics)|couple]] with a [[photon]] to create another quasiparticle called a plasmon [[polariton]].

The field of study and manipulation of plasmons is called [[plasmonics]].

== Derivation ==
The plasmon was initially proposed in 1952 by [[David Pines]] and [[David Bohm]]<ref>{{cite journal |last1=Pines |first1=David |last2=Bohm |first2=David |title=A Collective Description of Electron Interactions: II. Collective vs Individual Particle Aspects of the Interactions |journal=Physical Review |date=15 January 1952 |volume=85 |issue=2 |pages=338–353 |doi=10.1103/PhysRev.85.338 |bibcode=1952PhRv...85..338P }} Cited after: {{cite book|author1=Dror Sarid|author2=William Challener|title=Modern Introduction to Surface Plasmons: Theory, Mathematica Modeling, and Applications|url=https://books.google.com/books?id=rXU1OLdjFUsC&pg=PA1|date=6 May 2010|publisher=Cambridge University Press|isbn=978-0-521-76717-0|page=1}}</ref> and was shown to arise from a [[Hamiltonian (quantum mechanics)|Hamiltonian]] for the long-range electron-electron correlations.<ref>{{cite journal|author1=David Bohm, David Pines|title=Coulomb Interactions in a Degenerate Electron Gas|journal=Phys. Rev.|date=1 November 1953|volume=92|issue=3|pages=609–625|series=A Collective Description of Electron Interactions: III.|doi=10.1103/physrev.92.609|bibcode = 1953PhRv...92..609B |s2cid=55594082}} Cited after: {{cite journal|title=Alternative derivation of the Bohm-Pines theory of electron-electron interactions|author=N. J. Shevchik |journal=J. Phys. C: Solid State Phys.|date=1974|volume=7|issue=21 |pages=3930–3936|doi=10.1088/0022-3719/7/21/013|bibcode = 1974JPhC....7.3930S }}</ref>

Since plasmons are the quantization of classical plasma oscillations, most of their properties can be derived directly from [[Maxwell's equations]].<ref name="electro">
{{cite book
 |author=Jackson, J. D.
 |chapter=10.8 Plasma Oscillations
 |year=1975
 |orig-date=1962
 |edition=2nd
 |title=Classical Electrodynamics
 |chapter-url=https://archive.org/details/classicalelectro00jack_0
 |chapter-url-access=registration
 |location=New York
 |publisher=[[John Wiley & Sons]]
 |oclc=535998 |isbn=978-0-471-30932-1
}}</ref>

== Explanation ==

Plasmons can be described in the classical picture as an [[oscillation]] of electron density with respect to the fixed positive [[ion]]s in a [[metal]].  To visualize a plasma oscillation, imagine a cube of metal placed in an external [[electric field]] pointing to the right. [[Electron]]s will move to the left side (uncovering positive ions on the right side) until they cancel the field inside the metal. If the electric field is removed, the electrons move to the right, repelled by each other and attracted to the positive ions left bare on the right side.  They oscillate back and forth at the [[plasma frequency]] until the [[energy]] is lost in some kind of [[Electrical resistance|resistance]] or [[Damping ratio|damping]]. Plasmons are a [[quantization (physics)|quantization]] of this kind of oscillation.

===Role===
Plasmons play a huge role in the [[optical]] properties of [[metal]]s and semiconductors. Frequencies of [[light]] below the [[plasma frequency]] are [[Reflection (physics)|reflected]] by a material because the electrons in the material [[Electric field screening|screen]] the [[electric field]] of the light. Light of frequencies above the plasma frequency is transmitted by a material because the electrons in the material cannot respond fast enough to screen it. In most metals, the plasma frequency is in the [[ultraviolet]], making them shiny (reflective) in the visible range. Some metals, such as [[copper]]<ref>
{{cite journal
 |date=1963
 |title=Energy Band Structure of Copper
 |journal=[[Physical Review]]
 |volume=129 |issue= 1|pages=138–150
 |bibcode= 1963PhRv..129..138B
 |doi=10.1103/PhysRev.129.138
 |last1= Burdick
 |first1= Glenn
}}</ref> and [[gold]],<ref>{{cite journal|author=S. Zeng|display-authors=etal|title=A review on functionalized gold nanoparticles for biosensing applications |journal=Plasmonics |volume=6|date=2011|pages= 491–506|doi=10.1007/s11468-011-9228-1|issue=3|s2cid=34796473}}</ref> have electronic interband transitions in the visible range, whereby specific light energies (colors) are absorbed, yielding their distinct color. In [[semiconductor]]s, the [[valence band|valence electron]] plasmon frequency is usually in the deep ultraviolet, while their electronic interband transitions are in the visible range, whereby specific light energies (colors) are absorbed, yielding their distinct color<ref>
{{cite book
 |last=Kittel |first=C.
 |date=2005
 |title=[[Introduction to Solid State Physics]] |edition=8th
 |publisher=[[John Wiley & Sons]]
 |page=403, table&nbsp;2
}}</ref><ref>
{{cite book
 |last=Böer |first=K. W.
 |title=Survey of Semiconductor Physics
 |volume=1 |edition=2nd
 |publisher=[[John Wiley & Sons]]
 |page=525
 |date=2002
}}</ref> which is why they are reflective. It has been shown that the plasmon frequency may occur in the mid-infrared and near-infrared region when semiconductors are in the form of [[nanoparticle]]s with heavy doping.<ref>{{cite journal |author1=Xin Liu |author2=Mark T. Swihart |title=Heavily-doped colloidal semiconductor and metal oxide nanocrystals: an emerging new class of plasmonic nanomaterials|journal=Chem. Soc. Rev.|date=2014|volume=43|issue=11 |pages=3908–3920|doi=10.1039/c3cs60417a|pmid=24566528 |s2cid=18960914 }}</ref><ref>{{cite journal|author1=Xiaodong Pi, Christophe Delerue|title=Tight-binding calculations of the optical response of optimally P-doped Si nanocrystals: a model for localized surface plasmon resonance|journal=Physical Review Letters|date=2013|volume=111|issue=17|page=177402|doi=10.1103/PhysRevLett.111.177402|bibcode=2013PhRvL.111q7402P|pmid=24206519|url=https://hal.archives-ouvertes.fr/hal-00877649/file/plasmon_Si_PRL_13.pdf}}</ref>

The plasmon energy can often be estimated in the [[free electron model]] as

:[[radiant energy|<math>E_{\rm p} = </math>]][[reduced Planck constant|<math> \hbar </math>]][[Plasma frequency|<math>\sqrt{\frac{n e^{2}}{m\epsilon_0}} = </math>]][[reduced Planck constant|<math>\hbar</math>]][[plasmon frequency|<math>\omega_{\rm p},</math>]]

where <math>n</math> is the [[conduction electron]] density, <math>e</math> is the [[elementary charge]], <math>m</math> is the [[electron mass]], <math>\epsilon_0</math> the [[permittivity of free space]], <math>\hbar</math> the [[reduced Planck constant]] and <math>\omega_{\rm p}</math> the [[plasmon frequency]].

== Surface plasmons ==
{{Main article|Surface plasmon}}
[[Surface plasmon]]s are those plasmons that are confined to surfaces and that interact strongly with light resulting in a [[polariton]].<ref>{{cite journal|title=Size dependence of Au NP-enhanced surface plasmon resonance based on differential phase measurement |journal=Sensors and Actuators B: Chemical |date=2013|doi=10.1016/j.snb.2012.09.073|volume=176|pages=1128–1133|display-authors=4|last1=Zeng|first1=Shuwen|last2=Yu|first2=Xia|last3=Law|first3=Wing-Cheung|last4=Zhang|first4=Yating|last5=Hu|first5=Rui|last6=Dinh|first6=Xuan-Quyen|last7=Ho|first7=Ho-Pui|last8=Yong|first8=Ken-Tye |bibcode=2013SeAcB.176.1128Z |url=http://www.unilim.fr/pages_perso/zeng/a13.pdf }}</ref> They occur at the interface of a material exhibiting positive real part of their relative permittivity, i.e. [[dielectric constant]], (e.g. vacuum, air, glass and other dielectrics) and a material whose real part of permittivity is negative at the given frequency of light, typically a metal or heavily doped semiconductors. In addition to opposite sign of the real part of the permittivity, the magnitude of the real part of the permittivity in the negative permittivity region should typically be larger than the magnitude of the permittivity in the positive permittivity region, otherwise the light is not bound to the surface (i.e. the surface plasmons do not exist) as shown in the famous book by [[Heinz Raether]].<ref>{{Cite book|title = Surface Plasmons on Smooth and Rough Surfaces and on Gratings|last = Raether|first = Heinz|publisher = Springer|year = 1988|isbn = 978-3-540-17363-2|page = 119}}</ref> At visible wavelengths of light, e.g. 632.8&nbsp;nm wavelength provided by a He-Ne laser, interfaces supporting surface plasmons are often formed by metals like silver or gold (negative real part permittivity) in contact with dielectrics such as air or silicon dioxide. The particular choice of materials can have a drastic effect on the degree of light confinement and propagation distance due to losses. Surface plasmons can also exist on interfaces other than flat surfaces, such as particles, or rectangular strips, v-grooves, cylinders, and other structures. Many structures have been investigated due to the capability of surface plasmons to confine light below the diffraction limit of light. One simple structure that was investigated was a multilayer system of copper and nickel.  Mladenovic ''et al.'' report the use of the multilayers as if its one plasmonic material.<ref>{{cite journal |last1=Mladenović |first1=I. |last2=Jakšić |first2=Z. |last3=Obradov |first3=M. |last4=Vuković |first4=S. |last5=Isić |first5=G. |last6=Tanasković |first6=D. |last7=Lamovec |first7=J. |title=Subwavelength nickel-copper multilayers as an alternative plasmonic material |journal=Optical and Quantum Electronics |date=17 April 2018 |volume=50 |issue=5 |page=203 |doi=10.1007/s11082-018-1467-3 |bibcode=2018OQEle..50..203M |s2cid=125180142 |url=http://cer.ihtm.bg.ac.rs/bitstream/id/23832/bitstream_23832.pdf }}</ref> Oxidation of the copper layers is prevented with the addition of the nickel layers. It is an easy path the integration of plasmonics to use copper as the plasmonic material because it is the most common choice for metallic plating along with nickel. The multilayers serve as a diffractive grating for the incident light. Up to 40 percent transmission can be achieved at normal incidence with the multilayer system depending on the thickness ratio of copper to nickel. Therefore, the use of already popular metals in a multilayer structure prove to be solution for plasmonic integration.

Surface plasmons can play a role in [[surface-enhanced Raman spectroscopy]] and in explaining anomalies in diffraction from metal [[diffraction grating|gratings]] ([[Robert W. Wood|Wood's]] anomaly), among other things. [[Surface plasmon resonance]] is used by [[biochemist]]s to study the mechanisms and kinetics of ligands binding to receptors (i.e. a substrate binding to an [[enzyme]]). [[Multi-parametric surface plasmon resonance]] can be used not only to measure molecular interactions but also nanolayer properties or structural changes in the adsorbed molecules, polymer layers or graphene, for instance.

Surface plasmons may also be observed in the X-ray emission spectra of metals. A dispersion relation for surface plasmons in the X-ray emission spectra of metals has been derived (Harsh and Agarwal).<ref>{{cite journal | doi=10.1016/0378-4363(88)90078-2 | volume=150 | issue=3 | title=Surface plasmon dispersion relation in the X-ray emission spectra of a semi-infinite rectangular metal bounded by a plane | journal=Physica B+C | pages=378–384|bibcode = 1988PhyBC.150..378H | last1=Harsh | first1=O. K | last2=Agarwal | first2=B. K | year=1988 }}</ref>

[[File:GothicRayonnantRose003.jpg|thumb|[[Gothic architecture|Gothic]] [[stained glass]] [[rose window]] of [[Notre-Dame de Paris]]. Some colors were achieved by [[colloid]]s of gold nano-particles.]]
More recently surface plasmons have been used to control colors of materials.<ref>{{cite news |url=http://news.bbc.co.uk/1/hi/sci/tech/4443854.stm | work=[[BBC News]] | title=LEDs work like butterflies' wings | date=November 18, 2005 | access-date=May 22, 2010}}</ref> This is possible since controlling the particle's shape and size determines the types of surface plasmons that can be coupled into and propagate across it. This, in turn, controls the interaction of light with the surface. These effects are illustrated by the historic [[stained glass]] which adorn medieval cathedrals. Some stained glass colors are produced by metal nanoparticles of a fixed size which interact with the optical field to give glass a vibrant red color. In modern science, these effects have been engineered for both visible light and [[microwave radiation]]. Much research goes on first in the microwave range because at this wavelength, material surfaces and samples can be produced mechanically because the patterns tend to be on the order of a few centimeters.  The production of optical range surface plasmon effects involves making surfaces which have features <400&nbsp;[[nanometer|nm]]. This is much more difficult and has only recently become possible to do in any reliable or available way.

Recently, graphene has also been shown to accommodate surface plasmons, observed via near field infrared optical microscopy techniques<ref>{{cite journal |author=Jianing Chen |author2=Michela Badioli |author3=Pablo Alonso-González |author4=Sukosin Thongrattanasiri |author5=Florian Huth |author6=Johann Osmond |author7=Marko Spasenović |author8=Alba Centeno |author9=Amaia Pesquera |author10=Philippe Godignon |author11=Amaia Zurutuza Elorza |author12=Nicolas Camara |author13=F. Javier García de Abajo |author14=Rainer Hillenbrand |author15=Frank H. L. Koppens |title=Optical nano-imaging of gate-tunable graphene plasmons |journal=Nature |volume=487 |issue=7405 |pages=77–81 |doi=10.1038/nature11254 |date=5 July 2012 |arxiv = 1202.4996 |bibcode = 2012Natur.487...77C |pmid=22722861|s2cid=4431470 }}</ref><ref>{{cite journal |title=Gate-tuning of graphene plasmons revealed by infrared nano-imaging |author=Z. Fei |author2=A. S. Rodin |author3=G. O. Andreev |author4=W. Bao |author5=A. S. McLeod |author6=M. Wagner |author7=L. M. Zhang |author8=Z. Zhao |author9=M. Thiemens |author10=G. Dominguez |author11=M. M. Fogler |author12=A. H. Castro Neto |author13=C. N. Lau |author14=F. Keilmann |author15=D. N. Basov |journal=Nature |volume=487 |issue=7405 |pages=82–85 |date=5 July 2012 |doi=10.1038/nature11253 |bibcode=2012Natur.487...82F|arxiv = 1202.4993 |pmid=22722866|s2cid=4348703 }}</ref> and infrared spectroscopy.<ref>{{cite journal |title=Damping pathways of mid-infrared plasmons in graphene nanostructures |author=Hugen Yan |author2=Tony Low |author3=Wenjuan Zhu |author4=Yanqing Wu |author5=Marcus Freitag |author6=Xuesong Li |author7=Francisco Guinea |author8=Phaedon Avouris |author9=Fengnian Xia |journal=Nature Photonics |volume=7 |issue=5 |pages=394–399 |date=2013 |doi=10.1038/nphoton.2013.57 |bibcode = 2013NaPho...7..394Y |arxiv=1209.1984 |s2cid=119225015 }}</ref> Potential applications of graphene plasmonics mainly addressed the terahertz to midinfrared frequencies, such as optical modulators, photodetectors, biosensors.<ref>{{cite journal |title=Graphene Plasmonics for Terahertz to Mid-Infrared Applications |author=Tony Low |author2=Phaedon Avouris |journal=ACS Nano |volume=8 |issue=2 |pages=1086–1101 |date=2014 |doi=10.1021/nn406627u |pmid=24484181|arxiv=1403.2799 |bibcode=2014arXiv1403.2799L |s2cid=8151572 }}</ref>

== Possible applications ==
The position and intensity of plasmon absorption and emission peaks are affected by molecular [[adsorption]], which can be used in [[molecular sensor]]s. For example, a fully operational device detecting [[casein]] in milk has been prototyped, based on detecting a change in [[absorption (electromagnetic radiation)|absorption]] of a gold layer.<ref>
{{cite journal
 |last=Heip |first=H. M.
 |display-authors=etal
 |date=2007
 |title=A localized surface plasmon resonance based immunosensor for the detection of casein in milk
 |journal=Science and Technology of Advanced Materials
 |volume=8 |issue= 4|pages=331–338
 |bibcode= 2007STAdM...8..331M
 |doi=10.1016/j.stam.2006.12.010
|s2cid=136613827
 |doi-access=free
 }}</ref> Localized surface plasmons of metal nanoparticles can be used for sensing different types of molecules, proteins, etc.

Plasmons are being considered as a means of transmitting information on [[Microprocessor|computer chips]], since plasmons can support much higher frequencies (into the 100&nbsp;[[Terahertz (unit)|THz]] range, whereas conventional wires become very lossy in the tens of [[GHz]]). However, for plasmon-based electronics to be practical, a plasmon-based amplifier analogous to the [[transistor]], called a [[plasmonstor]], needs to be created.<ref>
{{cite journal
 |date=2007
 |title=The Promise of Plasmonics
 |journal=SPIE Professional
 |doi=10.1117/2.4200707.07
 |last1= Lewotsky
 |first1= Kristin
}}</ref>

Plasmons have also been [[Plasmonic nanolithography|proposed]] as a means of high-resolution [[Photolithography|lithography]] and microscopy due to their extremely small wavelengths; both of these applications have seen successful demonstrations in the lab environment.

Finally, surface plasmons have the unique capacity to confine light to very small dimensions, which could enable many new applications.

Surface plasmons are very sensitive to the properties of the materials on which they propagate. This has led to their use to measure the thickness of monolayers on [[colloid]] films, such as screening and quantifying [[protein]] binding events. Companies such as [[Biacore]] have commercialized instruments that operate on these principles.  Optical surface plasmons are being investigated with a view to improve makeup by [[L'Oréal]] and others.<ref>
{{cite web
 |url=http://www.loreal.com/_en/_ww/loreal-art-science/2004winners.aspx?#part2
 |title=The L'Oréal Art & Science of Color Prize – 7th Prize Winners
}}</ref>

In 2009, a Korean research team found a way to greatly improve [[organic light-emitting diode]] efficiency with the use of plasmons.<ref>
{{cite web
 |date        = 9 July 2009
 |url         = http://www.kaist.edu/english/01_about/06_news_01.php?req_P=bv&req_BIDX=10&req_BNM=ed_news&pt=17&req_VI=2181
 |title       = Prof. Choi Unveils Method to Improve Emission Efficiency of OLED
 |publisher   = [[KAIST]]
 
 |archive-url  = https://web.archive.org/web/20110718022905/http://www.kaist.edu/english/01_about/06_news_01.php?req_P=bv&req_BIDX=10&req_BNM=ed_news&pt=17&req_VI=2181
 |archive-date = 18 July 2011
}}</ref>

A group of European researchers led by [[IMEC]] began work to improve [[solar cell]] efficiencies and costs through incorporation of metallic nanostructures (using plasmonic effects) that can enhance absorption of light into different types of solar cells: crystalline silicon (c-Si), high-performance III-V, organic, and dye-sensitized.<ref>{{cite web
 |date        = 30 March 2010
 |title       = EU partners eye metallic nanostructures for solar cells
 |url         = http://www.electroiq.com/index/display/photovoltaics-article-display/1202724884/articles/Photovoltaics-World/industry-news/2010/march/eu-partners_eye_metallic.html
 |publisher   = [[ElectroIQ]]
 |archive-url  = https://web.archive.org/web/20110308090541/http://www.electroiq.com/index/display/photovoltaics-article-display/1202724884/articles/Photovoltaics-World/industry-news/2010/march/eu-partners_eye_metallic.html
 |archive-date = 8 March 2011
}}</ref> However, for plasmonic [[photovoltaic]] devices to function optimally, ultra-thin [[transparent conducting oxide]]s are necessary.<ref>{{cite journal |author=Jephias Gwamuri |author2=Ankit Vora |author3=Rajendra R. Khanal |author4=Adam B. Phillips |author5=Michael J. Heben |author6=Durdu O. Guney |author7=Paul Bergstrom |author8=Anand Kulkarni |author9=Joshua M. Pearce |title=Limitations of ultra-thin transparent conducting oxides for integration into plasmonic-enhanced thin-film solar photovoltaic devices|journal=Materials for Renewable and Sustainable Energy|date=2015|volume=4|issue=12|doi=10.1007/s40243-015-0055-8 |doi-access=free|bibcode=2015MRSE....4...12G }}</ref>
Full color [[holograms]] using ''plasmonics''<ref name=Kawata2012>{{cite web|last=Kawata|first=Satoshi|title=New technique lights up the creation of holograms|url=http://phys.org/news/2012-03-technique-creation-holograms.html|publisher=Phys.org|access-date=24 September 2013}}</ref> have been demonstrated.
==Plasmon-soliton==
Plasmon-[[soliton]] mathematically refers to the hybrid solution of nonlinear amplitude equation e.g. for a metal-nonlinear media considering both the plasmon mode and solitary solution. A soliplasmon resonance is on the other hand considered as a quasiparticle combining the [[surface plasmon]] mode with spatial soliton as a
result of a resonant interaction.<ref>{{cite journal |last1=Ferrando |first1=Albert |title=Nonlinear plasmonic amplification via dissipative soliton-plasmon resonances |journal=Physical Review A |date=9 January 2017 |volume=95 |issue=1 |page=013816 |doi=10.1103/PhysRevA.95.013816 |bibcode=2017PhRvA..95a3816F |arxiv=1611.02180 |s2cid=119203392 }}</ref><ref>{{cite journal |last1=Feigenbaum |first1=Eyal |last2=Orenstein |first2=Meir |title=Plasmon-soliton |journal=Optics Letters |date=15 February 2007 |volume=32 |issue=6 |pages=674–6 |doi=10.1364/OL.32.000674 |pmid=17308598 |bibcode=2007OptL...32..674F |arxiv=physics/0605144 |s2cid=263798597 }}</ref><ref>{{cite journal |last1=Milián |first1=C. |last2=Ceballos-Herrera |first2=D. E. |last3=Skryabin |first3=D. V. |last4=Ferrando |first4=A. |title=Soliton-plasmon resonances as Maxwell nonlinear bound states |journal=Optics Letters |date=5 October 2012 |volume=37 |issue=20 |pages=4221–3 |doi=10.1364/OL.37.004221 |pmid=23073417 |s2cid=37487811 |url=http://opus.bath.ac.uk/31812/1/Milian_Optics_Letters_2012_37_20_4221.pdf }}</ref><ref>{{cite journal |last1=Bliokh |first1=Konstantin Y. |last2=Bliokh |first2=Yury P. |last3=Ferrando |first3=Albert |title=Resonant plasmon-soliton interaction |journal=Physical Review A |date=9 April 2009 |volume=79 |issue=4 |page=041803 |doi=10.1103/PhysRevA.79.041803 |bibcode=2009PhRvA..79d1803B |arxiv=0806.2183 |s2cid=16183901 }}</ref> To achieve one dimensional solitary propagation in a [[Hybrid plasmonic waveguide|plasmonic waveguide]] while the [[surface plasmons]] should be localized at the interface, the lateral distribution of the field envelope should also be unchanged.

A [[graphene]]-based waveguide is a suitable platform for supporting hybrid plasmon-solitons due to the large effective area and huge nonlinearity.<ref>{{cite journal |last1=Nesterov |first1=Maxim L. |last2=Bravo-Abad |first2=Jorge |last3=Nikitin |first3=Alexey Yu. |last4=García-Vidal |first4=Francisco J. |last5=Martin-Moreno |first5=Luis |title=Graphene supports the propagation of subwavelength optical solitons |journal=Laser & Photonics Reviews |date=March 2013 |volume=7 |issue=2 |pages=L7–L11 |doi=10.1002/lpor.201200079 |bibcode=2013LPRv....7L...7N |arxiv=1209.6184 |s2cid=44534095 }}</ref> For example, the propagation of solitary waves in a graphene-dielectric heterostructure may appear as in the form of higher order solitons or discrete solitons resulting from the competition between [[diffraction]] and nonlinearity.<ref>{{cite journal |last1=Bludov |first1=Yu. V. |last2=Smirnova |first2=D. A. |last3=Kivshar |first3=Yu. S. |last4=Peres |first4=N. M. R. |last5=Vasilevskiy |first5=M. I. |title=Discrete solitons in graphene metamaterials |journal=Physical Review B |date=21 January 2015 |volume=91 |issue=4 |page=045424 |doi=10.1103/PhysRevB.91.045424 |bibcode=2015PhRvB..91d5424B |arxiv=1410.4823 |s2cid=8245248 }}</ref><ref>{{cite journal |last1=Sharif |first1=Morteza A. |title=Spatio-temporal modulation instability of surface plasmon polaritons in graphene-dielectric heterostructure |journal=Physica E: Low-dimensional Systems and Nanostructures |date=January 2019 |volume=105 |pages=174–181 |doi=10.1016/j.physe.2018.09.011 |arxiv=2009.05854 |bibcode=2019PhyE..105..174S |s2cid=125830414 }}</ref>

==See also==
{{columns-list|colwidth=30em|
* [[Surface plasmon resonance]]
* [[Multi-parametric surface plasmon resonance]]
* [[Waves in plasmas]]
* [[Plasma oscillation]]
* [[Spinplasmonics]]
* [[Transformation optics]]
* [[Extraordinary optical transmission]]
* [[Phonon]]
* [[Graphene plasmonics]]
* [[Pines' demon]]
}}

==Footnotes==
{{reflist|20em}}

== References ==

*{{cite book | author=Stefan Maier | title=Plasmonics: Fundamentals and Applications | publisher=Springer | date=2007 | isbn=978-0-387-33150-8}}
*{{cite book | author=Michael G. Cottam | author2=David R. Tilley | name-list-style=amp | title=Introduction to Surface and Superlattice Excitations | publisher=Cambridge University Press | date=1989 | isbn=978-0-521-32154-9}}
*{{cite book | author=Heinz Raether | title=Excitation of plasmons and interband transitions by electrons | publisher=Springer-Verlag | date=1980 | isbn=978-0-387-09677-3}}
*{{cite journal |last=Barnes |first=W. L.|author2= Dereux, A. |author3=Ebbesen, Thomas W.| date=2003 | title=Surface plasmon subwavelength optics|journal=Nature| volume=424|pages=824–830|doi=10.1038/nature01937 |pmid=12917696 |issue=6950|bibcode = 2003Natur.424..824B |s2cid=116017}}
*{{cite journal |last=Zayats |first=Anatoly V. |author2=Smolyaninov, Igor I. |author3=Maradudin, Alexei A. |date=2005 |title=Nano-optics of surface plasmon polaritons |journal=Physics Reports |volume=408 |issue=3–4 |pages=131–314 |doi=10.1016/j.physrep.2004.11.001 |bibcode = 2005PhR...408..131Z }}
*{{cite journal |last=Atwater |first=Harry A. |date=2007 |title=The Promise of Plasmonics |journal=Scientific American |volume=296 |issue=4 |pages=56–63 |doi=10.1038/scientificamerican0407-56 |pmid=17479631 |bibcode=2007SciAm.296d..56A }}
*{{cite journal |last=Ozbay |first=Ekmel |date=2006 |title=Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions |journal=[[Science (journal)|Science]] |volume=311 |issue=5758 |pages=189–193 |doi=10.1126/science.1114849 |pmid=16410515 |bibcode = 2006Sci...311..189O |hdl=11693/38263 |s2cid=2107839 |url=http://repository.bilkent.edu.tr/bitstream/11693/38263/1/Plasmonics%20Merging%20Photonics%20and%20Electronics%20at%20Nanoscale%20Dimensions.pdf |hdl-access=free }}
*{{cite journal |display-authors=4 |last=Schuller |first=Jon |author2=Barnard, Edward |author3=Cai, Wenshan |author4=Jun, Young Chul |author5=White, Justin |author6= Brongersma, Mark L. |date=2010 |title=Plasmonics for Extreme Light Concentration and Manipulation |journal=Nature Materials |volume=9 |issue= 3|pages=193–204 |doi= 10.1038/nmat2630 |pmid=20168343 |bibcode = 2010NatMa...9..193S|s2cid=15233379 }}
*{{cite journal |last=Brongersma |first=Mark |author2=Shalaev, Vladimir |date=2010 |title=The case for plasmonics |journal=[[Science (journal)|Science]] |volume= 328 |issue= 5977|pages= 440–441 |doi=10.1126/science.1186905  |pmid=20413483 |bibcode = 2010Sci...328..440B|s2cid=206525334 }}

== External links ==
* [http://www.activeplasmonics.org Active plasmonics]
* [http://www.reactiveplasmonics.org Reactive plasmonics]
* [https://www.newscientist.com/article.ns?id=dn7164 Plasmonic computer chips move closer]




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[[Category:Plasma theory and modeling]]
[[Category:Quasiparticles]]
[[Category:Plasmonics]]